Conformal Scalar Propagation and Hawking Radiation

The construction of the conformal scalar propagator which has been obtained in the preceding two projects as an analytic function of the Schwarzschild black-hole space-time is completed with a boundary condition imposed by the physical context through contour integration in the exterior vicinity of the event horizon. It is shown that, as a consequence of the semi-classical character which the emitted quanta have in that exterior vicinity, the particle production by the Schwarzschild black hole which was formally established in the preceding project is identical to thermal Hawking radiation. By extension, it is established that such a particle production corresponds to a spectrum which detracts from thermality by the amount predicted by Parikh and Wilczek if energy conservation is properly imposed as a constraint on scalar propagation. The results obtained herein support the case made by S. Hawking on the relation between quantum propagation and observation of particles produced by a black hole.Comment: 18 pages, 2 figures, one footnote removed, motto added. Due to appear in General Relativity and Gravitatio

The Friedmann-Lemaitre-Robertson-Walker Big Bang singularities are well behaved

We show that the Big Bang singularity of the Friedmann-Lemaitre-Robertson-Walker model does not raise major problems to General Relativity. We prove a theorem showing that the Einstein equation can be written in a non-singular form, which allows the extension of the spacetime before the Big Bang. The physical interpretation of the fields used is discussed. These results follow from our research on singular semi-Riemannian geometry and singular General Relativity.Comment: 10 pages, 5 figure

Black hole microstate geometries from string amplitudes

In this talk we review recent calculations of the asymptotic supergravity fields sourced by bound states of D1 and D5-branes carrying travelling waves. We compute disk one-point functions for the massless closed string fields. At large distances from the branes, the effective open string coupling is small, even in the regime of parameters where the classical D1-D5-P black hole may be considered. The fields sourced by the branes differ from the black hole solution by various multipole moments, and have led to the construction of a new 1/8-BPS ansatz in type IIB supergravity.Comment: 14 pages, 3 figures, Contribution to the proceedings of the Black Objects in Supergravity School, Frascati, 201

Stable causality of Black Saturns

We prove that the Black Saturns are stably causal on the closure of the domain of outer communications.Comment: 10 page

Brick Walls and AdS/CFT

We discuss the relationship between the bulk-boundary correspondence in Rehren's algebraic holography (and in other 'fixed-background' approaches to holography) and in mainstream 'Maldacena AdS/CFT'. Especially, we contrast the understanding of black-hole entropy from the viewpoint of QFT in curved spacetime -- in the framework of 't Hooft's 'brick wall' model -- with the understanding based on Maldacena AdS/CFT. We show that the brick-wall modification of a Klein Gordon field in the Hartle-Hawking-Israel state on 1+2-Schwarzschild AdS (BTZ) has a well-defined boundary limit with the same temperature and entropy as the brick-wall-modified bulk theory. One of our main purposes is to point out a close connection, for general AdS/CFT situations, between the puzzle raised by Arnsdorf and Smolin regarding the relationship between Rehren's algebraic holography and mainstream AdS/CFT and the puzzle embodied in the 'correspondence principle' proposed by Mukohyama and Israel in their work on the brick-wall approach to black hole entropy. Working on the assumption that similar results will hold for bulk QFT other than the Klein Gordon field and for Schwarzschild AdS in other dimensions, and recalling the first author's proposed resolution to the Mukohyama-Israel puzzle based on his 'matter-gravity entanglement hypothesis', we argue that, in Maldacena AdS/CFT, the algebra of the boundary CFT is isomorphic only to a proper subalgebra of the bulk algebra, albeit (at non-zero temperature) the (GNS) Hilbert spaces of bulk and boundary theories are still the 'same' -- the total bulk state being pure, while the boundary state is mixed (thermal). We also argue from the finiteness of its boundary (and hence, on our assumptions, also bulk) entropy at finite temperature, that the Rehren dual of the Maldacena boundary CFT cannot itself be a QFT and must, instead, presumably be something like a string theory.Comment: 54 pages, 3 figures. Arguments strengthened in the light of B.S. Kay `Instability of Enclosed Horizons' arXiv:1310.739

Quantum Black Holes as the Link Between Microphysics and Macrophysics

There appears to be a duality between elementary particles, which span the mass range below the Planck scale, and black holes, which span the mass range range above it. In particular, the Black Hole Uncertainty Principle Correspondence posits a smooth transition between the Compton and Schwarzschild scales as a function of mass. This suggests that all black holes are in some sense quantum, that elementary particles can be interpreted as sub-Planckian black holes, and that there is a subtle connection between quantum and classical physics.Comment: 9 pages, 7 figures, 2015 Karl Schwarzschild Meeting on Gravitational Physics, eds. P. Nicolini, J. Mureika, M. Kaminski and M. Bleiche

