The Neutrinos escape from black holes

By Alfonso León Guillén Gómez

Independent scientific researcher


All rights reserved

Wednesday, January 25, 2012 1:07: SafeCreative # 1201250966392

This paper is the development of my thesis proposal in Universe Today, Disqus, on November 17, 2011 ( Neutrino still breaking speed limits. Guillen)

Esta obra también puede leerla en español presione aquí


There are virtual particles with speed > c, as the virtual photon and the virtual graviton, that due to its kinetic energy, they pass beyond the barriers of electric potential or gravitational potential, particularly of an event horizon of a black hole, according to Newtonian mechanics, because its kinetic energy is greater than the potential energy of the barrier. This phenomenon is not a quantum tunneling effect as was supposed. And in relativity the speed can not be greater than c, since in that case it travels in the past, which violates the principle of Novikov and the law of causality. Therefore, the valid physics to these particles are the Newtonian or the Superluminary Relativity of Anastasovski and the event horizon does not exist for the neutrinos as neither for the virtual photon and vitual graviton because its speed is greater than c, the threshold of the escape velocity, in which the kinetic energy is equal to the gravitational potential.

PACS 01.65. + G History of science

03.30. + P Special relativity

04.20.-q Classical General Relativity

Singularities and cosmic censorship 04.20.Dw

Numerical studies of 04.25.dg black holes and black-hole binaries

04.60.-m Quantum gravity

Classical black holes 04.70.Bw

Aspects of Quantum 04.70.Dy black holes, evaporation, thermodynamics

05.20.Gg Classical ensemble theory

05.60.Cd Classical transport

05.60.Gg Quantum transport

13.15. + G Neutrino Interactions

Table of Contents


1. Introduction

2. Black holes

3. Evaporation of black holes

4. The neutrinos whether escape of black-holes

5. Conclusions


1. Introduction

In the research laboratory "Gran Sasso", Italy, in the "Oscillation Project with Emulsion-Tracking Apparatus" (OPERA), a group of scientists accidentally discovered that the muon neutrino travels in a vacuum   with a velocity greater than c, in about .25 ten thousandth. This result was obtained according to the relation (muon neutrino velocity - c) / c = (2.37 ± 0.32 (statistical uncertainty) + (0.34, -0.24) (total systematic uncertainty)) x 10⁵ [1]. These scientists experimentally were investigating the first direct evidence of the oscillation between the neutrinos, muon and tau [2], which is the conversion of one in another due to changes in their quantity of mass, therefore, a phenomenon that only occurs in the particles with mass. However, in February 2012, they found defects in the infrastructure of the experiment, that obligate repeat it. Such failures were, according to a spokesman of OPERA, different  to the official, a faulty connection of a glass fiber cable which is connected to a small box, which converts the optical signal in an electronics and the other is the correction for the master clock of OPERA. Thus, the superluminal speed of the neutrino is in dispute. However, it is strange that the failures may have remained hidden during the long period when the experiment was repeated, before that OPERA reported on his findings. The results obtained in 2008, 2009, 2010 and 2011, in different repetitions, were consistent, when the failure of the cable depends on its inclination and its torsion, highly probable that vary with time. Furthermore, when the scientific comunity was wating for that OPERA repeat the experiment, after making the corrections of the failure, was ICARUS, a group  rival of OPERA who repeated the experiment, and in June 2012 the spokesman of CERN said that really the speed of neutrinos is lower than c; previously the spokesman of ICARUS said that OPERA does not know make the experiment. More worrying is that a few weeks before, a group, almost half of the members of OPERA, rebelled against their leader, Dr. Antonio Ereditato, and forced him to resign. Thus, Ereditato is added to Tom Van Flandern and Paul Marmet that for his disagreement with Einstein's relativity were relentlessly persecuted. The new result about the speed of the neutrino has had a low coverage by the  science magazines.  

