Quantization in black hole backgrounds

Quantum field theory in a semiclassical background can be derived as an approximation to quantum gravity from a weak-coupling expansion in the inverse Planck mass. Such an expansion is studied for evolution on "nice-slices" in the spacetime describing a black hole of mass M. Arguments for a breakdown of this expansion are presented, due to significant gravitational coupling between fluctuations, which is consistent with the statement that existing calculations of information loss in black holes are not reliable. For a given fluctuation, the coupling to subsequent fluctuations becomes of order unity by a time of order M^3. Lack of a systematic derivation of the weakly-coupled/semiclassical approximation would indicate a role for the non-perturbative dynamics of gravity, and possibly for the proposal that such dynamics has an essentially non-local quality.Comment: 28 pages, 4 figures, harvmac. v2: added refs, minor clarification

Relativistic Green functions in a plane wave gravitational background

We consider a massive relativistic particle in the background of a gravitational plane wave. The corresponding Green functions for both spinless and spin 1/2 cases, previously computed by A. Barducci and R. Giachetti \cite{Barducci3}, are reobtained here by alternative methods, as for example, the Fock-Schwinger proper-time method and the algebraic method. In analogy to the electromagnetic case, we show that for a gravitational plane wave background a semiclassical approach is also sufficient to provide the exact result, though the lagrangian involved is far from being a quadratic one.Comment: Last paper by Professor Arvind Narayan Vaidya, 18 pages, no figure

A Conformal Mapping and Isothermal Perfect Fluid Model

Instead of conformal to flat spacetime, we take the metric conformal to a spacetime which can be thought of as ``minimally'' curved in the sense that free particles experience no gravitational force yet it has non-zero curvature. The base spacetime can be written in the Kerr-Schild form in spherical polar coordinates. The conformal metric then admits the unique three parameter family of perfect fluid solution which is static and inhomogeneous. The density and pressure fall off in the curvature radial coordinates as $R^{-2},$ for unbounded cosmological model with a barotropic equation of state. This is the characteristic of isothermal fluid. We thus have an ansatz for isothermal perfect fluid model. The solution can also represent bounded fluid spheres.Comment: 10 pages, TeX versio

Asymptotically Flat Radiating Solutions in Third Order Lovelock Gravity

In this paper, we present an exact spherically symmetric solution of third order Lovelock gravity in $n$ dimensions which describes the gravitational collapse of a null dust fluid. This solution is asymptotically (anti-)de Sitter or flat depending on the choice of the cosmological constant. Using the asymptotically flat solution for $n \geq 7$ with a power-law form of the mass as a function of the null coordinate, we present a model for a gravitational collapse in which a null dust fluid radially injects into an initially flat and empty region. It is found that a naked singularity is inevitably formed whose strength is different for the $n = 7$ and $n \geq 8$ cases. In the $n=7$ case, the limiting focusing condition for the strength of curvature singularity is satisfied. But for $n \geq 8$, the strength of curvature singularity depends on the rate of increase of mass of the spacetime. These considerations show that the third order Lovelock term weakens the strength of the curvature singularity.Comment: 15 pages, no figure, references added, two appendix adde

A Spherically Symmetric Closed Universe as an Example of a 2D Dilatonic Model

We study the two-dimensional (2D) dilatonic model describing a massless scalar field minimally coupled to the spherically reduced Einstein-Hilbert gravity. The general solution of this model is given in the case when a Killing vector is present. When interpreted in four dimensions, the solution describes either a static or a homogeneous collision of incoming and outgoing null dust streams with spherical symmetry. The homogeneous Universe is closed.Comment: 5 pages, 2 figures, to appear in Physical Review