523 research outputs found

### Control of black hole evaporation?

Contradiction between Hawking's semi-classical arguments and string theory on
the evaporation of black hole has been one of the most intriguing problems in
fundamental physics. A final-state boundary condition inside the black hole was
proposed by Horowitz and Maldacena to resolve this contradiction. We point out
that original Hawking effect can be also regarded as a separate boundary
condition at the event horizon for this scenario. Here, we found that the
change of Hawking boundary condition may affect the information transfer from
the initial collapsing matter to the outgoing Hawking radiation during
evaporation process and as a result the evaporation process itself,
significantly.Comment: Journal of High Energy Physics, to be publishe

### The "physical process" version of the first law and the generalized second law for charged and rotating black holes

We investigate both the ``physical process'' version of the first law and the
second law of black hole thermodynamics for charged and rotating black holes.
We begin by deriving general formulas for the first order variation in ADM mass
and angular momentum for linear perturbations off a stationary, electrovac
background in terms of the perturbed non-electromagnetic stress-energy, $\delta
T_{ab}$, and the perturbed charge current density, $\delta j^a$. Using these
formulas, we prove the "physical process version" of the first law for charged,
stationary black holes. We then investigate the generalized second law of
thermodynamics (GSL) for charged, stationary black holes for processes in which
a box containing charged matter is lowered toward the black hole and then
released (at which point the box and its contents fall into the black hole
and/or thermalize with the ``thermal atmosphere'' surrounding the black hole).
Assuming that the thermal atmosphere admits a local, thermodynamic description
with respect to observers following orbits of the horizon Killing field, and
assuming that the combined black hole/thermal atmosphere system is in a state
of maximum entropy at fixed mass, angular momentum, and charge, we show that
the total generalized entropy cannot decrease during the lowering process or in
the ``release process''. Consequently, the GSL always holds in such processes.
No entropy bounds on matter are assumed to hold in any of our arguments.Comment: 35 pages; 1 eps figur

### Black Hole Entropy is Noether Charge

We consider a general, classical theory of gravity in $n$ dimensions, arising
from a diffeomorphism invariant Lagrangian. In any such theory, to each vector
field, $\xi^a$, on spacetime one can associate a local symmetry and, hence, a
Noether current $(n-1)$-form, ${\bf j}$, and (for solutions to the field
equations) a Noether charge $(n-2)$-form, ${\bf Q}$. Assuming only that the
theory admits stationary black hole solutions with a bifurcate Killing horizon,
and that the canonical mass and angular momentum of solutions are well defined
at infinity, we show that the first law of black hole mechanics always holds
for perturbations to nearby stationary black hole solutions. The quantity
playing the role of black hole entropy in this formula is simply $2 \pi$ times
the integral over $\Sigma$ of the Noether charge $(n-2)$-form associated with
the horizon Killing field, normalized so as to have unit surface gravity.
Furthermore, we show that this black hole entropy always is given by a local
geometrical expression on the horizon of the black hole. We thereby obtain a
natural candidate for the entropy of a dynamical black hole in a general theory
of gravity. Our results show that the validity of the ``second law" of black
hole mechanics in dynamical evolution from an initially stationary black hole
to a final stationary state is equivalent to the positivity of a total Noether
flux, and thus may be intimately related to the positive energy properties of
the theory. The relationship between the derivation of our formula for black
hole entropy and the derivation via ``Euclidean methods" also is explained.Comment: 16 pages, EFI 93-4

### Entropy Spectrum of a Carged Black Hole of Heterotic String Theory via Adiabatic Invariance

Using adiabatic invariance and the Bohr-Sommerfeld quantization rule we
investigate the entropy spectroscopy of a charged black hole of heterotic
string theory. It is shown that the entropy spectrum is equally spaced
identically to the Schwarzschild, Reissner-Nordstr\"om and Kerr black holes.
Since the adiabatic invariance method does not use quasinormal mode analysis,
there is no need to impose the small charge limit and no confusion on whether
the real part or imaginary part is responsible for the entropy spectrum.Comment: 8 pages, no figure

