Conservation laws and two-dimensional black holes in dilaton gravity (original) (raw)

Exact black hole and cosmological solutions in a two-dimensional dilaton-spectator theory of gravity

Classical and Quantum Gravity, 1995

Exact black hole and cosmological solutions are obtained for a special two-dimensional dilaton-spectator (φ − ψ) theory of gravity. We show how in this context any desired spacetime behaviour can be determined by an appropriate choice of a dilaton potential function V (φ) and a "coupling function" l(φ) in the action. We illustrate several black hole solutions as examples. In particular, asymptotically flat double-and multiple-horizon black hole solutions are obtained. One solution bears an interesting resemblance to the 2D string-theoretic black hole and contains the same thermodynamic properties; another resembles the 4D Reissner-Nordstrom solution. We find two characteristic features of all the black hole solutions. First the coupling constants in l(φ) must be set equal to constants of integration (typically the mass). Second, the spectator field ψ and its derivative ψ ′ both diverge at any event horizon. A test particle with "spectator charge" (i.e. one coupled either to ψ or ψ ′), will therefore encounter an infinite tidal force at the horizon or an "infinite potential barrier" located outside the horizon respectively. We also compute the Hawking temperature and entropy for our solutions. In 2D F RW cosmology, two nonsingular solutions which resemble two exact solutions in 4D string-motivated cosmology are obtained. In addition, we construct a singular model which describes the 4D standard non-inflationary big bang cosmology (big − bang → radiation → dust). Motivated by the similarities between 2D and 4D gravitational field equations in F RW cosmology, we briefly discuss a special 4D dilaton-spectator action constructed from the bosonic part of the low energy heterotic string action and get an exact solution which contains dust and radiation behaviour.

Black holes of a general two-dimensional dilaton gravity theory

Physical Review D, 1994

A general dilaton gravity theory in 1+1 spacetime dimensions with a cosmological constant λ and a new dimensionless parameter ω, contains as special cases the constant curvature theory of Teitelboim and Jackiw, the theory equivalent to vacuum planar General Relativity, the first order string theory, and a two-dimensional purely geometrical theory. The equations of this general two-dimensional theory admit several different black holes with various types of singularities. The singularities can be spacelike, timelike or null, and there are even cases without singularities. Evaluation of the ADM mass, as a charge density integral, is possible in some situations, by carefully subtrating the black hole solution from the corresponding linear dilaton at infinity.

On thermodynamics of 2D black holes in brane inflationary potentials

International Journal of Geometric Methods in Modern Physics, 2014

Inspired from the inflation brane world cosmology, we study the thermodynamics of a black hole solution in two dimensional dilaton gravity with an arctangent potential background. We first derive the two dimensional black hole geometry, then we examine its asymptotic behaviors. More precisely, we find that such behaviors exhibit properties appearing in some known cases including the Anti de Sitter and the Schwarzchild black holes. Using the complex path method, we compute the Hawking radiation. The entropy function can be related to the value of the potential at the horizon.

Thermodynamics of Two-Dimensional Black Holes

Modern Physics Letters A, 1992

We explore the thermodynamics of a general class of two-dimensional dilatonic black holes. A simple prescription is given that allows us to compute the mass, entropy and thermodynamic potentials, with results in agreement with those obtained by other methods, when available.

Black Holes and Nonperturbative Canonical 2D Dilaton Gravity

We investigate nonperturbative canonical quantization of two dimensional dilaton gravity theories with an emphasis on the CGHS model. We use an approach where a canonical transformation is constructed such that the constraints take a quadratic form. The required canonical transformation is obtained by using a method based on the Bäcklund transformation from the Liouville theory. We quantize dilaton gravity in terms of the new variables, where it takes a form of a bosonic string theory with background charges. Unitarity is then established by going into a light-cone gauge. As a direct consequence, black holes in this theory do not violate unitarity, and there is no information loss. We argue that the information escapes during the evaporation process. We also discuss the implications of this quantization scheme for the quantum fate of real black holes. The main conclusion is that black holes do not have to violate quantum mechanics.

Two-Dimensional Dilaton Black Holes

Proceedings of the 6th Canadian Conference on General Relativity and Relativistic Astrophysics, 1997

The two-dimensional CGHS model provides an interesting toymodel for the study of black hole evaporation. For this model, a quantum effective action, which incorporates Hawking radiation and backreaction, can be explicitly constructed. In this paper, we study a generalization of this effective action. In our extended model, it is possible to remove certain curvature singularities arising for the original theory. We also find that the flux of Hawking radiation is identical to that encountered in other two-dimensional models.

Unified approach to solvable models of dilaton gravity in two dimensions based on symmetry

Physical Review D, 1995

A large class of solvable models of dilaton gravity in two space-time dimensions, capable of describing black hole geometry, are analyzed in a unified way as non-linear sigma models possessing a special symmetry. This symmetry, which can be neatly formulated in the target-space-covariant manner, allows one to decompose the non-linearly interacting dilaton-gravity system into a free field and a field satisfying the Liouville equation with in general non-vanishing cosmological term. In this formulation, all the existent models are shown to fall into the category with vanishing cosmological constant. General analysis of the space-time structure induced by a matter shock wave is performed and new models, with and without the cosmological term, are discussed.

Back reaction effects in two-dimensional dilaton gravity

Physical Review D, 1996

In this work we find static black hole solutions in the context of the twodimensional dilaton gravity, which is modified by the addition of an R 2 term. This term arises from the one-loop effective action of a massive scalar field in its large mass approximation. The basic feature of this term is that it does not contribute to the Hawking radiation of the classical black hole backgrounds of the model. From this point of view a class of the solutions derived are interpreted as describing backreaction effects. In particular it is argued that evolution of a black hole via non-thermal signals is possible. Nevertheless this evolution seems to be 'soft', in the sence that it does not lead to the evaporation of a black hole, leaving the Hawking radiation as the dominant mechanism for this process.

On black holes in the theory of dilatonic gravity coupled to a scalar field

Physics Letters B, 1995

Taking advantage of the representation of dilatonic gravity with the R 2-term under the form of low-derivative dilatonic gravity coupled to an additonal scalar, we construct a general renormalizable model motivated by this theory. Exact black hole solutions are found for some specic versions of the model, and their thermodynamical properties are described in detail. In particular, their horizons and temperatures are calculated. Finally, the corresponding one-loop eective action is obtained in the conformal gauge, and a number of its properties |including the construction of one-loop nite models| are briey described.