Two-dimensional Dilaton Gravity Research Articles

STATIC AND NONSTATIC QUANTUM EFFECTS IN TWO-DIMENSIONAL DILATON GRAVITY

We study back-reaction effects in two-dimensional dilaton gravity. The back-reaction comes from an R2 term which is a part of the one-loop effective action arising from massive scalar field quantization in a certain approximation. The peculiarity of this term is that it does not contribute to the Hawking radiation of the classical black hole solution of the field equations. In the static case we examine the horizon and the physical singularity of the new black hole solutions. Studying the possibility of time dependence we see the generation of a new singularity. The particular solution found still has the structure of a black hole, indicating that nonthermal effects cannot lead, at least in this approximation, to black hole evaporation.

Gauge Symmetry of the Two-dimensional Dilaton Gravity Theory

Gauge Symmetry of the Two-dimensional Dilaton Gravity Theory

Classical and quantum cosmology in a model of two-dimensional dilaton gravity

Classical and quantum cosmology in a model of two-dimensional dilaton gravity

(Generalized) conformal quantum mechanics of 0-branes and two-dimensional dilaton gravity

We study the relation between the (generalized) conformal quantum mechanics of 0-branes and two-dimensional dilaton gravity. The two-dimensional actions obtained from the supergravity effective actions for the (dilatonic) 0-branes through the compactification on a sphere are related to known two-dimensional dilaton gravity models. The SL(2, R) symmetry of the (generalized) conformal quantum mechanics is realized within such two-dimensional models. The two-dimensional dilatonic gravity model derived from the non-dilatonic 0-brane action is related to the Liouville theory and therefore is conformal, whereas the two-dimensional model derived from the dilatonic 0-brane action does not have the conformal symmetry.

Two-dimensional dilaton gravity and spacetimes with finite curvature at the horizon away from the Hawking temperature

It is shown that static solutions with a finite curvature at the horizon may exist in dilaton gravity at temperatures $T\neq T_{H}$ (including T=0) where $T_{H} $is the Hawking one. Hawking radiation is absent and the state of a system represents thermal excitation over the Boulware vacuum. The horizon remains unattainable for a observer because of thermal divergences in the stress-energy of quantum fields there. However, the curvature at the horizon is finite, when measured from outside, since these divergences are compensated by those in gradients of a dilaton field. Spacetimes under consideration are geodesically incomplete and the coupling between dilaton and gravity diverges at the horizon, so we have ''singularity without singularity''.

Black hole thermodynamics and two-dimensional dilaton gravity theory

We relate various black hole solutions in the near-horizon region to black hole solutions in two-dimensional dilaton gravity theories in order to argue that the thermodynamics of black holes in $D>~4$ can be effectively described by the thermodynamics of black holes in two-dimensional dilaton gravity theories. We show that the Bekenstein-Hawking entropies of single-charged dilatonic black holes and dilatonic p branes with an arbitrary dilaton coupling parameter in arbitrary spacetime dimensions are exactly reproduced by the Bekenstein-Hawking entropy of the two-dimensional black hole in the associated two-dimensional dilaton gravity model. We comment that the thermodynamics of a nonextreme stringy four-dimensional black hole with four charges and a five-dimensional black hole with three charges may be effectively described by the thermodynamics of black hole solutions with a constant dilaton field in two-dimensional dilaton gravity theories.

HAWKING RADIATION IN THE DILATON GRAVITY WITH A NONMINIMALLY COUPLED SCALAR FIELD

We discuss the two-dimensional dilaton gravity with a scalar field as the source matter where the coupling with gravity is given, besides the minimal one, trough an external field. This coupling generalizes the conformal anomaly in the same way as those found in recent literature, but with a different motivation. The modification to the Hawking radiation is calculated explicitly and show an additional term that introduces a dependence on the (effective) mass of the black-hole.

Normalization of Killing vectors and energy conservation in two-dimensional gravity

We explicitly show that, in the context of a recently proposed two-dimensional dilaton gravity theory, energy conservation requires the ``natural'' Killing vector to have, asymptotically, an unusual normalization. The Hawking temperature ${T}_{H}$ is then calculated according to this prescription.

Dimensional reduction of 4D heterotic string black holes

We perform a spherical symmetric dimensional reduction $4\stackrel{\ensuremath{\rightarrow}}{d}2d$ of heterotic string theory. We find a class of two-dimensional (2D) dilaton gravity models that gives a general description of the near-horizon, near-extremal behavior of four-dimensional (4D) heterotic string black holes. We show that the duality group of the 4D theory is realized in two dimensions in terms of Weyl transformations of the metric. We use the 2D dilaton gravity theory to compute the statistical entropy of a near-extremal 4D, $a=1/\sqrt{3},$ black hole.

Wormhole as the end state of two-dimensional black hole evaporation

We present a specific two-dimensional dilaton gravity model in which a black hole evaporates leaving a wormhole at the end state. As the black hole formed by infalling matter in a initially static spacetime evaporates by emitting Hawking radiation, the black hole singularity that is initially hidden behind a timelike apparent horizon meets the shrinking horizon. At this intersection point, we imposed boundary conditions which require disappearance of the black hole singularity and generation of the exotic matter which is the source of the wormhole as the end state of the black hole. These, of course, preserve energy conservation and continuity of the metric.

