131 research outputs found

### Conformal Transformation, Near Horizon Symmetry, Virasoro Algebra and Entropy

There are certain black hole solutions in general relativity (GR) which are
conformally related to the stationary solutions in GR. It is not obvious that
the horizon entropy of these spacetimes is also one quarter of the area of
horizon, like the stationary ones. Here I study this topic in the context of
Virasoro algebra and Cardy formula. Using the fact that the conformal spacetime
admits conformal Killing vector and the horizon is determined by the vanishing
of the norm of it, the diffemorphisms are obtained which keep the near horizon
structure invariant. The Noether charge and a bracket among them corresponding
to these vectors are calculated in this region. Finally, they are evaluated for
the Sultana-Dyer (SD) black hole, which is conformal to the Schwarzschild
metric. It is found that the bracket is identical to the usual Virasoro algebra
with the central extension. Identifying the zero mode eigenvalue and the
central charge, the entropy of the SD horizon is obtained by using Cardy
formula. Interestingly, this is again one quarter of the horizon area. Only
difference in this case is that the area is modified by the conformal factor
compared to that of the stationary one. The analysis gives a direct proof of
the earlier assumption.Comment: Minor comments added, to appear in Phys. Rev.

### Thermodynamics of Sultana-Dyer Black Hole

The thermodynamical entities on the dynamical horizon are not naturally
defined like the usual static cases. Here I find the temperature, Smarr formula
and the first law of thermodynamics for the Sultana-Dyer metric which is
related to the Schwarzschild spacetime by a time dependent conformal factor. To
find the temperature ($T$), the chiral anomaly expressions for the two
dimensional spacetime are used. This shows an application of the anomaly method
to study Hawking effect for a dynamical situation. Moreover, the analysis
singles out one expression for temperature among two existing expressions in
the literature. Interestingly, the present form satisfies the first law of
thermodynamics. Also, it relates the Misner-Sharp energy ($\bar{E}$) and the
horizon entropy ($\bar{S}$) by an algebraic expression $\bar{E}=2\bar{S}T$
which is the general form of the Smarr formula. This fact is similar to the
usual static black hole cases in Einstein's gravity where the energy is
identified as the Komar conserved quantity.Comment: typos corrected, to appear in JCA

### Entropy function from the gravitational surface action for an extremal near horizon black hole

It is often argued that {\it all the information of a gravitational theory is
encoded in the surface term of the action}; which means one can find several
physical quantities just from the surface term without incorporating the bulk
part of the action. This has been observed in various instances; e.g.
derivation of the Einstein's equations, surface term calculated on the horizon
leads to entropy, etc. Here I investigate the role of it in the context of
entropy function and entropy of extremal near horizon black holes. Considering
only the Gibbons-Hawking-York (GHY) surface term to define an entropy function
for the extremal near horizon black hole solution, it is observed that the
extremization of such function leads to the exact value of the horizon entropy.
This analysis again supports the previous claim that there exists a ``{\it
holographic}'' nature in the gravitational action -- surface term contains the
information of the bulk.Comment: Matches with the accepted version, to appear in EPJ

### Vacuum condition and the relation between response parameter and anomaly coefficient in (1+3) dimensions

The role of Israel-Hartle-Hawking vacuum is discussed for anomalous fluid in
presence of both the gauge and gravitational anomalies in ($1+3$) dimensions. I
show that imposition of this vacuum condition leads to the relation
$\tilde{c}_{4d}=-8\pi^2c_m$ between the response parameter ($\tilde{c}_{4d}$)
and the anomaly coefficient ($c_m$). This establishes a connection between the
coefficients appearing in a first order and a third order derivative terms in
the constitutive relation.Comment: Comments added, to appear in JHE

### 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.

### Anomalous effective action, Noether current, Virasoro algebra and Horizon entropy

Several investigations show that in a very small length scale there exists
corrections to the entropy of black hole horizon. Due to fluctuations of the
background metric and the external fields the action incorporates corrections.
In the low energy regime, the one loop effective action in four dimensions
leads to trace anomaly. We start from the Noether current corresponding to the
Einstein-Hilbert plus the one loop effective action to calculate the charge for
the diffeomorphisms which preserve the Killing horizon structure. Then a
bracket among the charges is calculated. We show that the Fourier modes of the
bracket is exactly similar to Virasoro algebra. Then using Cardy formula the
entropy is evaluated. Finally, the explicit terms of the entropy expression is
calculated for a classical background. It turns out that the usual expression
for entropy; i.e. the Bekenstein-Hawking form, is not modified.Comment: Minor modifications, to appear in EPJ

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