The experiment of direct observation of neutrino oscillation is of great complexity. At CERN in Geneva, in the Super Proton Synchrotron (SPS), protons are accelerated to the maximum possible energy for this type of experiment, to 400 GeV / c, with a cycle of 6 s. These protons, in the target chamber (TC), are addressed by two magnetic dipoles (magnets) against targets of graphite 2 m long, through two extractions; one takes place in room B and the other in the room C, separated by 50 ms; each extraction has a duration of 10.5 μ s [3]. The signal used for the release of protons is Coordinated Universal Time (UTC), and the length of each launch is 524 ± 5 ns. The two extraction system generates two distributions of protons, which in turn produces, in time, two distributions of neutrinos on departure at CERN, and on arrival at the Gran Sasso. This redundancy is for to make the estimation of statistical and systematic uncertainties and the statistical adjustment with the maximum likelihood method [4], which allows the calculation of the speed of neutrinos. The product of  the collision of protons against graphite, in the   TC, are mesons (hadrons composed of a quark and antiquark pair), with electric charge, some are positives and other are negatives, highly unstable, which decay in: kaon → 2 pions or kaon → 3 pions and 1 pion → 2 gamma rays, 1 electron muon and 1 neutrino, inside a decay rectilinear tunnel (DT), under vacuum, of 1095 m in length. For this tunnel, the electron muons and neutrinos go to a hadron stopping (18 ms in length). The particles, that pass, follow to the first muon electron detector (5 m in length), connected, through a pipe 67 meters long, to a second muon electron detector (5 m in length). Of this last detector, the almost pure beam of muon neutrinos leave with an electron neutrinos contamination of  ~ 0.9%   [5]. The neutrinos   were cleaned by a magnet placed in each detector, which separated the neutrinos from the muon electron who have escaped from the hadron stopping; the muon electron were deflected in the opposite direction to its negative charge, while the neutrinos traveled straight. The neutrinos, through a channel   rectilinear underground. of   730 kilometers, traveled at a constant speed until the OPERA detector in the Gran Sasso laboratory. Within the channel   (νμ → ντ)) the beam of muon neutrinos, traveled with an average energy of Eν   ~ 17 GeV. In this experiment, the energy of the neutrinos depended on the energy of the pions and the energy of these of the energy of the protons at the time of its collision with the graphite; in general, depends on the energy of the triggering event of its production process. The detection of the neutrino beam at the Gran Sasso, is produced under the charged weak interaction, ie, via boson W ± (the other way is via the interaction neutral boson Z0),   with atomic electrons of the detector at Gran Sasso. The minimum energy required for this interaction is > 11 GeV [6]. The energy distribution of neutrinos in the range (with an average total of ~ 17 GeV) of the experiment, had no effect on its speed,   since the speed for higher energy (average ~ 43 GeV) was the same for the lower energy (average of ~ 14 GeV)   [7]. The constant speed of neutrinos, in addition to its mass of positive energy, cause that neutrinos are classified in the category of the particles that are not tachyons [7].    In the CERN and the Gran Sasso two identical systems are installed to measure the time in UTC, consisting of a GPS receiver,   Septentrio PolaRx2e [8] and an atomic clock, Symmetricom CS4000 [9]. The clocks are synchronized by the GPS, with an error of 2 ns [10]. This experiment, with several modifications, was performed in 2008, 2009, 2010 and 2011 and has supplied statistics, high accuracy, for calculate the speed of muon neutrino [1].

In the paper of September 22 and in the review of Nov. 17, 2011,   submitted to the "Journal of High Energy Physics", and also stored in the digital database ArXiv, with very high certainty, was confirmed the superluminal speed of the muon neutrino, which was presented by   Antonio Ereditato, OPERA spokesman on behalf of 179 scientists, mainly from Europe and Asia, belonging to 48 scientific institutions in Germany, Belgium, North and South Korea, Croatia,   Russia, France, Greece, Italy, Israel, Japan, Turkey and   Switzerland [1].

