General relativity becomes vastly simpler in three spacetime dimensions: all vacuum solutions have constant curvature, and the moduli space of can be almost completely characterized. As a result, this lower dimensional setting an ideal test bed for wide range approaches to quantum gravity, from reduced phase quantization covariant canonical path integral methods asymptotic "edge states." Here I review variety classical descriptions broad quantizations, with special attention implications...

I review the classical and quantum properties of (2 + 1)-dimensional black hole Bañados, Teitelboim Zanelli. This solution Einstein field equations in three spacetime dimensions shares many characteristics Kerr hole: it has an event horizon, inner ergosphere; occurs as endpoint gravitational collapse; exhibits mass inflation; a non-vanishing Hawking temperature interesting thermodynamic properties. At same time, its structure is simple enough to allow number exact computations, particularly...

On a manifold with boundary, the constraint algebra of general relativity may acquire central extension, which can be computed using covariant phase space techniques. When boundary is (local) Killing horizon, natural set conditions leads to Virasoro subalgebra calculable charge. Conformal field theory methods then used determine density states at boundary. I consider number cases---black holes, Rindler space, de Sitter Taub-NUT and Taub-Bolt spaces, dilaton gravity---and show that resulting...

The presence of a horizon breaks the gauge invariance (2+1)-dimensional general relativity, leading to appearance new physical states at horizon. I show that entropy black hole can be obtained as logarithm number these microscopic states.

In three spacetime dimensions, general relativity becomes a topological field theory, whose dynamics can be largely described holographically by two-dimensional conformal theory at the 'boundary' of spacetime. I review what is known about this reduction—mainly within context pure (2 + 1)-dimensional gravity—and discuss its implications for our understanding statistical mechanics and quantum black holes.

We discuss the quantum mechanics and thermodynamics of (2+1)-dimensional black hole, using both minisuperspace methods exact results from Chern-Simons theory. In particular, we evaluate first correction to hole entropy. show that dynamical variables arise possibility a deficit angle at (Euclidean) horizon, briefly speculate as how they may provide basis for statistical picture thermodynamics.

In view of the enormous difficulties we seem to face in quantizing general relativity, should perhaps consider possibility that gravity is a fundamentally classical interaction. Theoretical arguments against such mixed classical-quantum models are strong, but not conclusive, and question ultimately one for experiment. I review some work progress on experimental tests, exploiting nonlinearity coupling, could help settle this question.

We study topologically massive (2+1)-dimensional gravity with a negative cosmological constant. The masses of the linearized curvature excitations about AdS3 backgrounds are not only shifted from their flat background values but also, more surprisingly, split according to chirality. For all finite topological mass, we find single bulk degree freedom positive energy, and exhibit complete set normalizable, finite-energy wave packet solutions. This model can also be written as sum two...

The discovery in the early 1970s that black holes radiate as bodies has radically affected our understanding of general relativity, and offered us some hints about nature quantum gravity. In this paper, will review hole thermodynamics summarize many independent ways obtaining thermodynamic (perhaps) statistical mechanical properties holes. I then describe remaining puzzles, including microstates, problem universality, information loss paradox.

With the recent discovery that many aspects of black hole thermodynamics can be effectively reduced to problems in three spacetime dimensions, it has become increasingly important understand ``statistical mechanics'' (2+1)-dimensional Banados, Teitelboim, and Zanelli (BTZ). Several conformal field theoretic derivations BTZ entropy exist, but none is completely satisfactory, questions remain open: there no consensus as what fields provide relevant degrees freedom or where these excitations...

Views Icon Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Twitter Facebook Reddit LinkedIn Tools Reprints and Permissions Cite Search Site Citation Steven Carlip; Spontaneous Dimensional Reduction in Short‐Distance Quantum Gravity?. AIP Conference Proceedings 15 December 2009; 1196 (1): 72–80. https://doi.org/10.1063/1.3284402 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search...

We extend the discrete Regge action of causal dynamical triangulations to include versions curvature squared terms appearing in continuum (2+1)-dimensional projectable Horava-Lifshitz gravity. Focusing on an ensemble spacetimes whose spacelike hypersurfaces are 2-spheres, we employ Markov chain Monte Carlo simulations study path integral defined by this extended action. demonstrate existence known and novel macroscopic phases spacetime geometry, present preliminary evidence for consistency...

Near the horizon, obvious symmetries of a black hole spacetime-the horizon-preserving diffeomorphisms-are enhanced to larger symmetry group with three-dimensional Bondi-Metzner-Sachs algebra. Using dimensional reduction and covariant phase space techniques, I investigate this augmented show that it is strong enough determine entropy in any dimension.

Perhaps standard effective field theory arguments are right, and vacuum fluctuations really do generate a huge cosmological constant. I show that if one does not assume homogeneity an arrow of time at the Planck scale, very large class general relativistic initial data exhibit expansions, shears, curvatures enormous small scales, but quickly average to zero macroscopically. Subsequent evolution is more complex, argue quantum may preserve these properties. The resulting picture version...

Near an event horizon, the action of general relativity acquires a new asymptotic conformal symmetry. Using two-dimensional dilaton gravity as test case, I show that this symmetry results in chiral Virasoro algebra with calculable classical central charge, and Cardy's formula for density states reproduces Bekenstein-Hawking entropy. This result lends support to notion universal nature black hole entropy is controlled by near horizon.

The standard (Euclidean) action principle for the gravitational field implies that spacetimes with black hole topology, opening angle at horizon and area are canonical conjugates. It is shown bears same relation to time separation mass infinity. dependence of wave function on this new degree freedom governed by an extended Wheeler-DeWitt equation. Summing over all areas yields entropy.

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