QUANTUM gravitational effects are usually ignored in calculations of the formation and evolution of black holes. The justification for this is that the radius of curvature of space-time outside the event horizon is very large compared to the Planck length (Għ/c3)1/2 ≈ 10−33 cm, the length scale on which quantum fluctuations of the metric are expected to be of order unity. This means that the energy density of particles created by the gravitational field is small compared to the space-time curvature. Even though quantum effects may be small locally, they may still, however, add up to produce a significant effect over the lifetime of the Universe ≈ 1017 s which is very long compared to the Planck time ≈ 10−43 s. The purpose of this letter is to show that this indeed may be the case: it seems that any black hole will create and emit particles such as neutrinos or photons at just the rate that one would expect if the black hole was a body with a temperature of (κ/2π) (ħ/2k) ≈ 10−6 (M/M)K where κ is the surface gravity of the black hole1. As a black hole emits this thermal radiation one would expect it to lose mass. This in turn would increase the surface gravity and so increase the rate of emission. The black hole would therefore have a finite life of the order of 1071 (M/M)−3 s. For a black hole of solar mass this is much longer than the age of the Universe. There might, however, be much smaller black holes which were formed by fluctuations in the early Universe2. Any such black hole of mass less than 1015 g would have evaporated by now. Near the end of its life the rate of emission would be very high and about 1030 erg would be released in the last 0.1 s. This is a fairly small explosion by astronomical standards but it is equivalent to about 1 million 1 Mton hydrogen bombs. It is often said that nothing can escape from a black hole. But in 1974, Stephen Hawking realized that, owing to quantum effects, black holes should emit particles with a thermal distribution of energies — as if the black hole had a temperature inversely proportional to its mass. In addition to putting black-hole thermodynamics on a firmer footing, this discovery led Hawking to postulate 'black hole explosions', as primordial black holes end their lives in an accelerating release of energy.

Black Hole Explosions

Superstring theoryをめぐって(放談室)

Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics

EDDINGTON'S “Internal Constitution of the Stars” was published in 1926 and gives what now ranks as a classical account of his own researches and of the general state of the theory at that time. Since then, a tremendous amount of work has appeared. Much of it has to do with the construction of stellar models with different equations of state applying in different zones. Other parts deal with the effects of varying chemical composition, with pulsation and tidal and rotational distortion of stars, and with the precise relations between the interior and the atmosphere of a star. The striking feature of all this work is that so much can be done without assuming any particular mechanism of stellar energy-generation. Only such very comprehensive assumptions are made about the distribution and behaviour of the energy sources that we may expect future knowledge of their mechanism to lead mainly to more detailed results within the framework of the existing general theory. An Introduction to the Study of Stellar Structure By S. Chandrasekhar. (Astrophysical Monographs sponsored by The Astrophysical Journal.) Pp. ix+509. (Chicago: University of Chicago Press; London: Cambridge University Press, 1939.) 50s. net.

An Introduction to the Study of Stellar Structure

Now more than ever, Gravitation and Spacetime, Second Edition, by Hans C. Ohanian and new coauthor Remo Ruffini, deserves John Wheeler's praise as "the best book on the market today of 500 pages or less on gravitation and general relativity." Gravitation and Spacetime has been thoroughly updated with the most exciting finds and hottest theoretical topics in general relativity and cosmology. Highlights of the revision include the rise and fall of the fifth force, principles and applications of gravitational lensing, COBE's spectacular confirmation of the blackbody spectrum of the cosmic thermal radiation, theories of dark matter and inflation, and the early universe as a testing ground for particle physicists' unification theories, and much, much more. The ideal choice for a graduate-level introduction to general relativity, Gravitation and Spacetime is also suitable for an advanced undergaduate course.

Gravitation and spacetime.

We study the Hawking thermal spectrum in dragging coordinate system and the tunneling radiation characteristics of hot NUT–Kerr–Newman–Kasuya spacetime. The tunneling rates at the event and cosmological horizons are found to be related to the change of Bekenstein–Hawking entropy. The radiation spectrum is not pure thermal and thus there is a correction to the Hawking thermal spectrum.

https://iopscience.iop.org/article/10.1088/0264-9381/24/23/008/pdf

Hawking radiation via tunneling from hot NUT–Kerr–Newman–Kasuya spacetime

We study the Hawking thermal spectrum in dragging coordinate system and the tunneling radiation characteristics of hot NUT-Kerr-Newman-Kasuya spacetime. The tunneling rates at the event and cosmological horizon are found to be related to the change of Bekenstein-Hawking entropy. The radiation spectrum is not pure thermal and thus there is a correction to the Hawking thermal spectrum.

Hawking Radiation via Tunneling from Hot NUT-Kerr-Newman-Kasuya Spacetime

The Korteweg-de Vries Burgers (KdVB)-like equation is derived to study the characteristics of nonlinear propagation of ion acoustic solitions in a highly relativistic plasma containing relativistic ions and nonextensive distribution of electrons and positrons using the well known reductive perturbation technique. The KdVB-like equation is solved employing the Bernoulli's equation method taking unperturbed positron to electron concentration ratio, electron to positron temperature ratio, strength of nonextensivity, ion kinematic viscosity, and highly relativistic streaming factor. It is found that these parameters significantly modify the structures of the solitonic excitation. The ion acoustic shock profiles are observed due to the influence of ion kinematic viscosity. In the absence of dissipative term to the KdVB equation, compressive and rarefactive solitons are observed in case of superthermality, but only compressive solitons are found for the case of subthermality.

Ion acoustic shock and solitary waves in highly relativistic plasmas with nonextensive electrons and positrons

We study the Hawking radiation as charged particles’ tunneling across the horizons of the Hot-NUT-Kerr-Newman-Kasuya spacetime by considering the spacetime background as dynamical and incorporating the self-gravitation effect of the emitted particles when the energy conservation, the angular momentum conservation, and the electric charge conservation are taken into account. Our result shows that the tunneling rate is related to the change of Bekenstein-Hawking entropy and the radiant spectrum is not pure thermal, but is consistent with an underlying unitary theory. The emission process is a reversible one, and the information is preserved as a natural result of the first law of black hole thermodynamics.

Charged Particles’ Tunneling from Hot-NUT-Kerr-Newman-Kasuya Spacetime

Quantum nonthermal radiation of a nonstationary Kerr-Newman-de Sitter black hole is investigated. A crossing of the positive and negative Dirac energy levels occurs in a region near the event horizon of the hole, and spontaneous quantum nonthermal radiation takes place in the overlap region.

M. Hossain Ali

Papers

Hawking radiation via tunneling from hot NUT–Kerr–Newman–Kasuya spacetime

Hawking Radiation via Tunneling from Hot NUT-Kerr-Newman-Kasuya Spacetime

Ion acoustic shock and solitary waves in highly relativistic plasmas with nonextensive electrons and positrons

Charged Particles’ Tunneling from Hot-NUT-Kerr-Newman-Kasuya Spacetime

Letter: Quantum Nonthermal Radiation of Nonstationary Kerr-Newman-de Sitter Black Holes