Non-existence of a dilaton gravity action for the exact string black hole (original) (raw)

Dilatonic black holes in higher curvature string gravity

Physics Letters B, 1995

We give analytical arguments and demonstrate numerically the existence of black hole solutions of the 4D4D4D Effective Superstring Action in the presence of Gauss-Bonnet quadratic curvature terms. The solutions possess non-trivial dilaton hair. The hair, however, is of ``secondary" type", in the sense that the dilaton charge is expressed in terms of the black hole mass. Our solutions are not covered by the assumptions of existing proofs of the ``no-hair" theorem. We also find some alternative solutions with singular metric behaviour, but finite energy. The absence of naked singularities in this system is pointed out.

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.

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.

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.

Dilaton Black Holes, Naked Singularities and Strings

Europhysics Letters (EPL), 1994

We extend a previous calculation which treated Schwarzschild black hole horizons as quantum mechanical objects to the case of a charged, dilaton black hole. We show that for a unique value of the dilaton parameter a, which is determined by the condition of unitarity of the S matrix, black holes transform at the extremal limit into strings.

Dilatonic black holes in higher curvature string gravity. II. Linear stability

Physical Review D, 1997

We demonstrate linear stability of the dilatonic Black Holes appearing in a string-inspired higher-derivative gravity theory with a Gauss- Bonnet curvature-squared term. The proof is accomplished by mapping the system to a one-dimensional Schrodinger problem which admits no bound states. This result is important in that it constitutes a linearly stable example of a black hole that bypasses the `no-hair conjecture'. However, the dilaton hair is `secondary'in the sense that it is not accompanied by any new quantum number for the black hole solution.

String-corrected dilatonic black holes in d dimensions

Physical Review D, 2011

We solve the dilaton field equation in the background of a spherically symmetric black hole in bosonic or heterotic string theory with curvature-squared corrections in arbitrary d spacetime dimensions. We then apply this result to obtain a spherically symmetric black hole solution with dilatonic charge and curvature-squared corrections in bosonic or heterotic string theory compactified on a torus. For this black hole we obtain its free energy, entropy, temperature, specific heat and mass.

The gravitational field of string matter when the dilaton is massive

Physics Letters B, 1992

We study numerically the gravitational field of a star made of massive and neutral string states for the case in which the dilaton is massive. The solution exhibits very simple scaling properties in the dilaton mass. There is no horizon and the singularity is surrounded by a halo (the physical size of which is inversely proportional to the dilaton mass) where the scalar curvature is very large and proportional to the square of the dilaton mass.

Dilaton gravity and no-hair theorem in two dimensions

Physics Letters B, 1992

We study a general class of two-dimensional theories of the dilaton-gravity type inspired by string theory and show that they admit charged multiple-horizon black holes. These solutions are proved to satisfy scalar no-hair theorems.