In the experiment of November there was a new package beam particles of about 3 nanoseconds in duration separated by up to 524 nanoseconds. That compared to September is narrower and shorter as this was 10 nanoseconds, period considered as a possible source of error. Thereby, measuring the speed of the muon neutrino is more accurate, in addition, was improved accuracy by obtaining a lower beam intensity, "only 20 neutrino events have been collected by OPERA in this new test, compared to 15,000 analyzed in the former "[11].

The neutrino, which exists in the states of electron, muon and tau, interchangeable during your oscillating, was postulated by Wolfgang Pauli in 1930 and was observed for the first time in 1956. The neutrino oscillation was proposed in 1950 and was observed in 1998. The neutrino is a lepton, an elementary particle, without charge, that together to the quarks, are constituent of the matter, which only experiences the weak interaction and the gravitational force generated in the decay of the proton. The neutrino has mass, according to the four-momentum vector, which is equivalent in energy  to (= 0.24 eV, <15.5 MeV) [12].   The muon neutrino resulting of the oscillation of the electron neutrino has a mass <170 keV (in the OPERA experiment, the maximum value is 2 eV [1]).  


The first consequence of the OPERA experiment is that particles with mass can exceed c and, therefore, is false the postulate of Special Relativity on such impossibility. The second consequence is that in my alternative theory about the existence in nature of superluminal speeds, as would the speed of the graviton, it requieres in the model to explain his speed, when the particles have similar energies, as is the case of the muon neutrino with an energy that falls between classes Y = Gamma Radiation and NUV = Ultravioleta [13] and the energy of the photons, includ, as a possible determinant of its speed difference, the types of interaction since, possibly the neutrino speed > c is because while the photon is subject to electromagnetic and gravitational interactions in change, the neutrino is subcjet to weak force and gravitational interactions, as result, the neutrino travels in vacuum with little interaction while the photon in the vacuum with a major interaction, since, the weak interaction is limited, while the static electromagnetic interaction abounds. Another crucial consequence is that the neutrino escapes from black holes, since they meet with the physical condition of to travel above c.

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2. Black holes

Because of the corpuscular theory of light of Newton, his equations about: movement, gravity and escape speed, in 1783, John Michell formulated the existence of stars, with a great mass, which would be invisible because light could not escape of their gravity. In 1915, Albert Einstein showed that light is indeed subject to gravity and Karl Schwarzschild, in applying for a spherical body, according ​​the equations of General Relativity, confirmed that a star with a mass and a certain radius, called the event horizon, its gravity catches the light. In 1930, Subrahmanyan Chandrasekhar determined the critical mass at 1.5 times the Sun and in 1939, Robert Oppenheimer found that a top mass can produce the gravitational collapse of the star. In 1967, Stephen Hawking and Roger Penrose proved that any solution of the equations of General Relativity for a collapsed star generates a singularity. In 1969, John Wheeler called, to the singularity, black hole [14, 15].

According to the equations of General Relativity physically the black hole is defined by the 3 qualities: mass, momentum and electric charge (Uniqueness theorem or absence of hair from Carter-Robinson). To quantitatively determine it, it requires 11 parameters: 1 mass, 1 electric charge, 3 linear momentum, 3 angular momentum and 3 position [16].

The black hole, according to astronomical observations, is classified according to their amount of mass in [17]:

- Supermassive, with several million times the mass of the Sun. This black hole is the center of galaxies with spherical, ellipsoid or spiral form and sucks matter, in such great quantities, that it fails to go into the hole and the excess of matter collects in a large accretion disk (formation of a body from others), which by its very high temperature, to the black hole becomes in a quasar, whose core is the black hole, which emits an enormous amount of radiation and strong magnetic field due to that black hole produces 2 relativistic jets (subject to a speed close to c, maybe it reaches a superluminal speed that has not been tested yet) above and below of the disk.

