71 research outputs found
Midisuperspace-Induced Corrections to the Wheeler De Witt Equation
We consider the midisuperspace of four dimensional spherically symmetric
metrics and the Kantowski-Sachs minisuperspace contained in it. We discuss the
quantization of the midisuperspace using the fact that the dimensionally
reduced Einstein Hilbert action becomes a scalar-tensor theory of gravity in
two dimensions. We show that the covariant regularization procedure in the
midisuperspace induces modifications into the minisuperspace Wheeler DeWitt
equation.Comment: 7 page
TWO DIMENSIONAL DILATON GRAVITY COUPLED TO AN ABELIAN GAUGE FIELD
The most general two-dimensional dilaton gravity theory coupled to an Abelian
gauge field is considered. It is shown that, up to spacetime diffeomorphisms
and gauge transformations, the field equations admit a two-parameter
family of distinct, static solutions.
For theories with black hole solutions, coordinate invariant expressions are
found for the energy, charge, surface gravity, Hawking temperature and entropy
of the black holes. The Hawking temperature is proportional to the surface
gravity as expected, and both vanish in the case of extremal black holes in the
generic theory. A Hamiltonian analysis of the general theory is performed, and
a complete set of (global) Dirac physical observables is obtained. The theory
is then quantized using the Dirac method in the WKB approximation. A connection
between the black hole entropy and the imaginary part of the WKB phase of the
Dirac quantum wave functional is found for arbitrary values of the mass and
charge. The imaginary part of the phase vanishes for extremal black
holes and for eternal, non-extremal Reissner-Nordstrom black holes.Comment: Minor revisions only. Some references have been added, and some
typographical errors correcte
Observables for Two-Dimensional Black Holes
We consider the most general dilaton gravity theory in 1+1 dimensions. By
suitably parametrizing the metric and scalar field we find a simple expression
that relates the energy of a generic solution to the magnitude of the
corresponding Killing vector. In theories that admit black hole solutions, this
relationship leads directly to an expression for the entropy ,
where is the value of the scalar field (in this parametrization) at
the event horizon. This result agrees with the one obtained using the more
general method of Wald. Finally, we point out an intriguing connection between
the black hole entropy and the imaginary part of the ``phase" of the exact
Dirac quantum wave functionals for the theory.Comment: 14 pages, late
Geometrodynamics of Schwarzschild Black Holes
The curvature coordinates of a Schwarz\-schild spacetime are turned
into canonical coordinates on the phase space of spherically
symmetric black holes. The entire dynamical content of the Hamiltonian theory
is reduced to the constraints requiring that the momenta vanish. What remains is a conjugate pair of canonical variables and
whose values are the same on every embedding. The coordinate is the
Schwarzschild mass, and the momentum the difference of parametrization
times at right and left infinities. The Dirac constraint quantization in the
new representation leads to the state functional which describes an unchanging superposition of black holes with different
masses. The new canonical variables may be employed in the study of collapsing
matter systems.Comment: 44 pages, Latex file, UU-REL-94/3/
Integrable models and degenerate horizons in two-dimensional gravity
We analyse an integrable model of two-dimensional gravity which can be
reduced to a pair of Liouville fields in conformal gauge. Its general solution
represents a pair of ``mirror'' black holes with the same temperature. The
ground state is a degenerate constant dilaton configuration similar to the
Nariai solution of the Schwarzschild-de Sitter case. The existence of
solutions and their relation with the solution given by the 2D
Birkhoff's theorem is then investigated in a more general context. We also
point out some interesting features of the semiclassical theory of our model
and the similarity with the behaviour of AdS black holes.Comment: Latex, 16 pages, 1 figur
Quantum Decay of Domain Walls in Cosmology II: Hamiltonian Approach
This paper studies the decay of a large, closed domain wall in a closed
universe. Such walls can form in the presence of a broken, discrete symmetry.
