18 research outputs found
Global Charges in Chern-Simons theory and the 2+1 black hole
We use the Regge-Teitelboim method to treat surface integrals in gauge
theories to find global charges in Chern-Simons theory. We derive the affine
and Virasoro generators as global charges associated with symmetries of the
boundary. The role of boundary conditions is clarified. We prove that for
diffeomorphisms that do not preserve the boundary there is a classical
contribution to the central charge in the Virasoro algebra. The example of
anti-de Sitter 2+1 gravity is considered in detail.Comment: Revtex, no figures, 26 pages. Important changes introduced. One
section added
Black Hole Entropy and the Dimensional Continuation of the Gauss-Bonnet Theorem
The Euclidean black hole has topology . It is
shown that -in Einstein's theory- the deficit angle of a cusp at any point in
and the area of the are canonical conjugates. The
black hole entropy emerges as the Euler class of a small disk centered at the
horizon multiplied by the area of the there.These results are
obtained through dimensional continuation of the Gauss-Bonnet theorem. The
extension to the most general action yielding second order field equations for
the metric in any spacetime dimension is given.Comment: 7 pages, RevTe
Aspects of Black Hole Quantum Mechanics and Thermodynamics in 2+1 Dimensions
We discuss the quantum mechanics and thermodynamics of the (2+1)-dimensional
black hole, using both minisuperspace methods and exact results from
Chern-Simons theory. In particular, we evaluate the first quantum correction to
the black hole entropy. We show that the dynamical variables of the black hole
arise from the possibility of a deficit angle at the (Euclidean) horizon, and
briefly speculate as to how they may provide a basis for a statistical picture
of black hole thermodynamics.Comment: 20 pages and 2 figures, LaTeX, IASSNS-HEP-94/34 and UCD-94-1
Supersymmetry of the 2+1 black holes
The supersymmetry properties of the asymptotically anti-de Sitter black holes
of Einstein theory in 2+1 dimensions are investigated. It is shown that (i) the
zero mass black hole has two exact super- symmetries; (ii) extreme
black holes with have only one; and (iii) generic black holes do
not have any. It is also argued that the zero mass hole is the ground state of
(1,1)-adS supergravity with periodic (``Ramond") boundary conditions on the
spinor fields.Comment: 9 pages LaTeX file, ULB-PMIF-93/0
The Statistical Mechanics of the (2+1)-Dimensional Black Hole
The presence of a horizon breaks the gauge invariance of (2+1)-dimensional
general relativity, leading to the appearance of new physical states at the
horizon. I show that the entropy of the (2+1)-dimensional black hole can be
obtained as the logarithm of the number of these microscopic states.Comment: 12 pages, UCD-94-32 and NI-9401
A comparison of Noether charge and Euclidean methods for Computing the Entropy of Stationary Black Holes
The entropy of stationary black holes has recently been calculated by a
number of different approaches. Here we compare the Noether charge approach
(defined for any diffeomorphism invariant Lagrangian theory) with various
Euclidean methods, specifically, (i) the microcanonical ensemble approach of
Brown and York, (ii) the closely related approach of Ba\~nados, Teitelboim, and
Zanelli which ultimately expresses black hole entropy in terms of the Hilbert
action surface term, (iii) another formula of Ba\~nados, Teitelboim and Zanelli
(also used by Susskind and Uglum) which views black hole entropy as conjugate
to a conical deficit angle, and (iv) the pair creation approach of Garfinkle,
Giddings, and Strominger. All of these approaches have a more restrictive
domain of applicability than the Noether charge approach. Specifically,
approaches (i) and (ii) appear to be restricted to a class of theories
satisfying certain properties listed in section 2; approach (iii) appears to
require the Lagrangian density to be linear in the curvature; and approach (iv)
requires the existence of suitable instanton solutions. However, we show that
within their domains of applicability, all of these approaches yield results in
agreement with the Noether charge approach. In the course of our analysis, we
generalize the definition of Brown and York's quasilocal energy to a much more
general class of diffeomorphism invariant, Lagrangian theories of gravity. In
an appendix, we show that in an arbitrary diffeomorphism invariant theory of
gravity, the ``volume term" in the ``off-shell" Hamiltonian associated with a
time evolution vector field always can be expressed as the spatial
integral of , where are the constraints
associated with the diffeomorphism invariance.Comment: 29 pages (double-spaced) late
Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
We consider a general, classical theory of gravity with arbitrary matter
fields in dimensions, arising from a diffeomorphism invariant Lagrangian,
\bL. We first show that \bL always can be written in a ``manifestly
covariant" form. We then show that the symplectic potential current
-form, , and the symplectic current -form, \om, for the
theory always can be globally defined in a covariant manner. Associated with
any infinitesimal diffeomorphism is a Noether current -form, \bJ, and
corresponding Noether charge -form, \bQ. We derive a general
``decomposition formula" for \bQ. Using this formula for the Noether charge,
we prove that the first law of black hole mechanics holds for arbitrary
perturbations of a stationary black hole. (For higher derivative theories,
previous arguments had established this law only for stationary perturbations.)
