108 research outputs found
Thermodynamics and Statistical Mechanics of Induced Liouville Gravity
In this paper we describe a Liouville gravity which is induced by a set of
quantum fields (constituents) and represents a two-dimensional analog of
Sakharov's induced gravity. The important feature of the considered theory is
the presence of massless constituents which are responsible for the appearance
of the induced Liouville field. The role of the massive constituents is only to
induce the cosmological constant. We consider the instanton solutions of the
Euclidean Liouville gravity with negative and zero cosmological constants, some
instantons being interpreted as two-dimensional anti-de Sitter black
holes. We study thermodynamics of all the solutions and conclude that their
entropy is completely determined by the statistical-mechanical entropy of the
massless constituents. This shows, in particular, that the constituents of the
induced gravity are the true degrees of freedom of black holes. Special
attention is also paid to the induced Liouville gravity with zero cosmological
constant on a torus. We demonstrate the equivalence of its thermodynamics to
the thermodynamics of BTZ black holes and comment on computations of the BTZ
black hole entropy.Comment: 22 pages, latex, no figure
Back Reaction of Hawking Radiation on Black Hole Geometry
We propose a model for the geometry of a dynamical spherical shell in which
the metric is asymptotically Schwarzschild, but deviates from Ricci-flatness in
a finite neighbourhood of the shell. Hence, the geometry corresponds to a
`hairy' black hole, with the hair originating on the shell. The metric is
regular for an infalling shell, but it bifurcates, leading to two disconnected
Schwarzschild-like spacetime geometries. The shell is interpreted as either
collapsing matter or as Hawking radiation, depending on whether or not the
shell is infalling or outgoing. In this model, the Hawking radiation results
from tunnelling between the two geometries. Using this model, the back reaction
correction from Hawking radiation is calculated.Comment: Latex file, 15 pages, 4 figures enclosed, uses eps
The Generalized Ricci Flow for 3D Manifolds with One Killing Vector
We consider 3D flow equations inspired by the renormalization group (RG)
equations of string theory with a three dimensional target space. By modifying
the flow equations to include a U(1) gauge field, and adding carefully chosen
De Turck terms, we are able to extend recent 2D results of Bakas to the case of
a 3D Riemannian metric with one Killing vector. In particular, we show that the
RG flow with De Turck terms can be reduced to two equations: the continual Toda
flow solved by Bakas, plus its linearizaton. We find exact solutions which flow
to homogeneous but not always isotropic geometries
Explicit Global Coordinates for Schwarzschild and Reissner-Nordstroem
We construct coordinate systems that cover all of the Reissner-Nordstroem
solution with m>|q| and m=|q|, respectively. This is possible by means of
elementary analytical functions. The limit of vanishing charge q provides an
alternative to Kruskal which, to our mind, is more explicit and simpler. The
main tool for finding these global charts is the description of highly
symmetrical metrics by two-dimensional actions. Careful gauge fixing yields
global representatives of the two-dimensional theory that can be rewritten
easily as the corresponding four-dimensional line elements.Comment: 12 pages, 3 Postscript figures, sign error in Eq. (37) and below
corrected, references and Note added; to appear in Class. Quantum Gra
Quantum Theory of Black Holes
A solvable 2-dimensional conformally invariant midi-superspace model for
black holes is obtained by imposing spherical symmetry in 4-dimensional
conformally invariant Einstein gravity. The Wheeler-DeWitt equation for the
theory is solved exactly to obtain the unique quantum wave functional for an
isolated black hole with fixed mass. By suitably relaxing the boundary
conditions, a non-perturbative ansatz is obtained for the wave functional of a
black hole interacting with its surroundings.Comment: Plain-TeX, 13 pages, no figures, WIN-92-9, UNB Tech. Rep. 92-0
The Geometrodynamics of Sine-Gordon Solitons
The relationship between N-soliton solutions to the Euclidean sine-Gordon
equation and Lorentzian black holes in Jackiw-Teitelboim dilaton gravity is
investigated, with emphasis on the important role played by the dilaton in
determining the black hole geometry. We show how an N-soliton solution can be
used to construct ``sine-Gordon'' coordinates for a black hole of mass M, and
construct the transformation to more standard ``Schwarzchild-like''
coordinates. For N=1 and 2, we find explicit closed form solutions to the
dilaton equations of motion in soliton coordinates, and find the relationship
between the soliton parameters and the black hole mass. Remarkably, the black
hole mass is non-negative for arbitrary soliton parameters. In the one-soliton
case the coordinates are shown to cover smoothly a region containing the whole
interior of the black hole as well as a finite neighbourhood outside the
horizon. A Hamiltonian analysis is performed for slicings that approach the
soliton coordinates on the interior, and it is shown that there is no boundary
contribution from the interior. Finally we speculate on the sine-Gordon
solitonic origin of black hole statistical mechanics.Comment: Latex, uses epsf, 30 pages, 6 figures include
Gravitation and Cosmology in Generalized (1+1)-dimensional dilaton gravity
The actions of the ``'' and string-inspired theories of gravity in (1+1)
dimensions are generalized into one single action which is characterized by two
functions. We discuss differing interpretations of the matter stress-energy
tensor, and show how two such different interpretations can yield two different
sets of field equations from this action. The weak-field approximation,
post-Newtonian expansion, hydrostatic equilibrium state of star and
two-dimensional cosmology are studied separately by using the two sets of field
equations. Some properties in the ``'' and string-inspired theories are
shown to be generic in the theory induced by the generalized action.Comment: 34 page
Quantum Structure of Space Near a Black Hole Horizon
We describe a midi-superspace quantization scheme for generic single horizon
black holes in which only the spatial diffeomorphisms are fixed. The remaining
Hamiltonian constraint yields an infinite set of decoupled eigenvalue
equations: one at each spatial point. The corresponding operator at each point
is the product of the outgoing and ingoing null convergences, and describes the
scale invariant quantum mechanics of a particle moving in an attractive
potential. The variable that is analoguous to particle position is the
square root of the conformal mode of the metric. We quantize the theory via
Bohr quantization, which by construction turns the Hamiltonian constraint
eigenvalue equation into a finite difference equation. The resulting spectrum
gives rise to a discrete spatial topology exterior to the horizon. The spectrum
approaches the continuum in the asymptotic region.Comment: References added and typos corrected. 21 pages, 1 figur
Exact Dirac Quantization of All 2-D Dilaton Gravity Theories
The most general dilaton gravity theory in 2 spacetime dimensions is
considered. A Hamiltonian analysis is performed and the reduced phase space,
which is two dimensional, is explicitly constructed in a suitable
parametrization of the fields. The theory is then quantized via the Dirac
method in a functional Schrodinger representation. The quantum constraints are
solved exactly to yield the (spatial) diffeomorphism invariant quantum wave
functional for all theories considered. This wave function depends explicitly
on the (single) configuration space coordinate as well as on the imbedding of
space into spacetime (i.e. on the choice of time).Comment: 11 pages, LateX, (Equations (36) and (37) have been corrected and the
discussion of them modified.
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