29 research outputs found
Quantum Tunneling, Blackbody Spectrum and Non-Logarithmic Entropy Correction for Lovelock Black Holes
We show, using the tunneling method, that Lovelock black holes Hawking
radiate with a perfect blackbody spectrum. This is a new result. Within the
semiclassical (WKB) approximation the temperature of the spectrum is given by
the semiclassical Hawking temperature. Beyond the semiclassical approximation
the thermal nature of the spectrum does not change but the temperature
undergoes some higher order corrections. This is true for both black hole
(event) and cosmological horizons. Using the first law of thermodynamics the
black hole entropy is calculated. Specifically the -dimensional static,
chargeless black hole solutions which are spherically symmetric and
asymptotically flat, AdS or dS are considered. The interesting property of
these black holes is that their semiclassical entropy does not obey the
Bekenstein-Hawking area law. It is found that the leading correction to the
semiclassical entropy for these black holes is not logarithmic and next to
leading correction is also not inverse of horizon area. This is in contrast to
the black holes in Einstein gravity. The modified result is due to the presence
of Gauss-Bonnet term in the Lovelock Lagrangian. For the limit where the
coupling constant of the Gauss-Bonnet term vanishes one recovers the known
correctional terms as expected in Einstein gravity. Finally we relate the
coefficient of the leading (non-logarithmic) correction with the trace anomaly
of the stress tensor.Comment: minor modifications, two new references added, LaTeX, JHEP style, 34
pages, no figures, to appear in JHE
Glassy Phase Transition and Stability in Black Holes
Black hole thermodynamics, confined to the semi-classical regime, cannot
address the thermodynamic stability of a black hole in flat space. Here we show
that inclusion of correction beyond the semi-classical approximation makes a
black hole thermodynamically stable. This stability is reached through a phase
transition. By using Ehrenfest's scheme we further prove that this is a glassy
phase transition with a Prigogine-Defay ratio close to 3. This value is well
placed within the desired bound (2 to 5) for a glassy phase transition. Thus
our analysis indicates a very close connection between the phase transition
phenomena of a black hole and glass forming systems. Finally, we discuss the
robustness of our results by considering different normalisations for the
correction term.Comment: v3, minor changes over v2, references added, LaTeX-2e, 18 pages, 3 ps
figures, to appear in Eour. Phys. Jour.
Exact Differential and Corrected Area Law for Stationary Black Holes in Tunneling Method
We give a new and conceptually simple approach to obtain the first law of
black hole thermodynamics from a basic thermodynamical property that entropy
(S) for any stationary black hole is a state function implying that dS must be
an exact differential. Using this property we obtain some conditions which are
analogous to Maxwell's relations in ordinary thermodynamics. From these
conditions we are able to explicitly calculate the semiclassical
Bekenstein-Hawking entropy, considering the most general metric represented by
the Kerr-Newman spacetime. We extend our method to find the corrected entropy
of stationary black holes in (3+1) dimensions. For that we first calculate the
corrected Hawking temperature considering both scalar particle and fermion
tunneling beyond the semiclassical approximation. Using this corrected Hawking
temperature we compute the corrected entropy, based on properties of exact
differentials. The connection of the coefficient of the leading (logarithmic)
correction with the trace anomaly of the stress tensor is established . We
explicitly calculate this coefficient for stationary black holes with various
metrics, emphasising the role of Komar integrals.Comment: references added, typos corrected, LaTeX, 28 pages, no figures, to
appear in JHE