Finally, we propose a local, geometrical prescription for the entropy,
, of a dynamical black hole. This prescription agrees with the Noether
charge formula for stationary black holes and their perturbations, and is
independent of all ambiguities associated with the choices of \bL, , and
\bQ. However, the issue of whether this dynamical entropy in general obeys a
``second law" of black hole mechanics remains open. In an appendix, we apply
some of our results to theories with a nondynamical metric and also briefly
develop the theory of stress-energy pseudotensors.Comment: 30 pages, LaTe
Mass Spectrum of Strings in Anti de Sitter Spacetime
We perform string quantization in anti de Sitter (AdS) spacetime. The string
motion is stable, oscillatory in time with real frequencies and the string size and energy are bounded. The
string fluctuations around the center of mass are well behaved. We find the
mass formula which is also well behaved in all regimes. There is an {\it
infinite} number of states with arbitrarily high mass in AdS (in de Sitter (dS)
there is a {\it finite} number of states only). The critical dimension at which
the graviton appears is as in de Sitter space. A cosmological constant
(whatever its sign) introduces a {\it fine structure} effect
(splitting of levels) in the mass spectrum at all states beyond the graviton.
The high mass spectrum changes drastically with respect to flat Minkowski
spacetime. For {\it
independent} of and the level spacing {\it grows} with the
eigenvalue of the number operator, The density of states grows
like \mbox{Exp}[(m/\sqrt{\mid\Lambda\mid}\;)^{1/2}] (instead of
\rho(m)\sim\mbox{Exp}[m\sqrt{\alpha'}] as in Minkowski space), thus {\it
discarding} the existence of a critical string temperature.
For the sake of completeness, we also study the quantum strings in the black
string background, where strings behave, in many respects, as in the ordinary
black hole backgrounds. The mass spectrum is equal to the mass spectrum in flat
Minkowski space.Comment: 31 pages, Latex, DEMIRM-Paris-9404
Critical Behavior of Dimensionally Continued Black Holes
The critical behavior of black holes in even and odd dimensional spacetimes
is studied based on Ba\~nados-Teitelboim-Zanelli (BTZ) dimensionally continued
black holes. In even dimensions it is found that asymptotically flat and anti
de-Sitter Reissner-Nordstr\"om black holes present up to two second order phase
transitions. The case of asymptotically anti-de-Sitter Schwarzschild black
holes present only one critical transition and a minimum of temperature, which
occurs at the transition. Finally, it is shown that phase transitions are
absent in odd dimensions.Comment: 21 pages in Latex format, no figures, vastly improved version to
appear in Phys. Rev.
One-loop Renormalization of Black Hole Entropy Due to Non-minimally Coupled Matter
The quantum entanglement entropy of an eternal black hole is studied. We
argue that the relevant Euclidean path integral is taken over fields defined on
-fold covering of the black hole instanton. The statement that
divergences of the entropy are renormalized by renormalization of gravitational
couplings in the effective action is proved for non-minimally coupled scalar
matter. The relationship of entanglement and thermodynamical entropies is
discussed.Comment: 17 pages, latex, no figure