48 research outputs found
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.
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
Exact Physical Black Hole States in Generic 2-D Dilaton Gravity
The quantum mechanics of black holes in generic 2-D dilaton gravity is
considered. The Hamiltonian surface terms are derived for boundary conditions
corresponding to an eternal black hole with slices on the interior ending on
the horizon bifurcation point. The quantum Dirac constraints are solved exactly
for these boundary conditions to yield physical eigenstates of the energy
operator. The solutions are obtained in terms of geometrical phase space
variables that were originally used by Cangemi, Jackiw and Zwiebach in the
context of string inspired dilaton gravity. The spectrum is continuous in the
Lorentzian sector, but in the Euclidean sector the thermodynamic entropy must
be where is an integer. The general class of models considered
contains as special cases string inspired dilaton gravity, Jackiw-Teitelboim
gravity and spherically symmetry gravity.Comment: 11 pages, Revte
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
Hamiltonian Thermodynamics of Charged Black Holes
We consider the most general diffeomorphism invariant action in 1+1 spacetime
dimensions that contains a metric, dilaton and Abelian gauge field, and has at
most second derivatives of the fields. Our action contains a topological term
(linear in the Abelian field strength) that has not been considered in previous
work. We impose boundary conditions appropriate for a charged black hole
confined to a region bounded by a surface of fixed dilaton field and
temperature. By making some simplifying assumptions about the quantum theory,
the Hamiltonian partition function is obtained. This partition function is
analyzed in some detail for the Reissner-Nordstrom black hole and for the
rotating BTZ black hole.Comment: 30 pages, Latex, 1 figur
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
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
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 Corrections to the Thermodynamics of Charged 2-D Black Holes
We consider one-loop quantum corrections to the thermodynamics of a black
hole in generic 2-dimensional dilaton gravity. The classical action is the most
general diffeomorphism invariant action in 1+1 space-time dimensions that
contains a metric, dilaton, and Abelian gauge field, and having at most second
derivatives of the fields. Quantum corrections are introduced by considering
the effect of matter fields conformally coupled to the metric and non-minimally
coupled to the dilaton. Back reaction of the matter fields (via non-vanishing
trace conformal anomaly) leads to quantum corrections to the black hole
geometry. Quantum corrections also lead to modifications in the gravitational
action and hence in expressions for thermodynamic quantities. One-loop
corrections to both geometry and thermodynamics (energy, entropy) are
calculated for the generic dilaton theory. This formalism is applied to a
charged black hole in spherically symmetric gravity and to a rotating BTZ black
hole.Comment: 36 pages, Latex The calculation has been extended to include general
matter-dilaton coupling. Several references have been adde