48 research outputs found
P-V criticality of AdS black holes in a general framework
In black hole thermodynamics, it has been observed that AdS black holes
behave as van der Waals system if one interprets the cosmological constant as a
pressure term. Also the critical exponents for the phase transition of AdS
black holes and the van der Waals systems are same. Till now this type of
analysis is done by two steps. In the first step one shows that a particular
metric allows phase transition and in the second step, using this information,
one calculates the exponents. Here, we present a different approach based on
two universal inputs (the general forms of the Smarr formula and the first law
of thermodynamics) and one assumption regarding the existence of van der Waal
like critical point for a metric. We find that the same values of the critical
exponents can be obtained by this approach. Thus we demonstrate that, though
the existence of van der Waal like phase transition depends on specific
metrics, the values of critical exponents are then fixed for that set of
metrics.Comment: Extensively modified version, to appear in Phys. Lett.
Entropy corresponding to the interior of a Schwarzschild black hole
Interior volume within the horizon of a black hole is a non-trivial concept
which turns out to be very important to explain several issues in the context
of quantum nature of black hole. Here we show that the entropy, contained by
the {\it maximum} interior volume for massless modes, is proportional to the
Bekenstein-Hawking expression. The proportionality constant is less than unity
implying the horizon bears maximum entropy than that by the interior. The
derivation is very systematic and free of any ambiguity. To do so the precise
value of the energy of the modes, living in the interior, is derived by
constraint analysis. Finally, the implications of the result are discussed.Comment: Two new references and additional discussions added, to appear in
Phys. Lett.
Gravitational surface Hamiltonian and entropy quantization
The surface Hamiltonian corresponding to the surface part of a gravitational
action has structure where is conjugate momentum of . Moreover, it
leads to on the horizon of a black hole. Here and are temperature
and entropy of the horizon. Imposing the hermiticity condition we quantize this
Hamiltonian. This leads to an equidistant spectrum of its eigenvalues. Using
this we show that the entropy of the horizon is quantized. This analysis holds
for any order of Lanczos-Lovelock gravity. For general relativity, the area
spectrum is consistent with Bekenstein's observation. This provides a more
robust confirmation of this earlier result as the calculation is based on the
direct quantization of the Hamiltonian in the sense of usual quantum mechanics.Comment: Revised version, accepted in Phys. Lett.