25 research outputs found
Hawking Radiation as Tunneling through the Quantum Horizon
Planck-scale corrections to the black-hole radiation spectrum in the
Parikh-Wilczek tunneling framework are calculated. The corrective terms arise
from modifications in the expression of the surface gravity in terms of the
mass-energy of the black hole-emitted particle system. The form of the new
spectrum is discussed together with the possible consequences for the fate of
black holes in the late stages of evaporation.Comment: 13 pages; the contents of this paper overlap somewhat with the
earlier submissions hep-th/0504188 and gr-qc/0505015; (v2) references added
and various cosmetic (but no physics) changes, to appear in JHE
On the Existence of the Logarithmic Correction Term in Black Hole Entropy-Area Relation
In this paper we consider a model universe with large extra dimensions to
obtain a modified black hole entropy-area relation. We use the generalized
uncertainty principle to find a relation between the number of spacetime
dimensions and the presence or vanishing of logarithmic prefactor in the black
hole entropy-area relation. Our calculations are restricted to the
microcanonical ensembles and we show that in the modified entropy-area
relation, the microcanonical logarithmic prefactor appears only when spacetime
has an even number of dimensions.Comment: 9 Pages, No Figure
On the Kerr Quantum Area Spectrum
Suppose that there is a quantum operator that describes the horizon area of a
black hole. Then what would be the form of the ensuing quantum spectrum? In
this regard, it has been conjectured that the characteristic frequencies of the
black hole oscillations can be used to calibrate the spacing between the
spectral levels. The current article begins with a brief review of this
conjecture and some of its subsequent developments. We then suggest a simple
but vital modification to a recent treatment on the Kerr (or rotating black
hole) spectrum. As a consequence of this refinement, we are able to rectify a
prior inconsistency (as was found between two distinct calculations) and to
establish, unambiguously, a universal form for the Kerr and Schwarzschild
spectra.Comment: Roughly 8 pages; (v2) added references and very minor change
Thermal Fluctuations and Black Hole Entropy
In this paper, we consider the effect of thermal fluctuations on the entropy
of both neutral and charged black holes. We emphasize the distinction between
fixed and fluctuating charge systems; using a canonical ensemble to describe
the former and a grand canonical ensemble to study the latter. Our novel
approach is based on the philosophy that the black hole quantum spectrum is an
essential component in any such calculation. For definiteness, we employ a
uniformly spaced area spectrum, which has been advocated by Bekenstein and
others in the literature. The generic results are applied to some specific
models; in particular, various limiting cases of an (arbitrary-dimensional)
AdS-Reissner-Nordstrom black hole. We find that the leading-order quantum
correction to the entropy can consistently be expressed as the logarithm of the
classical quantity. For a small AdS curvature parameter and zero net charge, it
is shown that, independent of the dimension, the logarithmic prefactor is +1/2
when the charge is fixed but +1 when the charge is fluctuating.We also
demonstrate that, in the grand canonical framework, the fluctuations in the
charge are large, , even when .
A further implication of this framework is that an asymptotically flat,
non-extremal black hole can never achieve a state of thermal equilibrium.Comment: 25 pages, Revtex; references added and corrected, and some minor
change
Area spectra of the rotating BTZ black hole from quasinormal modes
Following Bekenstein's suggestion that the horizon area of a black hole
should be quantized, the discrete spectrum of the horizon area has been
investigated in various ways. By considering the quasinormal mode of a black
hole, we obtain the transition frequency of the black hole, analogous to the
case of a hydrogen atom, in the semiclassical limit. According to Bohr's
correspondence principle, this transition frequency at large quantum number is
equal to classical oscillation frequency. For the corresponding classical
system of periodic motion with this oscillation frequency, an action variable
is identified and quantized via Bohr-Sommerfeld quantization, from which the
quantized spectrum of the horizon area is obtained. This method can be applied
for black holes with discrete quasinormal modes. As an example, we apply the
method for the both non-rotating and rotating BTZ black holes and obtain that
the spectrum of the horizon area is equally spaced and independent of the
cosmological constant for both cases
Black hole area quantization
It has been argued by several authors that the quantum mechanical spectrum of
black hole horizon area must be discrete. This has been confirmed in different
formalisms, using different approaches. Here we concentrate on two approaches,
the one involving quantization on a reduced phase space of collective
coordinates of a Black Hole and the algebraic approach of Bekenstein. We show
that for non-rotating, neutral black holes in any spacetime dimension, the
approaches are equivalent. We introduce a primary set of operators sufficient
for expressing the dynamical variables of both, thus mapping the observables in
the two formalisms onto each other. The mapping predicts a Planck size remnant
for the black hole.Comment: 7 pages, uses MPLA style file (included). Revised version with
changes in notation for clarity and consistency. To appear in MPL
Algebraic approach to quantum black holes: logarithmic corrections to black hole entropy
The algebraic approach to black hole quantization requires the horizon area
eigenvalues to be equally spaced. As shown previously, for a neutral
non-rotating black hole, such eigenvalues must be -fold degenerate if
one constructs the black hole stationary states by means of a pair of creation
operators subject to a specific algebra. We show that the algebra of these two
building blocks exhibits symmetry, where the area
operator generates the U(1) symmetry. The three generators of the SU(2)
symmetry represent a {\it global} quantum number (hyperspin) of the black hole,
and we show that this hyperspin must be zero. As a result, the degeneracy of
the -th area eigenvalue is reduced to for large , and
therefore, the logarithmic correction term should be added to the
Bekenstein-Hawking entropy. We also provide a heuristic approach explaining
this result, and an evidence for the existence of {\it two} building blocks.Comment: 15 pages, Revtex, to appear in Phys. Rev.
