Person:

Strominger, Andrew

New chiral boundary conditions are found for quantum gravity with matter on (AdS_3). The associated asymptotic symmetry group is generated by a single right-moving U(1) Kac-Moody-Virasoro algebra with (c_R=\frac{3ℓ}{2G}). The Kac-Moody zero mode generates global left-moving translations and equals, for a BTZ black hole, the sum of the total mass and spin. The level is positive about the global vacuum and negative in the black hole sector, corresponding to ergosphere formation. Realizations arising in Chern-Simons gravity and string theory are analyzed. The new boundary conditions are shown to naturally arise for warped (AdS_3) in the limit that the warp parameter is taken to zero.

Classical two-dimensional Liouville gravity is often considered in conformal gauge which has a residual left and right Virasoro symmetry algebra. We consider an alternate, chiral, gauge which has a residual right Virasoro Kac-Moody algebra, and no left Virasoro algebra. The Kac-Moody zero mode is the left-moving energy. Dirac brackets of the constrained Hamiltonian theory are derived, and the residual symmetries are shown to be generated by integrals of the conserved chiral currents. The central charge and Kac-Moody level are computed. The possible existence of a corresponding quantum theory is discussed.

A D4-D0 black hole can be deconstructed into a bound state of D0 branes with a D6-D6 pair containing worldvolume fluxes. The exact spacetime solution is known and resembles a D0 accretion disk surrounding a D6-D6 core. We find a scaling limit in which the disk and core drop inside an AdS2 throat. Crossing this AdS2 throat and the D0 accretion disk into the core, we find a second scaling region describing the D6-D6 pair. It is shown that the M-theory lift of this region is AdS3 ×S2. Surprisingly, time translations in the far asymptotic region reduce to global, rather than Poincare, time translations in this core AdS3. We further find that the quantum mechanical ground state degeneracy reproduces the Bekenstein-Hawking entropy-area law.

We consider finite deformations of the p + 2-dimensional Schwarzschild geometry which obey the vacuum Einstein equation, preserve the mean curvature and induced conformal metric on a sphere a distance λ from the horizon and are regular on the future horizon. We show perturbatively that in the limit λ → 0 the deformations are given by solutions of the nonlinear incompressible Navier-Stokes equation on the p-sphere. This relation provides a link between global existence for p-dimensional incompressible Navier-Stokes fluids and a novel form of cosmic censorship in p + 2-dimensional general relativity.