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

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

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 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