Two-dimensional Dilaton Gravity Model Research Articles

2D black holes, conformal vacua and CFTs on the cylinder

We investigate two-dimensional dilaton gravity models with a power-law dilaton potential, whose black hole solutions contain, among others, the dimensional reduction of the Schwarzschild black hole, the anti-de Sitter black hole and Rindler spacetime. We show that the ground state of these models satisfies simple transformation laws under the SL (2, R ) conformal group. We use these transformation laws to explain the scaling behavior of the thermodynamical parameters of the black hole and the nonextensivity of the thermodynamical system. The black hole thermodynamical behavior, in particular its entropy, is reproduced by a mapping into a two-dimensional conformal field theory on the cylinder.

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.

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.

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.

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.

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.

Free fields via canonical transformations of matter-coupled two-dimensional dilaton gravity models

It is shown that the (1+1)-dimensional matter-coupled Jackiw-Teitelboim model and the model with an exponential potential can be converted by means of appropriate canonical transformations into a theory of free fields with an indefinite metric. This makes it possible to consistently impose all the Virasoro constraints in the functional Schr\"odinger representation, thus generalizing recent results on the CGHS theory.

Solvable model of two-dimensional dilaton gravity coupled to a massless scalar field

We present a solvable model of two-dimensional dilaton-gravity coupled to a massless scalar field. We locally integrate the field equations and briefly discuss the properties of the solutions. For a particular choice of the coupling between the dilaton and the scalar field the model can be interpreted as the two-dimensional effective theory of $2+1$ cylindrical gravity minimally coupled to a massless scalar field.

Exact solutions in two-dimensional string cosmology with back reaction

We present analytic cosmological solutions in a model of two-dimensional dilaton gravity with back reaction. One of these solutions exhibits a graceful exit from the inflationary to the FRW phase and is nonsingular everywhere. A duality related second solution is found to exist only in the ``pre-big-bang'' epoch and is singular at $\tau = 0$. In either case back reaction is shown to play a crucial role in determining the specific nature of these geometries.

Loop corrections in the spectrum of two-dimensional Hawking radiation

We determine the one- and two-loop backreaction corrections in the spectrum of the Hawking radiation for the Callan - Giddings - Harvey - Strominger (CGHS) model of two-dimensional dilaton gravity by evaluating the Bogoliubov coefficients for a massless scalar field propagating on the corresponding backgrounds. Since the backreaction can induce a small shift in the position of the classical horizon, we find that a positive shift leads to a non-Planckian late-time spectrum, while a null or a negative shift leads to a Planckian late-time spectrum in the leading-order stationary-point approximation. In the one-loop case there are no corrections to the classical Hawking temperature, while in the two-loop case the temperature is three times greater than the classical value. We argue that these results are consistent with the behaviour of the Hawking flux obtained from the operator quantization only for times which are not too late, in accordance with the limits of validity of the semiclassical approximation.

The two-dimensional analogue of the Reissner - Nordström solution

A two-dimensional dilaton gravity model, whose static solutions have the same features as the Reissner - Nordström solutions, is obtained from the dimensional reduction of a four-dimensional dilaton gravity theory invariant under duality transformations. The black-hole solutions of the two-dimensional model and their relationship to those of the four-dimensional theory are discussed.

Soluble models in two-dimensional dilaton gravity.

A one-parameter class of simple models of two-dimensional dilaton gravity, which can be exactly solved including back-reaction effects, is investigated at both classical and quantum levels. This family contains the RST model as a special case, and it continuously interpolates between models having a flat (Rindler) geometry and a constant curvature metric with a non-trivial dilaton field. The processes of formation of black hole singularities from collapsing matter and Hawking evaporation are considered in detail. Various physical aspects of these geometries are discussed, including the cosmological interpretation.

Black holes and gravitational effects in two-dimensional dilaton gravity.

We consider the model of two-dimensional dilaton gravity inspired by string theory modified by the inclusion of an additional term. We solve the model exactly in a Schwarzschild-like gauge to obtain a black hole solution. We also examine the post-Newtonian and the weak-field approximations as well as stellar structure in the model.

Trace anomaly and the Hawking effect in generic two-dimensional dilaton gravity theories

Black hole solutions in the context of a generic matter-coupled two-dimensional dilaton gravity theory are discussed both at the classical and semiclassical level. Starting from general assumptions, a criterion for the existence of black holes is given. The relationship between the conformal anomaly and Hawking radiation is extended to a broad class of two-dimensional dilaton gravity models. A general and simple formula relating the magnitude of the Hawking effect to the dilaton potential evaluated on the horizon is derived. \textcopyright{} 1996 The American Physical Society.

Quantization of the reduced phase space of two-dimensional dilaton gravity.

We study some two-dimensional dilaton gravity models using the formal theory of partial differential equations. This allows us to prove that the reduced phase space is two-dimensional without an explicit construction. By using a convenient (static) gauge we reduce the theory to coupled \ode s and we are able to derive for some potentials of interest closed-form solutions. We use an effective (particle) Lagrangian for the reduced field equations in order to quantize the system in a finite-dimensional setting leading to an exact partial differential Wheeler-DeWitt equation instead of a functional one. A WKB approximation for some quantum states is computed and compared with the classical Hamilton-Jacobi theory. The effect of minimally coupled matter is examined.

On the conformal equivalence between 2D black holes and Rindler spacetime

We study a two-dimensional dilaton gravity model related by a conformal transformation of the metric to the Callan-Giddings-Harvey-Strominger model. We find that most of the features and problems of the latter can be simply understood in terms of the classical and semiclassical dynamics of accelerated observers in two-dimensional Minkowski space.

Black hole formation by sine-Gordon solitons in two-dimensional dilaton gravity.

The CGHS model of two-dimensional dilaton gravity coupled to a sine-Gordon matter field is considered. The theory is exactly solvable classically, and the solutions of kink- and two-kink-type solitons are studied in connection with black hole formation.

Quantum cosmology of generalized two-dimensional dilaton-gravity models.

The quantum cosmology of two-dimensional dilaton-gravity models is investigated. A class of models is mapped onto the constrained oscillator-ghost-oscillator model. A number of exact and approximate solutions to the corresponding Wheeler-DeWitt equation are presented. A wider class of minisuperspace models that can be solved in this fashion is identified. Supersymmetric extensions to the induced gravity theory and the bosonic string theory are then considered and closed-form solutions to the associated quantum constraints are derived. The possibility of applying the third-quantization procedure to two-dimensional dilaton gravity is briefly discussed.