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 [7] directly derived the black body spectrum for both bosons and fermions from a BH with standard

Hawking temperature. The analysis in [7] was improved by one of us, Christian Corda [15], 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