Near-horizon Bondi-Metzner-Sachs symmetry, dimensional reduction, and black hole entropy

In an earlier short paper [Phys. Rev. Lett. 120, 101301 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.101301], I argued that the horizon-preserving diffeomorphisms of a generic black hole are enhanced to a larger three-dimensional Bondi-Metzner-Sachs symmetry, which is powerful enough to determine the Bekenstein-Hawking entropy. Here, I provide details and extensions of that argument, including a loosening of horizon boundary conditions and a more thorough treatment of dimensional reduction and meaning of a "near-horizon symmetry.

Aspects of the BMS/CFT correspondence

After a review of symmetries and classical solutions involved in the AdS3/CFT2 correspondence, we apply a similar analysis to asymptotically flat spacetimes at null infinity in 3 and 4 dimensions. In the spirit of two dimensional conformal field theory, the symmetry algebra of asymptotically flat spacetimes at null infinity in 4 dimensions is taken to be the semi-direct sum of supertranslations with infinitesimal local conformal transformations and not, as usually done, with the Lorentz algebra. As a first application, we derive how the symmetry algebra is realized on solution space. In particular, we work out the behavior of Bondi's news tensor, mass and angular momentum aspects under local conformal transformations.Comment: 40 pages Latex fil

Bondi-Metzner-Sachs symmetry, holography on null-surfaces and area proportionality of "light-slice" entropy

It is shown that certain kinds of behavior, which hitherto were expected to be characteristic for classical gravity and quantum field theory in curved spacetime, as the infinite dimensional Bondi-Metzner-Sachs symmetry, holography on event horizons and an area proportionality of entropy, have in fact an unnoticed presence in Minkowski QFT. This casts new light on the fundamental question whether the volume propotionality of heat bath entropy and the (logarithmically corrected) dimensionless area law obeyed by localization-induced thermal behavior are different geometric parametrizations which share a common primordeal algebraic origin. Strong arguments are presented that these two different thermal manifestations can be directly related, this is in fact the main aim of this paper. It will be demonstrated that QFT beyond the Lagrangian quantization setting receives crucial new impulses from holography onto horizons. The present paper is part of a project aimed at elucidating the enormous physical range of "modular localization". The latter does not only extend from standard Hamitonian heat bath thermal states to thermal aspects of causal- or event- horizons addressed in this paper. It also includes the recent understanding of the crossing property of formfactors whose intriguing similarity with thermal properties was, although sometimes noticed, only sufficiently understood in the modular llocalization setting.Comment: 42 pages, changes, addition of new results and new references, in this form the paper will appear in Foundations of Physic

Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions

The symmetry algebra of asymptotically flat spacetimes at null infinity in three dimensions is the semi-direct sum of the infinitesimal diffeomorphisms on the circle with an abelian ideal of supertranslations. The associated charge algebra is shown to admit a non trivial classical central extension of Virasoro type closely related to that of the anti-de Sitter case.Comment: 4 sign mistakes due to a change of conventions are corrected in section 2, none of the conclusions are affected, takes precedence over published version, including corrigendu

Asymptotic Symmetries in the Gauge Fixing Approach and the BMS Group

These notes are an introduction to asymptotic symmetries in gauge theories, with a focus on general relativity in four dimensions. We explain how to impose consistent sets of boundary conditions in the gauge fixing approach and how to derive the asymptotic symmetry parameters. The different procedures to obtain the associated charges are presented. As an illustration of these general concepts, the examples of four-dimensional general relativity in asymptotically (locally) (A)dS$_4$ and asymptotically flat spacetimes are covered. This enables us to discuss the different extensions of the Bondi-Metzner-Sachs-van der Burg (BMS) group and their relevance for holography, soft gravitons theorems, memory effects, and black hole information paradox. These notes are based on lectures given at the XV Modave Summer School in Mathematical Physics.Comment: 56 pages, 2 figures, published versio

Entropy of three-dimensional asymptotically flat cosmological solutions

The thermodynamics of three-dimensional asymptotically flat cosmological solutions that play the same role than the BTZ black holes in the anti-de Sitter case is derived and explained from holographic properties of flat space. It is shown to coincide with the flat-space limit of the thermodynamics of the inner black hole horizon on the one hand and the semi-classical approximation to the gravitational partition function associated to the entropy of the outer horizon on the other. This leads to the insight that it is the Massieu function that is universal in the sense that it can be computed at either horizon.Comment: 16 pages Latex file, v2: references added, cosmetic changes, v3: 1 reference adde

Most general flat space boundary conditions in three-dimensional Einstein gravity

We consider the most general asymptotically flat boundary conditions in three-dimensional Einstein gravity in the sense that we allow for the maximal number of independent free functions in the metric, leading to six towers of boundary charges and six associated chemical potentials. We find as associated asymptotic symmetry algebra an isl(2)_k current algebra. Restricting the charges and chemical potentials in various ways recovers previous cases, such as BMS_3, Heisenberg or Detournay-Riegler, all of which can be obtained as contractions of corresponding AdS_3 constructions. Finally, we show that a flat space contraction can induce an additional Carrollian contraction. As examples we provide two novel sets of boundary conditions for Carroll gravity.Comment: 23 pp, invited for CQG BMS Focus Issue edited by Geoffrey Compere, v2: added minor clarifications and ref

Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited

It is argued that the symmetry algebra of asymptotically flat spacetimes at null infinity in 4 dimensions should be taken as the semi-direct sum of supertranslations with infinitesimal local conformal transformations and not, as usually done, with the Lorentz algebra. As a consequence, two dimensional conformal field theory techniques will play as fundamental a role in this context of direct physical interest as they do in three dimensional anti-de Sitter gravity.Comment: 7 pages Latex file, references added, comments on Poincare algebra and angular momentum adde