Canonical and functional Schrödinger quantization of two-dimensional dilaton gravity

We discuss the relation between canonical and Schrödinger quantization of the CGHS model. We also discuss the situation when background charges are added to cancel the Virasoro anomaly. New physical states are found when the square of the background charges vanishes.

Geometrodynamical formulation of two-dimensional dilaton gravity

Two-dimensional matterless dilaton gravity with an arbitrary dilatonic potential can be discussed in a unitary way, both in the Lagrangian and canonical frameworks, by introducing suitable field redefinitions. The new fields are directly related to the original spacetime geometry and in the canonical picture they generalize the well-known geometrodynamical variables used in the discussion of the Schwarzschild black hole. So the model can be quantized using the techniques developed for the latter case. The resulting quantum theory exhibits the Birkhoff theorem at the quantum level.

One-loop corrections for a Schwarzschild black hole via 2D dilaton gravity

We study quantum corrections for the Schwarzshild black hole by considering it as a vacuum solution of a two-dimensional (2D) dilaton gravity theory obtained by spherical reduction of 4D gravity coupled with matter. We find perturbatively the vacuum solution for the standard one-loop effective action in the case of null-dust matter and in the case of minimally coupled scalar field. The corresponding state is in both cases a 2D Hartle-Hawking vacuum, and we evaluate the corresponding quantum corrections for the thermodynamic parameters of the black hole. We also find that the standard effective action does not allow boundary conditions corresponding to a 4D Hartle-Hawking vacuum state.

Exactly solvable models of two-dimensional dilaton gravity and quantum eternal black holes

New approach to exact solvability of dilaton gravity theories is suggested which appeals directly to structure of field equations. It is shown that black holes regular at the horizon are static and their metric is found explicitly. If a metric possesses singularities the whole spacetime can be divided into different sheets with one horizon on each sheet between neighboring singularities with a finite value of dilaton field (addition horizons may arise at infinite value of it), neighboring sheets being glued along the singularity. The position of singularities coincide with the values of dilaton in solutions with a constant dilaton field. Quantum corrections to the Hawking temperature vanish. For a wide subset of these models the relationship between the total energy and the total entropy of the quantum finite size system is the same as in the classical limit. For another subset the metric itself does not acquire quantum corrections. The present paper generalizes Solodukhin's results on the RST model in that instead of a particular model we deal with whole classes of them. Apart from this, the found models exhibit some qualitatively new properties which are absent in the RST model. The most important one is that there exist quantum black holes with geometry regular everywhere including infinity.

Solutions for Two-Dimensional Dilaton Gravity

In a recent paper Frolov, Hendy, and Larsen(1996) obtained a set of two nonlinear second-ordercoupled partial differential equations of 2D dilatongravity. They obtained a special solution assuming all the dependent variables were independent oftime. In the present work we reduce the above set ofequations to a simple form, from which we obtain a classof solutions that includes the solution of Frolov, Hendy, and Larsen as a special case.

Generalized two-dimensional dilaton gravity with matter fields

We extend the classical integrability of the CGHS model of two-dimensional (2D) gravity (Callan et al 1992 Phys. Rev. D 45 R1005) to a larger class of models, allowing the gravitational part of the action to depend more generally on the dilaton field and, simultaneously, adding fermion and ) gauge fields to the scalar matter. On the other hand, we provide the complete solution of the most general dilaton-dependent 2D gravity action coupled to chiral fermions. The latter analysis is generalized to a chiral fermion multiplet with a non-Abelian gauge symmetry as well as to the (anti-)self-dual sector of a scalar field f.

Two-dimensional dilaton gravity made compact

We show that the equations of motion of two-dimensional dilaton gravity conformally coupled to a scalar field can be reduced to a single nonlinear second-order partial differential equation when the coordinates are chosen to coincide with the two scalar fields, the matter field f and the dilaton , which are present in the theory. This result may help solve and understand two- and higher-dimensional classical and quantum gravity.

Two-dimensional dilaton gravity coupled to massless spinors

We derive exact solutions of two-dimensional dilaton gravity coupled to massless spinors for some particular choices of the dilatonic potential. For constant dilatonic potential the model turns out to be completely solvable and the general solution is found. For linear and exponential dilatonic potentials we present the class of exact solutions with a Killing vector.

2D extremal black holes as solitons

We discuss the relationship between two-dimensional (2D) dilaton gravity models and sine-Gordon-like field theories. We show that there is a one-to-one correspondence between the solutions of 2D dilaton gravity and the solutions of a (two fields) generalization of the sine-Gordon model. In particular, we find a connection between the soliton solutions of the generalized sine-Gordon model and extremal black hole solutions of 2D dilaton gravity. As a by-product of our calculations we find a easy way to generate cosmological solutions of 2D dilaton gravity.

IRREVERSIBLE TIME FLOW IN A TWO-DIMENSIONAL DILATON BLACK HOLE WITH MATTER

We show that an exact solution of two-dimensional dilaton gravity with matter discovered previously exhibits an irreversible temporal flow towards flat space with a vanishing cosmological constant. This time flow is induced by the back reaction of matter on the space–time geometry. We demonstrate that the system is not in equilibrium if the cosmological constant is nonzero, whereas the solution with zero cosmological constant is stable. The flow of the system towards this stable end point is derived from the renormalization-group flow of the Zamolodchikov function. This behavior is interpreted in terms of noncritical Liouville string, with the Liouville field identified as the target time.