- Stellar, more than 1.5 times the mass of the Sun. This black hole abounds in galaxies.

Also, according to astronomical observations, there are binary black holes spinning each one around of the other. For example, the binary Black Hole in 3C 75, composed of two supermassive distant at 25 thousand light years, which are the cores of two merging galaxies, located in the Abell 400 (cluster of galaxies compiled by George Abell in early 1950), however, between the galaxies there is near 300 million light years away [18].

The exact solutions of the equations of General Relativity given 4 possible theoretical types of black holes. These are [14, 15]:

- Schwarzschild non-rotating and has no electric charge.

- Kerr in rotating and has no electric charge.

- Reissner-Nordstrom non rotating and has electric charge (with a low probability of existence).

- Kerr-Newman rotating and has electric charge (with a low probability of existence).

According to the equations of General Relativity, black holes structure is composed of [14]:

- The singularity that is the point of collapse, without volume, therefore with spacetime zero and infinite curvature, where is concentrated all the mass of black hole with an infinite density. In charged black holes the singularity has a shape of ring.

- The event horizon is the border area whose radius depends on its mass. To the black hole non-rotating its form is spherical while for the black hole rotating is spheroid. This boundary defines the interior, beyond anything, matter or energy, including electromagnetic waves can not escape. Therefore, there is no communication between the inside and outside of the black hole. This property of the event horizon is because the escape speed from the inside, is greater than c, speed limit, according to Special Relativity.

Additionally the rotating black hole has [14]:

- The ergosphere, has an ellipsoidal shape, consisting of the space that is distorted by the drag due to rotation (inner gravitomagnetic field) around of the event horizon.

- The static limit between the ergosphere and the space normal.

Additionally the charged black hole has [19]:

- External to the event horizon, an electric field at a great distance, its intensity is the same as any other point of load (r ² Q/4Πε0) and only appears in front of other stars with electric charge.

- Internal to the event horizon is the Cauchy horizon, where it is suspending the fallen of the particles into the singularity and even has a region of stable orbits.

In the spacetime outside the black hole, there are three large areas of orbits [20]:

- Stable, more of 3 Schwarzschild radius (rs = 2GM/c2). The orbits are circular and remain over time, therefore, is a safe area.

- Unstable, above 1.5 Schwarzschild radius. Circular orbits that due to any disturbance, it escapes to infinity spacetime tangent or it falls into the black hole.

- The unstable photon sphere in the which the electromagnetic waves are rotating in circular orbits, exactly to 1.5 Schwarzschild radius. Due to any disturbance, the photons tangentially are launched to the infinite spacetime or they fall into the black hole.

- Fall in ellipses, <1.5 Schwarzschild radius. The ellipse orbits fall each time more closer to the event horizon until pass it.

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3. Evaporation of black holes

According to quantum mechanics from the interior of the black holes escape real particles and virtual particles to outer space, producing the global phenomenon of its evaporation, in the manner of the black body radiation with a finite temperature. This process is initially very slow, but steady, so that over time and black hole decreasing mass, accelerates evaporation, until the hole disappears in a burst. The cases currently recognized are the following:

- Hawking radiation is of  real photons and massive particles like the neutrino, and other, discovered in 1973 by the russian physicists Zeldovich and Alexander Starobinsky Yacob who demonstrated that rotating black hole, due to the uncertainty principle, it creates and radiates particles. In 1975, Stephen Hawking calculated, demonstrating throu gh the area theorem, that all types of   black hole radiates and is exactly equal to the black body thermal radiation, based on the work of Jacob Bekenstein, who deduced that the area of event horizon be can consider as a measure of the entropy of the black hole, as this area increases depending on the absorbed matter, therefore, the black hole has entropy which is the amount of disorder associated with the movement of all particles within the horizon and is equal to the area of the horizon divided by the square of the Planck length [21]. The entropy is inversely proportional to the amount of mass and directly proportional to temperature of the black hole, which is directly proportional to its surface gravity and inversely proportional to its mass, then the black hole must radiate to reach the thermodynamic equilibrium between the inner spacetimes and outside of the event horizon [22]. This radiation, in September 2010, was observed in the laboratory, by a team of scientists led by Franco Belgiorno, University of Milan [23]. And in the first half of 2011, was detected by different astronomers,   from a Schwarzschild hole [24].

