Their topics include a short scrapbook on classical black holes, the thermality of Hawking radiation: from Hartle-Hawking to Israel and Unruh, the Euclidean section and Hawking temperature
, the roots of analogue gravity, and Hawking radiation in a non-dispersive nonlinear Kerr dielectric.
Further, the effects of the GUP have also been considered in the tunneling formalism for Hawking radiation to evaluate the quantum-corrected Hawking temperature
and entropy of a Schwarzschild black hole [42-46].
However, the Hawking temperature
, h[c.sup.3]/8[pi][k.sub.B]GM, of a Planck mass black hole is normally assumed to be [T.sub.p]/8[pi], yielding a Planck acceleration of [a.sub.p] [approximately equal to] [1/4] [square root of [c.sup.7]/hG].
They employed the dynamical geometry approach to calculate the imaginary part of the action for the tunneling process of s-wave emission across the horizon and related it to the Boltzmann factor for the emission at the Hawking temperature
. Due to back-reaction effects included, this procedure gives a correction to the standard Hawking temperature
formula, which speeds up the process of black holes' evaporation.
If one is able to understand the need and importance of "universe being a black hole for ever", "CMBR temperature being the Hawking temperature
" and "angular velocity of cosmic black hole being the present Hubble's constant", a true unified model of "black hole universe" can be developed.
For a black hole with mass M, the Hawking temperature
is given by T = 1/8[pi]M [4, 5].
The significant connection between gravitation and thermodynamics is established after the remarkable discovery of black hole (BH) thermodynamics with Hawking temperature
as well as BH entropy [13-16].
Also, subsequently, by a novel formulation of the tunnelling formalism, Banerjee and Majhi  directly derived the black body spectrum for both bosons and fermions from a BH with standard Hawking temperature
. The analysis in  was improved by one of us, Christian Corda , who found as final result a nonstrictly black body spectrum in agreement with the emission probability in [2,3].
Considering the Hawking temperature
(similar to (12), we ignore the direct correction to the radius in the Hawking temperature
, and the changes of numbers of degrees of freedom directly stem from the corrections of the area of the apparent horizon) T = 1/2[pi][r.sub.A] and E = -([rho] + 3p)[??] with dark energy in the bulk, we obtain
Subsequently, using the modified Dirac equation, we calculate the tunneling probability of the Dirac particle by using the Hamilton-Jacobi method, and, then, we find the modified Hawking temperature
of the black hole.
Furthermore, the associated Hawking temperature
is expressed by
Here [T.sub.H] = [square root of (1 - [epsilon]d[OMEGA]/dt)]/8[pi]M is the Hawking temperature
. According to the first law of black hole thermodynamics, the entropy of Rutz-Schwarzschild black hole is calculated as