We study a novel process of quantum decay for such a wall, in which the vacuum
fluctuates from one discrete state to another throughout one half of the
universe, so that the wall decays into pure field energy. Equivalently, the
fluctuation can be thought of as the nucleation of a second closed domain wall
of zero size, followed by its growth by quantum tunnelling and its collision
with the first wall, annihilating both. We therefore study the 2-wall system
coupled to a spherically symmetric gravitational field. We derive a simple form
of the 2-wall action, use Dirac quantization, obtain the 2-wall wave function
for annihilation, find from it the barrier factor for this quantum tunneling,
and thereby get the decay probability. This is the second paper of a series.Comment: 27 pages LaTeX, using revtex and psfig. 3 figure
de Broglie-Bohm Interpretation for the Wave Function of Quantum Black Holes
We study the quantum theory of the spherically symmetric black holes. The
theory yields the wave function inside the apparent horizon, where the role of
time and space coordinates is interchanged. The de Broglie-Bohm interpretation
is applied to the wave function and then the trajectory picture on the
minisuperspace is introduced in the quantum as well as the semi-classical
region. Around the horizon large quantum fluctuations on the trajectories of
metrics and appear in our model, where the metrics are functions of
time variable and are expressed as . On the trajectories, the classical relation holds,
and the event horizon U=0 corresponds to the classical apparent horizon on
. In order to investigate the quantum fluctuation near the horizon, we
study a null ray on the dBB trajectory and compare it with the one in the
classical black hole geometry.Comment: 20 pages, Latex, 7 Postscript figure
Quantum gravity corrections to the Schwarzschild mass
Vacuum spherically symmetric Einstein gravity in dimensions can be
cast in a two-dimensional conformal nonlinear sigma model form by first
integrating on the -dimensional (hyper)sphere and then performing a
canonical transformation. The conformal sigma model is described by two fields
which are related to the Arnowitt-Deser-Misner mass and to the radius of the
-dimensional (hyper)sphere, respectively. By quantizing perturbatively
the theory we estimate the quantum corrections to the ADM mass of a black hole.Comment: 18 pages, 8 figures, LaTeX2e, uses epsfig package, accepted for
publication in Phys. Rev.
Graded Poisson-Sigma Models and Dilaton-Deformed 2D Supergravity Algebra
Fermionic extensions of generic 2d gravity theories obtained from the graded
Poisson-Sigma model (gPSM) approach show a large degree of ambiguity. In
addition, obstructions may reduce the allowed range of fields as given by the
bosonic theory, or even prohibit any extension in certain cases. In our present
work we relate the finite W-algebras inherent in the gPSM algebra of
constraints to algebras which can be interpreted as supergravities in the usual
sense (Neuveu-Schwarz or Ramond algebras resp.), deformed by the presence of
the dilaton field. With very straightforward and natural assumptions on them
--like demanding rigid supersymmetry in a certain flat limit, or linking the
anti-commutator of certain fermionic charges to the Hamiltonian constraint-- in
the ``genuine'' supergravity obtained in this way the ambiguities disappear, as
well as the obstructions referred to above. Thus all especially interesting
bosonic models (spherically reduced gravity, the Jackiw-Teitelboim model etc.)\
under these conditions possess a unique fermionic extension and are free from
new singularities. The superspace supergravity model of Howe is found as a
special case of this supergravity action. For this class of models the relation
between bosonic potential and prepotential does not introduce obstructions as
well.Comment: 22 pages, LaTeX, JHEP class. v3: Final version, to appear in JHE
Conformal anomaly for 2d and 4d dilaton coupled spinors
We study quantum dilaton coupled spinors in two and four dimensions. Making
classical transformation of metric, dilaton coupled spinor theory is
transformed to minimal spinor theory with another metric and in case of 4d
spinor also in the background of the non-trivial vector field. This gives the
possibility to calculate 2d and 4d dilaton dependent conformal (or Weyl)
anomaly in easy way. Anomaly induced effective action for such spinors is
derived. In case of 2d, the effective action reproduces, without any extra
terms, the term added by hands in the quantum correction for RST model, which
is exactly solvable. For 4d spinor the chiral anomaly which depends explicitly
from dilaton is also found. As some application we discuss SUSY Black Holes in
dilatonic supergravity with WZ type matter and Hawking radiation in the same
theory. As another application we investigate spherically reduced Einstein
gravity with 2d dilaton coupled fermion anomaly induced effective action and
show the existence of quantum corrected Schwarszchild-de Sitter (SdS) (Nariai)
BH with multiple horizon.Comment: LaTeX file, 15 page
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