At all points of spacetime inside and outside the event horizon, during the period of uncertainty, due to the oscillation of the zero point energy associated with the vacuum, constantly it creates pairs of virtual particles, the pair is composed of a particle and an antiparticle, which within the lapse they annihilate each other.

In the original model of Hawking, the radiation does not really exist, since he assumed the assumption that nothing can escape of the black hole, then the pair of virtual particles originates from the in vacuum outer of the event horizon, a particle virtual (positive energy) may fall or escape, changing to  real particle in the external vacuum;   when the particle escapes it creates the illusion that the particle was radiated; the other particle (negative energy) can fall without destroying a complementary virtual particle, due to that before, too, becomes a real particle with positive energy within the event horizon;   with increasing black hole mass, these virtual-real changes   are due to the intense gravitational field and only occur at random. Within this process of false irradiation, occurs loss of mass of the black hole, due to the flow from outside the virtual antiparticle with   negative energy when this does not become a real particle, event more likely that the opposite event, compensating the particles emitted falsely; the reducing of the mass does that the event horizon it reduces, and it augments the apparent temperature, and consequently, greater the apparent radiation [25, 26 , 27]. According to Hawking, the lifetime of the black hole is of 1071 mass 3 seconds [25].  

Despite that the theory, about the apparent radiation of Hawking is based on strictly mathematical terms, on the equations of General Relativity [26], the author prefers the alternative model under which the black hole really radiates. Although the author does not reject the original Hawking´s radiation, because whether there, but is not the main cause of this type of radiation, since, as a process of interaction of the black holewith the external vacuum, from the point of view thermodynamic, the external vacuum does not "warm" the black hole but the opposite, ie the black hole "warms" the external vacuum, and consequently the flow of radiation from the external vacuum toward the black hole is marginal regarding the flow from the black hole toward the external vacuum.

The model of the real radiation by the black hole is based on the theory of quantum tunneling in which a virtual particle with velocity ≤ c, of the pair created by the oscillation of the vacuum behind the event horizon, with a lower kinetic energy goes through the gravitational potential barrier with an energy greater of the edge of the horizon, and goes outside, which violates the principle of Newtonian mechanics whom states that the particle must have a kinetic energy exceeding the energy of the barrier to cross it. The tunnel effect in strict rigor   was formulated for electrical potential barriers (impedance) but too is applicable to the gravitational potential barrier. In quantum mechanics, due to wave-particle duality, it uses the Schrödinger equation, which assigns a certain probability that a particle, without lift the barrier, uses a energetic tunnel to cross the barrier, and the particle passes to the other side.

However, the author creates a new version, in the that changes the mechanism of the real radiation, thereby, he suppresses the tunnel effect, that is not required, and he explains that the virtual photon escapes due to its speed   > c, since in this case the kinetic energy is greater than the gravitational potential energy of the barrier, the same occurs in front of the electric potential barrier. And in his way of seeing the things, the author believes that Nimtz in their experiments achieves speeds > c, because he produced virtual photons through of the technique of dielectric photonic barriers that are of two types: the first type of barrier is constituted by the central part of the wave guide, which is a section sufficiently narrow, less than half the wavelength in both directions, perpendicular to the propagation, which only allows pass the lower wavelengths; the other barrier is the double prisms where microwaves suffer total reflection inside of the prism of input and the residue, that it refracting, passes through an air gap to the prism of exit [28]. Nimtz said that the evanescent waves, that it produces, is made ​​up of virtual photons that have superluminal speed, to which the author adds, that such virtual photons does not exceed the electrical potential due to tunneling but whether to its speed. Petar Anastasovski has found, as a result of his outstanding research in nuclear physics, a better understanding of nuclear phenomena if they are explained with speeds greater than c. And the author underlines, in general, a better understanding of quantum phenomena. Moreover, Anastasovski solves the mathematical problem of the Lorentz transformation for v > c, which maintain c as constant of the nature, for all inertial observers, in his Superluminal Relativity theory [28].  

