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 $U(1)$ 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 $U(1)$ 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 $S=2\pi \tau_0/G$, where $\tau_0$ 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

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 $\phi=const.$ 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$_2$ black holes.Comment: Latex, 16 pages, 1 figur

Edge States and Entropy of 2d Black Holes

In several recent publications Carlip, as well as Balachandran, Chandar and Momen, have proposed a statistical mechanical interpretation for black hole entropy in terms of ``would be gauge'' degrees of freedom that become dynamical on the boundary to spacetime. After critically discussing several routes for deriving a boundary action, we examine their hypothesis in the context of generic 2-D dilaton gravity. We first calculate the corresponding statistical mechanical entropy of black holes in 1+1 deSitter gravity, which has a gauge theory formulation as a BF-theory. Then we generalize the method to dilaton gravity theories that do not have a (standard) gauge theory formulation. This is facilitated greatly by the Poisson-Sigma-model formulation of these theories. It turns out that the phase space of the boundary particles coincides precisely with a symplectic leaf of the Poisson manifold that enters as target space of the Sigma-model. Despite this qualitatively appealing picture, the quantitative results are discouraging: In most of the cases the symplectic leaves are non-compact and the number of microstates yields a meaningless infinity. In those cases where the particle phase space is compact - such as, e.g., in the Euclidean deSitter theory - the edge state degeneracy is finite, but generically it is far too small to account for the semiclassical Bekenstein-Hawking entropy.Comment: 36 pages, Late

A Non-Singular Black Hole

We present a completely integrable deformation of the CGHS dilaton gravity model in two dimensions. The solution is a singularity free black hole that at large distances asymptoticaly joins to the CGHS solution.Comment: 11 pages, 1 figure, Latex 2

Dirac Constraint Quantization of a Dilatonic Model of Gravitational Collapse

We present an anomaly-free Dirac constraint quantization of the string-inspired dilatonic gravity (the CGHS model) in an open 2-dimensional spacetime. We show that the quantum theory has the same degrees of freedom as the classical theory; namely, all the modes of the scalar field on an auxiliary flat background, supplemented by a single additional variable corresponding to the primordial component of the black hole mass. The functional Heisenberg equations of motion for these dynamical variables and their canonical conjugates are linear, and they have exactly the same form as the corresponding classical equations. A canonical transformation brings us back to the physical geometry and induces its quantization.Comment: 37 pages, LATEX, no figures, submitted to Physical Review

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.Comment: 12 pages, LaTex, no figures, typos correcte

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 thermodynamics of black holes in D>=4 can be effectively described by 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 thermodynamics of non-extreme stringy four-dimensional black hole with four charges and five-dimensional black hole with three charges may be effectively described by thermodynamics of the black hole solutions with constant dilaton field in two-dimensional dilaton gravity theories.Comment: 15 pages, LaTeX, added reference

Universal conservation law and modified Noether symmetry in 2d models of gravity with matter

It is well-known that all 2d models of gravity---including theories with nonvanishing torsion and dilaton theories---can be solved exactly, if matter interactions are absent. An absolutely (in space and time) conserved quantity determines the global classification of all (classical) solutions. For the special case of spherically reduced Einstein gravity it coincides with the mass in the Schwarzschild solution. The corresponding Noether symmetry has been derived previously by P. Widerin and one of the authors (W.K.) for a specific 2d model with nonvanishing torsion. In the present paper this is generalized to all covariant 2d theories, including interactions with matter. The related Noether-like symmetry differs from the usual one. The parameters for the symmetry transformation of the geometric part and those of the matterfields are distinct. The total conservation law (a zero-form current) results from a two stage argument which also involves a consistency condition expressed by the conservation of a one-form matter ``current''. The black hole is treated as a special case.Comment: 3

Conserved Quasilocal Quantities and General Covariant Theories in Two Dimensions

General matterless--theories in 1+1 dimensions include dilaton gravity, Yang--Mills theory as well as non--Einsteinian gravity with dynamical torsion and higher power gravity, and even models of spherically symmetric d = 4 General Relativity. Their recent identification as special cases of 'Poisson--sigma--models' with simple general solution in an arbitrary gauge, allows a comprehensive discussion of the relation between the known absolutely conserved quantities in all those cases and Noether charges, resp. notions of quasilocal 'energy--momentum'. In contrast to Noether like quantities, quasilocal energy definitions require some sort of 'asymptotics' to allow an interpretation as a (gauge--independent) observable. Dilaton gravitation, although a little different in detail, shares this property with the other cases. We also present a simple generalization of the absolute conservation law for the case of interactions with matter of any type.Comment: 21 pages, LaTeX-fil