Black hole entropy and soft hair

Abstract A set of infinitesimal Virasoro L ⊗ Virasoro R diffeomorphisms are presented which act non-trivially on the horizon of a generic Kerr black hole with spin J. The covariant phase space formalism provides a formula for the Virasoro charges as surface integrals on the horizon. Integrability and associativity of the charge algebra are shown to require the inclusion of ‘Wald-Zoupas’ counterterms. A counterterm satisfying the known consistency requirement is constructed and yields central charges c L = c R = 12J. Assuming the existence of a quantum Hilbert space on which these charges generate the symmetries, as well as the applicability of the Cardy formula, the central charges reproduce the macroscopic area-entropy law for generic Kerr black holes.</jats:p

Phase structure of black branes in grand canonical ensemble

This is a companion paper of our previous work [1] where we studied the thermodynamics and phase structure of asymptotically flat black $p$-branes in a cavity in arbitrary dimensions $D$ in a canonical ensemble. In this work we study the thermodynamics and phase structure of the same in a grand canonical ensemble. Since the boundary data in two cases are different (for the grand canonical ensemble boundary potential is fixed instead of the charge as in canonical ensemble) the stability analysis and the phase structure in the two cases are quite different. In particular, we find that there exists an analog of one-variable analysis as in canonical ensemble, which gives the same stability condition as the rather complicated known (but generalized from black holes to the present case) two-variable analysis. When certain condition for the fixed potential is satisfied, the phase structure of charged black $p$-branes is in some sense similar to that of the zero charge black $p$-branes in canonical ensemble up to a certain temperature. The new feature in the present case is that above this temperature, unlike the zero-charge case, the stable brane phase no longer exists and `hot flat space' is the stable phase here. In the grand canonical ensemble there is an analog of Hawking-Page transition, even for the charged black $p$-brane, as opposed to the canonical ensemble. Our study applies to non-dilatonic as well as dilatonic black $p$-branes in $D$ space-time dimensions.Comment: 32 pages, 2 figures, various points refined, discussion expanded, references updated, typos corrected, published in JHEP 1105:091,201

The temperature and entropy of CFT on time-dependent backgrounds

We express the AdS-Schwarzschild black-hole configuration in coordinates such that the boundary metric is of the FLRW type. We review how this construction can be used in order to calculate the stress-energy tensor of the dual CFT on the FLRW background. We deduce the temperature and entropy of the CFT, which are related to the temperature and entropy of the black hole. We find that the entropy is proportional to the area of an apparent horizon, different from the black-hole event horizon. For a dS boundary we reproduce correctly the intrinsic temperature of dS space.Comment: 19 pages, major revision, several comments added, version to appear in JHE

The hidden horizon and black hole unitarity

We motivate through a detailed analysis of the Hawking radiation in a Schwarzschild background a scheme in accordance with quantum unitarity. In this scheme the semi-classical approximation of the unitary quantum - horizonless - black hole S-matrix leads to the conventional description of the Hawking radiation from a classical black hole endowed with an event horizon. Unitarity is borne out by the detailed exclusive S-matrix amplitudes. There, the fixing of generic out-states, in addition to the in-state, yields in asymptotic Minkowski space-time saddle-point contributions which are dominated by Planckian metric fluctuations when approaching the Schwarzschild radius. We argue that these prevent the corresponding macroscopic "exclusive backgrounds" to develop an event horizon. However, if no out-state is selected, a distinct saddle-point geometry can be defined, in which Planckian fluctuations are tamed. Such "inclusive background" presents an event horizon and constitutes a coarse-grained average over the aforementioned exclusive ones. The classical event horizon appears as a coarse-grained structure, sustaining the thermodynamic significance of the Bekenstein-Hawking entropy. This is reminiscent of the tentative fuzzball description of extremal black holes: the role of microstates is played here by a complete set of out-states. Although the computations of unitary amplitudes would require a detailed theory of quantum gravity, the proposed scheme itself, which appeals to the metric description of gravity only in the vicinity of stationary points, does not.Comment: 29 pages, 4 figures. Typos corrected. Two footnotes added (footnotes 3 and 5