The scene where the radiation process occurs is the space-time taken as the union of three subspaces: internal stationary spacetime of the event horizon + internal nonstationary spacetime of the black hole + external stationary spacetime of the event horizon. The internal spacetime is associated with the internal vacuum and the external spacetime is associated with the external vacuum [26]. A stationary spacetime "is a space-time where it can find a natural coordinate system in which none of the components of the metric tensor depends on the time coordinate" [29].   The real radiation mechanism according to the author, is that on the boundary of the event horizon, within the internal vacuum, due to the uncertainty principle, it creates a pair of virtual particles. The virtual antiparticle (negative energy) due to the extreme brevity of its existence, decays rapidly as a real particle; but too in the terms of the stochastic process, closed to the value of the maximum probability (p = 1), when the particle creates closed to the limit of the horizon, the particle maybe escapes, always that passes the horizon like yet a virtual particle. While the virtual particle (positive energy) passes to the external vacuum, due its greater lapse of existence, but also stochastically with a probability proportional to increasing the distance from the point of internal vacuum, where is created, with respect to the limit of the event horizon and until the point of the singularity (p = (0, 1)), in the internal vacuum, maybe the virtual particle it becomes a real particle. The escape of the particles from black holes is always due to superluminal speed, which have the virtual particles, and not to the quantum tunnel effect. The superluminal speed of the virtual photon was tested in the experiments with evanescent waves made, ​​since 1992, in Cologne, Germany   by Professor Günter Nimtz [28, 30, 31] and confirmed in the experiments of William   Walker, in 1998,   of   preformation of the electromagnetic wave in the nearfield [28, 32]. The black hole loses energy-mass, due to the emission, that causes the contraction of the event horizon. The change of particle between virtual-real, according to the author,   occurs inside or outside of the event horizon due to the high density of the gravitational potential energy as a result of the stream to a fabulous scale of virtual gravitons, of the external vacuum, when it is very close to the edge of the event horizon, or of the internal vacuum ( in Orthodoxy is said, to the immense gravity). This virtual-real change of course is not a deterministic process, since as a quantum process is always a stochastic process, thus, the virtual particle that escapes may also remain in the virtual state within the external vacuum and act to distance as a Lorentz force.

- The escape of static electromagnetic field (electric and magnetic fields uncoupled) or radiation of Carlip-Wiener is produced by the virtual photons escape from a charged black hole, always in front of other charged star, which may be another black hole, especially a black hole binary, which produce repelling. This radiation was discovered   in 1996,   by   Steve Carlip and Matthew P Wiener, whom   under the standard assumptions that c is the cosmic speed limit and "event horizon of black holes is where normal matter (and forces) must exceed the speed of light for escape, and therefore they are trapped". However, Carlip-Wiener implicitly distinguish and introduce forces whose transmitters are virtual particles with velocity between (<c, c) and the static electromagnetic force transmitted by the virtual photon with speed > c. Of course: "The horizon does not have sense for a virtual particle with enough speed. In particular, a charged black hole is a source of virtual photons "   [33].   Although they do not demonstrate or provide evidence of the superluminal speed of the virtual photon, for me is clear that they are based and recognize the experimental discovery of Günter Nimtz, at 1992, since no there is other antecedent known within the scientific community for support this declaration. For FAQ, before of this statement of Carlip-Wiener, and of the statement of Matt McIrvin [34], in 1994, in the same tone, ie. without evidence, the speed of all virtual particles could not exceed c.  