### A comparison of Noether charge and Euclidean methods for Computing the Entropy of Stationary Black Holes

The entropy of stationary black holes has recently been calculated by a
number of different approaches. Here we compare the Noether charge approach
(defined for any diffeomorphism invariant Lagrangian theory) with various
Euclidean methods, specifically, (i) the microcanonical ensemble approach of
Brown and York, (ii) the closely related approach of Ba\~nados, Teitelboim, and
Zanelli which ultimately expresses black hole entropy in terms of the Hilbert
action surface term, (iii) another formula of Ba\~nados, Teitelboim and Zanelli
(also used by Susskind and Uglum) which views black hole entropy as conjugate
to a conical deficit angle, and (iv) the pair creation approach of Garfinkle,
Giddings, and Strominger. All of these approaches have a more restrictive
domain of applicability than the Noether charge approach. Specifically,
approaches (i) and (ii) appear to be restricted to a class of theories
satisfying certain properties listed in section 2; approach (iii) appears to
require the Lagrangian density to be linear in the curvature; and approach (iv)
requires the existence of suitable instanton solutions. However, we show that
within their domains of applicability, all of these approaches yield results in
agreement with the Noether charge approach. In the course of our analysis, we
generalize the definition of Brown and York's quasilocal energy to a much more
general class of diffeomorphism invariant, Lagrangian theories of gravity. In
an appendix, we show that in an arbitrary diffeomorphism invariant theory of
gravity, the ``volume term" in the ``off-shell" Hamiltonian associated with a
time evolution vector field $t^a$ always can be expressed as the spatial
integral of $t^a {\cal C}_a$, where ${\cal C}_a = 0$ are the constraints
associated with the diffeomorphism invariance.Comment: 29 pages (double-spaced) late

### On the massive wave equation on slowly rotating Kerr-AdS spacetimes

The massive wave equation $\Box_g \psi - \alpha\frac{\Lambda}{3} \psi = 0$ is
studied on a fixed Kerr-anti de Sitter background
$(\mathcal{M},g_{M,a,\Lambda})$. We first prove that in the Schwarzschild case
(a=0), $\psi$ remains uniformly bounded on the black hole exterior provided
that $\alpha < {9/4}$, i.e. the Breitenlohner-Freedman bound holds. Our proof
is based on vectorfield multipliers and commutators: The usual energy current
arising from the timelike Killing vector field $T$ (which fails to be
non-negative pointwise) is shown to be non-negative with the help of a Hardy
inequality after integration over a spacelike slice. In addition to $T$, we
construct a vectorfield whose energy identity captures the redshift producing
good estimates close to the horizon. The argument is finally generalized to
slowly rotating Kerr-AdS backgrounds. This is achieved by replacing the Killing
vectorfield $T=\partial_t$ with $K=\partial_t + \lambda \partial_\phi$ for an
appropriate $\lambda \sim a$, which is also Killing and--in contrast to the
asymptotically flat case--everywhere causal on the black hole exterior. The
separability properties of the wave equation on Kerr-AdS are not used. As a
consequence, the theorem also applies to spacetimes sufficiently close to the
Kerr-AdS spacetime, as long as they admit a causal Killing field $K$ which is
null on the horizon.Comment: 1 figure; typos corrected, references added, introduction revised; to
appear in CM

### Angular momentum-mass inequality for axisymmetric black holes

In these notes we describe recent results concerning the inequality $m\geq
\sqrt{|J|}$ for axially symmetric black holes.Comment: 7 pages, 1 figur

### Ten Proofs of the Generalized Second Law

Ten attempts to prove the Generalized Second Law of Thermodyanmics (GSL) are
described and critiqued. Each proof provides valuable insights which should be
useful for constructing future, more complete proofs. Rather than merely
summarizing previous research, this review offers new perspectives, and
strategies for overcoming limitations of the existing proofs. A long
introductory section addresses some choices that must be made in any
formulation the GSL: Should one use the Gibbs or the Boltzmann entropy? Should
one use the global or the apparent horizon? Is it necessary to assume any
entropy bounds? If the area has quantum fluctuations, should the GSL apply to
the average area? The definition and implications of the classical,
hydrodynamic, semiclassical and full quantum gravity regimes are also
discussed. A lack of agreement regarding how to define the "quasi-stationary"
regime is addressed by distinguishing it from the "quasi-steady" regime.Comment: 60 pages, 2 figures, 1 table. v2: corrected typos and added a
footnote to match the published versio

### The Bousso entropy bound in selfgravitating gas of massless particles

The Bousso entropy bound is investigated in a static spherically symmetric
spacetime filled with an ideal gas of massless bosons or fermions. Especially
lightsheets generated by spheres are considered. Statistical description of the
gas is given. Conditions under which the Bousso bound can be violated are
discussed and it is shown that a possible violating region cannot be
arbitrarily large and it is contained inside a sphere of unit Planck radius if
number of independent polarization states $g_s$ is small enough. It is also
shown that central temperature must exceed the Planck temperature to get a
violation of the Bousso bound for $g_s$ not too large.Comment: 14 pages, 4 figures, a paragraph added, version published in Gen.
Rel. Gra

### The black hole dynamical horizon and generalized second law of thermodynamics

The generalized second law of thermodynamics for a system containing a black
hole dynamical horizon is proposed in a covariant way. Its validity is also
tested in case of adiabatically collapsing thick light shells.Comment: JHEP style, 8 pages, 2 figures, version to appear in JHEP with typos
correcte

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