7 research outputs found
Holography for the Lorentz Group Racah Coefficients
A known realization of the Lorentz group Racah coefficients is given by an
integral of a product of 6 ``propagators'' over 4 copies of the hyperbolic
space. These are ``bulk-to-bulk'' propagators in that they are functions of two
points in the hyperbolic space. It is known that the bulk-to-bulk propagator
can be constructed out of two bulk-to-boundary ones. We point out that there is
another way to obtain the same object. Namely, one can use two bulk-to-boundary
and one boundary-to-boundary propagator. Starting from this construction and
carrying out the bulk integrals we obtain a realization of the Racah
coefficients that is ``holographic'' in the sense that it only involves
boundary objects. This holographic realization admits a geometric
interpretation in terms of an ``extended'' tetrahedron.Comment: 12 pages, 2 figures; v2: minor changes; v3: "extended" tetrahedron
interpretation adde
Einstein black holes, free scalars and AdS/CFT correspondence
We investigate AdS/CFT correspondence for two families of Einstein black
holes in d > 3 dimensions, modelling the boundary CFT by a free conformal
scalar field and evaluating the boundary two-point function in the bulk
geodesic approximation. For the d > 3 counterpart of the nonrotating BTZ hole
and for its Z_2 quotient, the boundary state is thermal in the expected sense,
and its stress-energy reflects the properties of the bulk geometry and suggests
a novel definition for the mass of the hole. For the generalised
Schwarzschild-AdS hole with a flat horizon of topology R^{d-2}, the boundary
stress-energy has a thermal form with energy density proportional to the hole
ADM mass, but stress-energy corrections from compactified horizon dimensions
cannot be consistently included at least for d=5.Comment: 32 pages. LaTeX with amsfonts, amsmath, amssymb. (v2: References
added. v3: Geodesic horizon-crossing clarified in section 2; comparison with
quasilocal energy-momentum included in section 4.
Toward a Quantization of Null Dust Collapse
Spherically symmetric, null dust clouds, like their time-like counterparts,
may collapse classically into black holes or naked singularities depending on
their initial conditions. We consider the Hamiltonian dynamics of the collapse
of an arbitrary distribution of null dust, expressed in terms of the physical
radius, , the null coordinates, for a collapsing cloud or for an
expanding cloud, the mass function, , of the null matter, and their
conjugate momenta. This description is obtained from the ADM description by a
Kucha\v{r}-type canonical transformation. The constraints are linear in the
canonical momenta and Dirac's constraint quantization program is implemented.
Explicit solutions the constraints are obtained for both expanding and
contracting null dust clouds with arbitrary mass functions.Comment: 10 pages, 2 figures (eps), RevTeX4. The last two sections have been
revised and corrected. To appear in Phys. Rev.
Mass Quantization of the Schwarzschild Black Hole
We examine the Wheeler-DeWitt equaton for a static, eternal Schwarzschild
black hole in Kucha\v r-Brown variables and obtain its energy eigenstates.
Consistent solutions vanish in the exterior of the Kruskal manifold and are
non-vanishing only in the interior. The system is reminiscent of a particle in
a box. States of definite parity avoid the singular geometry by vanishing at
the origin. These definite parity states admit a discrete energy spectrum,
depending on one quantum number which determines the Arnowitt-Deser-Misner
(ADM) mass of the black hole according to a relation conjectured long ago by
Bekenstein, . If attention is restricted only to these
quantized energy states, a black hole is described not only by its mass but
also by its parity. States of indefinite parity do not admit a quantized mass
spectrum.Comment: Change in eq. (13). Factors of 4 cleaned up. Refs. adde
Eternal Black Holes in AdS
We propose a dual non-perturbative description for maximally extended
Schwarzschild Anti-de-Sitter spacetimes. The description involves two copies of
the conformal field theory associated to the AdS spacetime and an initial
entangled state. In this context we also discuss a version of the information
loss paradox and its resolution.Comment: v4: New section added on black holes with only one asymptotic
boundary, v5,6: More references adde
Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe
In three spacetime dimensions, general relativity drastically simplifies,
becoming a ``topological'' theory with no propagating local degrees of freedom.
Nevertheless, many of the difficult conceptual problems of quantizing gravity
are still present. In this review, I summarize the rather large body of work
that has gone towards quantizing (2+1)-dimensional vacuum gravity in the
setting of a spatially closed universe.Comment: 61 pages, draft of review for Living Reviews; comments, criticisms,
additions, missing references welcome; v2: minor changes, added reference