- The gravitational escape or radiation of Van Flandern is produced by the virtual gravitons escape from all types of black hole, that in the distance behaves as the gravitational field of a spherical star with a mass equal to the of the radiating black hole. This radiation was discovered, in 1998, by Tom van Flandern, who showed that virtual graviton travels at least 20.000 millones c and, therefore, it escapes the event horizon of the black hole. Tom first reflects about how the black hole has gravity? As long as its source of gravity is behind the event horizon, exactly at the singularity, where it has gone throughout its substance. "If nothing can escape the event horizon because nothing can propagate faster than light, how exists a gravity field out of a black hole?. The answer always is that the gravity field around of a black hole, it froze in the surrounding space-time before of the collapse of the star behind of the event horizon, and has remained in that state ever since." Tom rejects this response due to lack of causal agents, in addition is unable to respond in front of the black hole's binary, whose orbital connection requires of those agents. "suppose we have a black hole binary, with the two stars that collapsed in an elliptical orbit around each other. In this way, each field must be continuously updated by the change of orbital field contribution from the other. How does each field know what to do if it no longer communicating with its mass, its gravity source, hidden behind the event horizon? "." if the mass of each source when interacts with the other obligates to the two black holes to accelerate, why each point of the field with a certain curvature suffers exactly the same acceleration as the source of gravity, along the entire field (infinitely?) "." Without communication, how can the system remain intact and coherent? ". Tom concludes that the external gravitational field continually it regenerates and, therefore, it is connected with the singularity, using a causal link. Thus, the propagation speed of these causal entities, virtual gravitons, "largely exceed the speed of light." Tom with this reflection on the binary black hole, along with other of astronomical character, lead him to justify a model of quantum gravity regardless of whether exists or not a theory adequate. And under such circumstances, he find a formula to measure the speed of virtual gravitons; in fact, he proves the superluminal speed of the virtual graviton [35]. As the event horizon does not exist for virtual graviton then it escapes into space, producing the black hole's gravitational field.

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4. The neutrinos whether escape of black holes

According to General Relativity, inside of the event horizon, all the geodesies carry the particles to the singularity until that the particles fall in it, except for the charged black hole, case where the geodesies, inside of the Cauchy horizon [19], they curve backward, toward the event horizon, causing the particles do not end up swallowed by the singularity, but this hole is very unlikely to exist. Therefore, the absence of geodesies leading to outside, do impossible that the particles, while travel spacelike or lightlike, escape. Both the real particle with mass, according the four-vector momentum, as the real photon are swallowed by the singularity. Also, the virtual particles, with speed ≤ c, fall into the singularity, althought before, they become real particles.

The Relativity was formulated, in the absence of the distinction between real and virtual particles, therefore all particles in nature have a speed   ≤ c. Even when quantum mechanics introduced the division between real and virtual particles, from the principle of   Heisenberg's uncertainty, and when, in 1929,   virtual particle was discovered by Paul Dirac, this restriction is maintained. For this reason, the black hole evaporation is presented in Hawking's theory like only apparent, and in the alternative theory through of the quantum tunneling effect. In no case because, the virtual particles have a velocity > c.

From the scientists recognized by the scientific community, only Nimtz, Carlip-Wiener and Walker, have said that the virtual photon has a velocity > c, and Van Flandern and Walker that the virtual graviton has a superluminal speed. But Carlip after that he said on behalf of FAQ, where, in 1994, was first formulated by Matt McIrvin, in his later papers, he assumes the defense of orthodox relativistic thinking and Van Flandern, vexed in life, after his death, he simply is ignored.


