Hawking Radiation for Non-minimally Coupled Matter from Generalized 2D Black Hole Models

It is well known that spherically symmetric reduction of General Relativity (SSG) leads to non-minimally coupled scalar matter. We generalize (and correct) recent results to Hawking radiation for a class of dilaton models which share with the Schwarzschild black hole non-minimal coupling of scalar fields and the basic global structure. An inherent ambiguity of such models (if they differ from SSG) is discussed. However, for SSG we obtain the rather disquieting result of a negative Hawking flux at infinity, if the usual recipe for such calculations is applied.Comment: 8 page

Effective Action and Hawking Flux from Covariant Perturbation Theory

The computation of the radiation flux related to the Hawking temperature of a Schwarzschild Black Hole or another geometric background is still well-known to be fraught with a number of delicate problems. In spherical reduction, as shown by one of the present authors (W. K.) with D.V. Vassilevich, the correct black body radiation follows when two ``basic components'' (conformal anomaly and a ``dilaton'' anomaly) are used as input in the integrated energy-momentum conservation equation. The main new element in the present work is the use of a quite different method, the covariant perturbation theory of Barvinsky and Vilkovisky, to establish directly the full effective action which determines these basic components. In the derivation of W. K. and D.V. Vassilevich the computation of the dilaton anomaly implied one potentially doubtful intermediate step which can be avoided here. Moreover, the present approach also is sensitive to IR (renormalisation) effects. We realize that the effective action naturally leads to expectation values in the Boulware vacuum which, making use of the conservation equation, suffice for the computation of the Hawking flux in other quantum states, in particular for the relevant Unruh state. Thus, a rather comprehensive discussion of the effects of (UV and IR) renormalisation upon radiation flux and energy density is possible.Comment: 26 page

Global properties of warped solutions in General Relativity

Assuming the four-dimensional space-time to be a general warped product of two surfaces we reduce the four-dimensional Einstein equations to a two-dimensional problem which can be solved. All global vacuum solutions are explicitly constructed and analysed. The classification of the solutions includes the Schwarzschild, the (anti-)de Sitter, and other well-known solutions but also many exact ones whose detailed global properties to our knowledge have not been discussed before. They have a natural physical interpretation describing single or several wormholes, domain walls of curvature singularities, cosmic strings, cosmic strings surrounded by domain walls, solutions with closed timelike curves, etc.Comment: 35 pages, 5 eps figures, minor change

Midisuperspace-Induced Corrections to the Wheeler De Witt Equation

We consider the midisuperspace of four dimensional spherically symmetric metrics and the Kantowski-Sachs minisuperspace contained in it. We discuss the quantization of the midisuperspace using the fact that the dimensionally reduced Einstein Hilbert action becomes a scalar-tensor theory of gravity in two dimensions. We show that the covariant regularization procedure in the midisuperspace induces modifications into the minisuperspace Wheeler DeWitt equation.Comment: 7 page

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

S-matrix for s-wave gravitational scattering

In the s-wave approximation the 4D Einstein gravity with scalar fields can be reduced to an effective 2D dilaton gravity coupled nonminimally to the matter fields. We study the leading order (tree level) vertices. The 4-particle matrix element is calculated explicitly. It is interpreted as scattering with formation of a virtual black hole state. As one novel feature we predict the gravitational decay of s-waves.Comment: 9 pages, 1 figure, added clarifying comments in the introduction, the conclusion, and the virtual black hole sectio

Absolute conservation law for black holes

In all 2d theories of gravity a conservation law connects the (space-time dependent) mass aspect function at all times and all radii with an integral of the matter fields. It depends on an arbitrary constant which may be interpreted as determining the initial value together with the initial values for the matter field. We discuss this for spherically reduced Einstein-gravity in a diagonal metric and in a Bondi-Sachs metric using the first order formulation of spherically reduced gravity, which allows easy and direct fixations of any type of gauge. The relation of our conserved quantity to the ADM and Bondi mass is investigated. Further possible applications (ideal fluid, black holes in higher dimensions or AdS spacetimes etc.) are straightforward generalizations.Comment: LaTex, 17 pages, final version, to appear in Phys. Rev.

Two-Dilaton Theories in Two Dimensions from Dimensional Reduction

Dimensional reduction of generalized gravity theories or string theories generically yields dilaton fields in the lower-dimensional effective theory. Thus at the level of D=4 theories, and cosmology many models contain more than just one scalar field (e.g. inflaton, Higgs, quintessence). Our present work is restricted to two-dimensional gravity theories with only two dilatons which nevertheless allow a large class of physical applications. The notions of factorizability, simplicity and conformal simplicity, Einstein form and Jordan form are the basis of an adequate classification. We show that practically all physically motivated models belong either to the class of factorizable simple theories (e.g. dimensionally reduced gravity, bosonic string) or to factorizable conformally simple theories (e.g. spherically reduced Scalar-Tensor theories). For these theories a first order formulation is constructed straightforwardly. As a consequence an absolute conservation law can be established.Comment: 23 pages, 1 tabl

Nonperturbative path integral of 2d dilaton gravity and two-loop effects from scalar matter

Performing an nonperturbative path integral for the geometric part of a large class of 2d theories without kinetic term for the dilaton field, the quantum effects from scalar matter fields are treated as a perturbation. When integrated out to two-loops they yield a correction to the Polyakov term which is still exact in the geometric part. Interestingly enough the effective action only experiences a renormalization of the dilaton potential.Comment: 15 page

Geometrodynamics of Schwarzschild Black Holes

The curvature coordinates $T,R$ of a Schwarz\-schild spacetime are turned into canonical coordinates $T(r), {\sf R}(r)$ on the phase space of spherically symmetric black holes. The entire dynamical content of the Hamiltonian theory is reduced to the constraints requiring that the momenta $P_{T}(r), P_{\sf R}(r)$ vanish. What remains is a conjugate pair of canonical variables $m$ and $p$ whose values are the same on every embedding. The coordinate $m$ is the Schwarzschild mass, and the momentum $p$ the difference of parametrization times at right and left infinities. The Dirac constraint quantization in the new representation leads to the state functional $\Psi (m; T, {\sf R}] = \Psi (m)$ which describes an unchanging superposition of black holes with different masses. The new canonical variables may be employed in the study of collapsing matter systems.Comment: 44 pages, Latex file, UU-REL-94/3/