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

We update the constraints on the fraction of the Universe going into primordial black holes in the mass range ${10}^{9}--{10}^{17}\text{ }\text{ }\mathrm{g}$ associated with the effects of their evaporations on big bang nucleosynthesis and the extragalactic photon background. We include for the first time all the effects of quark and gluon emission by black holes on these constraints and account for the latest observational developments. We then discuss the other constraints in this mass range and show that these are weaker than the nucleosynthesis and photon background limits, apart from a small range ${10}^{13}--{10}^{14}\text{ }\text{ }\mathrm{g}$, where the damping of cosmic microwave background anisotropies dominates. Finally we review the gravitational and astrophysical effects of nonevaporating primordial black holes, updating constraints over the broader mass range $1--{10}^{50}\text{ }\text{ }\mathrm{g}$.

New cosmological constraints on primordial black holes

The concept of parity-time symmetric systems is rooted in non-Hermitian quantum mechanics where complex potentials obeying this symmetry could exhibit real spectra. The concept has applications in many fields of physics, e.g., in optics, metamaterials, acoustics, Bose-Einstein condensation, electronic circuitry, etc. The inclusion of nonlinearity has led to a number of new phenomena for which no counterparts exist in traditional dissipative systems. Several examples of nonlinear parity-time symmetric systems in different physical disciplines are presented and their implications discussed.

Nonlinear waves in PT -symmetric systems

心臓病診療プラクティス 16. 心不全を癒す

▪ Abstract The gamma ray burst phenomenon is reviewed from a theoretical point of view, with emphasis on the fireball shock scenario of the prompt emission and the longer wavelength afterglow. Rece...

Theories of Gamma-Ray Bursts

Comment on: “Spherical Kadomtsev Petviashvili equation and nebulons for dust ion-acoustic waves with symbolic computation” [Phys. Lett. A 340 (2005) 243]

Optical solitary wave solutions for the higher order nonlinear Schrödinger equation with cubic-quintic non-Kerr terms

Auto-Bäcklund transformation and analytic solutions for general variable-coefficient KdV equation

Previously we identified some short burst events from the BATSE 1B catalog that were consistent with an origin of primordial black hole evaporation at the quark-gluon phase transition. We showed that these events are also consistent with arising from a homogeneous spatial distribution. Recently the PHEBUS group has also indicated that the short bursts are consistent with V/Vmax ~ 1/2. In this paper we describe the results of the study of the BATSE 3B catalog shape that confirm the results from BATSE 1B.

http://iopscience.iop.org/article/10.1086/304480/pdf

Woo-Pyo Hong

Papers

Comment on: “Spherical Kadomtsev Petviashvili equation and nebulons for dust ion-acoustic waves with symbolic computation” [Phys. Lett. A 340 (2005) 243]

Optical solitary wave solutions for the higher order nonlinear Schrödinger equation with cubic-quintic non-Kerr terms

Auto-Bäcklund transformation and analytic solutions for general variable-coefficient KdV equation

Further Evidence for Some Gamma-Ray Bursts Consistent with Primordial Black Hole Evaporation

Modulational instability of optical waves in the high dispersive cubic–quintic nonlinear Schrödinger equation