As theoretical solutions of the equations we have: In General Relativity, if the speed of the particle > c then the particle travels timelike, exactly in a geodesy in the past light cone, that under the intense gravitational field of a black hole is a geodesy in a closed curve timelike, found by Kurt Gödel in 1949. And, in Special Relativity the tachyon always with speed > c, independently found by Arnold Sommerfeld, George Sudarshan, Olexa-Myron Bilaniuk, Vijay Deshpande and Gerald Feinberg in the 1960s. A particle, in a closed curve timelike, violates the principle of consistency of Novikov which postulates that if an event exists and causes a paradox, or any changes to the past than causes the paradox, then the probability of that event is zero, too, violates the chronology protection conjecture of Hawking and, in general, causality law. And the tachyon in quantum field theory, due to its imaginary mass, is too unstable as to that it consideres real, additionally, it violates the causality law.

The only consistent solution of the equations of General Relativity, about a superluminal speed is the that Hawking presents in wormholes, at 2010, which only allows time travel into the future, to through of a shortcut in the spacetime (How to build a time machine. Published by Mail online). As in the case of Hawking's radiation this superluminal speed is a apparent effect, due to that locally (inside wormhole) only is possible subluminal speeds.

Now, with the experimental discovery of the superluminal speed of the neutrino, due to that Gödel´s solution also applies in the spacetime inside the event horizon, therefore the neutrinos coming from the exterior that are trapped by the gravity of the black hole and the neutrinos produced inside of the black hole when the mass falls into of the singularity, then, the neutrino travels in the past light cone, inside of a closed geodesy, just in the past. The neutrino, that is a real particle with mass according to the four-vector momentum, is a totally new phenomenon of particle with a superluminal speed. What means physically that neutrino travels in the past?. Can the neutrino violate the principle of Novikov?. Can the neutrino breaking the law of causality?. In reality there is no physically acceptable solution in General Relativity. The speed > c of a particle, not causes that the particle escapes of the event horizon, therefore, is not really possible in General Relativity. And the solution of Anastasovski, in the Superluminal Relativity, is not known within the scientific community, less accepted.

According to the mechanic of Newton the escape speed is the speed neccesary for be released of the gravity of a body. Exactly, is the speed in which the kinetic energy is greater than the gravitational potential energy. For a spherical-symmetric body, such as black hole,   the escape speed is: G > √ 2GM / r. Where G is the gravitational constant (G = 6.67 × 10 -11  m 3 kg -1  s -2), M the   black hole mass and r is the distance from the singularity extended to the event horizon. This escape speed is > c. The neutrino as the virtual photon and the graviton virtual meet this condition, then for the neutrino, the event horizon does not exist and the neutrino escapes beyond of event horizon, into the exterior spacetime.

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5. Conclusions

The experimental discovery of the speed > c of the neutrino has no place in Relativity. This brings us back to the mechanics of Newton. Therefore, if we apply the concept of escape speed to a black hole we find that the neutrino will escape of the event horizon. But due to that the speed c is a constant of the nature then only is possible the solution of the Superluminal Relativity.

On the other hand, the Relativity limits the causal link between events to actions that can communicate with a velocity = c. By now, the OPERA experiment this limit the remplace by the superluminal speed of the neutrino.

For press return Index


[1] OPERA. Measurement of the neutrino velocity with the OPERA detector in the CNGS beam

[2] Oscillation Project with Emulsion-tRacking Apparatus.

[3] Stipcevic, Mario. Superluminal anomaly in OPERA experiment.  Croacia. 2011.

[4] Ereditato, Antonio. Measurement of the neutrino velocity with the OPERA detector in the CNGS beam. Suiza. 2011.

[5] Gornushkin, Yu. Search for oscillations νμ → ντ  in appearance mode in the OPERA experiment. Federación Rusia. 2011.

[6] Thomson, Mark. Particle Physics. England. 2009.

[7]  Francis, E. Por qué los neutrinos de OPERA no pueden ser taquiones. 2011.

[8] Septentrio PolaRx2e.

[9]  Symmetricom Cs4000.

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[11] Muy Interesante. El experimento OPERA confirma la medida de neutrinos más rápidos que la luz. Noviembre, 2011.

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