Anatomy of a Bounce
Holographic considerations are used in the scrutiny of a special class of
brane-world cosmologies. Inherently to this class, the brane typically bounces,
at a finite size, as a consequence of a charged black hole in the bulk. Whereas
a prior treatment [hep-th/0301010] emphasized a brane that is void of
standard-model matter, the analysis is now extended to include an intrinsic
(radiation-dominated) matter source. An interesting feature of this generalized
model is that a bounce is no longer guaranteed but, rather, depends on the
initial conditions. Ultimately, we demonstrate that compliance with an
appropriate holographic bound is a sufficient prerequisite for a bounce to
occur.Comment: 14 pages, Revtex; (v2) minor revisions; (v3) reference adde
Of Bounces, Branes and Bounds
Some recent studies have considered a Randall-Sundrum-like brane world
evolving in the background of an anti-de Sitter Reissner-Nordstrom black hole.
For this scenario, it has been shown that, when the bulk charge is
non-vanishing, a singularity-free ``bounce'' universe will always be obtained.
However, for the physically relevant case of a de Sitter brane world, we have
recently argued that, from a holographic (c-theorem) perspective, such brane
worlds may not be physically viable. In the current paper, we reconsider the
validity of such models by appealing to the so-called ``causal entropy bound''.
In this framework, a paradoxical outcome is obtained: these brane worlds are
indeed holographically viable, provided that the bulk charge is not too small.
We go on to argue that this new finding is likely the more reliable one.Comment: 15 pages, Revtex; references added and very minor change
Entropy Corrections for Schwarzschild and Reissner-Nordstr\"om Black Holes
Schwarzschild black hole being thermodynamically unstable, corrections to its
entropy due to small thermal fluctuations cannot be computed. However, a
thermodynamically stable Schwarzschild solution can be obtained within a cavity
of any finite radius by immersing it in an isothermal bath. For these boundary
conditions, classically there are either two black hole solutions or no
solution. In the former case, the larger mass solution has a positive specific
heat and hence is locally thermodynamically stable. We find that the entropy of
this black hole, including first order fluctuation corrections is given by:
{\cal S} = S_{BH} - \ln[\f{3}{R} (S_{BH}/4\p)^{1/2} -2]^{-1} + (1/2)
\ln(4\p), where is its Bekenstein-Hawking entropy and is the
radius of the cavity. We extend our results to four dimensional
Reissner-Nordstr\"om black holes, for which the corresponding expression is:
{\cal S} = S_{BH} - \f{1}{2} \ln [ {(S_{BH}/\p R^2) ({3S_{BH}}/{\p R^2} -
2\sqrt{{S_{BH}}/{\p R^2 -\a^2}}) \le(\sqrt{{S_{BH}}/{\p R^2}} - \a^2 \ri)}/
{\le({S_{BH}}/{\p R^2} -\a^2 \ri)^2} ]^{-1} +(1/2)\ln(4\p). Finally, we
generalise the stability analysis to Reissner-Nordstr\"om black holes in
arbitrary spacetime dimensions, and compute their leading order entropy
corrections. In contrast to previously studied examples, we find that the
entropy corrections in these cases have a different character.Comment: 6 pages, Revtex. References added, minor changes. Version to appear
in Class. Quant. Gra