THE PARADOX OF THE HAWKING THEORY

In the classical theory black holes can only absorb and not emit particles. However it is shown that quantum mechanical effects cause black holes to create and emit particles as if they were hot bodies with temperature! The first paper in which the concept of Hawking Radiation was introduced!

This paper describes a particularly transparent derivation of the Hawking effect for massive particles in black holes. The calculations are performed with the help of Painlevé-Gullstrand’s coordinates which are associated with a radially free-falling observer that starts at rest from infinity. It is shown that if the energy per unit rest mass, e, is assumed to be related to the Killing constant, k, by k2 = 2e – 1 then e, must be greater than ?. For particles that are confined below the event horizon (EH), k is negative. In the quantum creation of particle pairs at the EH with k = 1, the time component of the particle’s four velocity that lies below the EH is compatible only with the time component of an outgoing particle above the EH, i.e, the outside particle cannot fall back on the black hole. Energy conservation requires that the particles inside, and outside the EH has the same value of e, and is created at equal distances from the EH, (1 – rin = rout – 1). Global energy conservations force then the mass of the particle below the EH to be negative, and equal to minus the mass the particle above the EH, i.e., the black hole looses energy as a consequence of pair production.

New Journal of Physics, 2005

An inexhaustive review of Hawking radiation and black hole thermodynamics is given, focusing especially upon some of the historical aspects as seen from the biased viewpoint of a minor player in the field on and off for the past thirty years. * Alberta-Thy-18-04, hep-th/0409024, review article solicited for a celebratory Focus Issue on Relativity, "Spacetime 100 Years Later," to be published in New Journal of Physics.

Physical Review D, 1997

International Journal of Modern Physics D, 2003

There are numerous derivations of the Hawking effect available in the literature. They emphasise different features of the process, and sometimes make markedly different physical assumptions. This article presents a "minimalist" argument, and strips the derivation of as much excess baggage as possible. All that is really necessary is quantum physics plus a slowly evolving future apparent horizon (not an event horizon). In particular, neither the Einstein equations nor Bekenstein entropy are necessary (nor even useful) in deriving Hawking radiation.

It is shown that the close connection between event horizons and thermodynamics which has been found in the case of black holes can be extended to cosmological models with a repulsive cosmological constant. An observer in these models will have an event horizon whose area can be interpreted as the entropy or lack of information of the observer about the regions which he cannot see. Associated with the event horizon is a surface gravity v which enters a classical "first law of event horizons*' in a manner similar to that in which temperature occurs in the first law of thermodynamics. It is shown that this similarity is more than an analogy: An observer with a particle detector will indeed observe a background of thermal radiation coming apparently from the cosmological event horizon. If the observer absorbs some of this radiation, he will gain energy and entropy at the expense of the region beyond his ken and the event horizon will shrink. The derivation of these results involves abandoning the idea that particles should be defined in an observerindependent manner. They also suggest that one has to use something like the Everett-Wheeler interpretation of quantum mechanics because the back reaction and hence the spacetime metric itself appear to be observerdependent, if one assumes, as seems reasonable, that the detection of a particle is accompanied by a change in the gravitational field.

Astrophysics and Space Science, 2013

We study mechanism of formation of black holes (BHs) from collisions of particles in the vicinity of the supermassive black hole acting as a particle accelerator trough BSW (Banados-Silk-West) effect. Moreover, we also investigate BH-BH collision, in which stellar black holes colliding near the horizon of a rotating supermassive black hole can reach large values of the center-of-mass energy. This result implies that high arbitrary energy of collisions causes to be transformed into radiation energy and particles, which might bring possible visible signals through the astrophysical observations. We study the radiation energy from a collision of two accelerating stellar black holes and find a maximal value of the radiation energy to be nearly E rad ≈ 2.5 • 10 56 erg for the ultrarelativistic value of v/c = 0.99 from BH-BH collisions.

2002

This talk is about results obtained by Kirill Melnikov and myself pertaining to the canonical quantization of a massless scalar field in the presence of a Schwarzschild black hole. After a brief summary of what we did and how we reproduce the familiar Hawking temperature and energy flux, I focus attention on how our discussion differs from other treatments. In particular I show that we can define a system which fakes an equilibrium thermodynamic object whose entropy is given by the A/4 (where A is the area of the black hole horizon), but for which the assignment of a classical entropy to the system is incorrect. Finally I briefly discuss a discretized version of the theory which seems to indicate that things work in a surprising way near r = 0.

Arxiv preprint hep-th/9202014, 1992

It is argued that the qualitative features of black holes, regarded as quantum mechanical objects, depend both on the parameters of the hole and on the microscopic theory in which it is embedded. A thermal description is inadequate for extremal holes. In particular, extreme holes of the charged dilaton family can have zero entropy but non-zero, and even (for $a>1$) formally infinite, temperature. The existence of a tendency to radiate at the extreme, which threatens to overthrow any attempt to identify the entropy as available internal states and also to expose a naked singularity, is at first sight quite disturbing. However by analyzing the perturbations around the extreme holes we show that these holes are protected by mass gaps, or alternatively potential barriers, which remove them from thermal contact with the external world. We suggest that the behavior of these extreme dilaton black holes, which from the point of view of traditional black hole theory seems quite bizarre, can reasonably be interpreted as the holes doing their best to behave like normal elementary particles. The $a<1$ holes behave qualitatively as extended objects.