Table of contents

A three-parameter solution of Einstein's equations for the interior of a uniformly rotating, stationary, axisymmetric perfect fluid is presented. The solution is analytically simple, behaves properly on the axis, and has finite non-rotating and vacuum limits. It is algebraically general and has no higher symmetry. The equation of state is , and the fluid's vorticity and acceleration vectors are parallel.

We show that there exists at least one point at which the pressure is positive for any static general relativistic stellar model. This supports the intuition that one needs positive pressure in order to balance the gravitational force.

Thermal properties of the recently discovered black holes in 2+1-dimensional gravity with a negative cosmological constant are investigated. The validity of the first law of thermodynamics is justified directly. It is shown that a canonical ensemble for such black holes exists at arbitrary temperature while a grand canonical one is well defined only in the low-temperature domain. The canonical and grand canonical pressure ensembles for black holes prove to be unstable.

The N = 4 super-Beltrami parametrization is formulated in the two-dimensional harmonic superspace. The N = 4 superconformal anomaly and its compensating action are constructed. Then the anomalous Ward identities are derived and the operator product expansions of the N = 4 super-stress--energy tensors are obtained.

We investigate the space of classical solutions of Witten's formulation of 2+1 gravity on the manifold . is connected, unlike the spaces of classical solutions in the cases where is replaced by a higher genus surface. Although is neither Hausdorff nor a manifold, removing from a set of measure zero yields a manifold which is naturally viewed as the cotangent bundle over a non-Hausdorff base space . We discuss the relation of the various parts of with spacetime metrics, and various possibilities of quantizing . There exist quantizations in which the exponentials of certain momentum operators, when operating on states whose support is entirely on the part of corresponding to conventional spacetime metrics, give states whose support is entirely outside this part of . Similar results hold when the gauge group is replaced by SU(1,1).

For a (1+1)-dimensional theory of gravity different approaches to the formulation of a quantum theory are presented. They are shown to lead to the same finite dimensional quantum system. Conceptual questions of quantum gravity such as, e.g., the problem of time are discussed in this framework.

In this paper we study the probability of excitation of an inertial monopole detector interacting with a Hermitian massless scalar field in the vacuum state, and in a thermal state in the presence of a straight cosmic string. This probability is evaluated for a finite time interval. We show how the conical structure of spacetime modifies the spontaneous and induced emission rate of the detector.

We analyze the global structure of a family of Einstein-Maxwell solutions parametrized by mass, charge and cosmological constant. In a qualitative classification there are: (i) generic black-hole solutions, describing a Wheeler wormhole in a closed cosmos of spatial topology ; (ii) generic naked-singularity solutions, describing a pair of `point' charges in a closed cosmos; (iii) extreme black-hole solutions, describing a pair of `horned' particles in an otherwise closed cosmos; (iv) extreme naked-singularity solutions, in which a pair of point charges forms and then evaporates, in a way which is not even weakly censored; and (v) an ultra-extreme solution. We discuss the properties of the solutions and of various coordinate systems, and compare with the Kastor-Traschen multi-black-hole solutions.

A Kaluza--Klein (KK) type of inhomogeneous cosmological model is obtained with a matter field in the form of a dust. Under suitable conditions our solution either reduces to a recent inhomogeneous model of the present authors or to some other well known homogeneous KK cosmologies. It is observed that, depending on initial conditions, both the spaces either expand or as the usual scale expands the extra scale contracts exhibiting the desirable feature of dimensional reduction. Further, our spacetime may give wormhole configuration at the classical level. It is also found that aside from the singularity at the big bang the model is spatially nonsingular.

We present a discussion of power-law inflation in higher-order gravity theories. Using the conformal equivalence theorem, we find power-law solutions in the context of pure higher-order gravity theories in arbitrary dimension. We also find a family of polar inflationary solutions. We give a perturbation analysis which establishes that the power-law solutions are stable against homogeneous and isotropic perturbations but that the polar solutions are not.

A Hamiltonian treatment of gauge-invariant cosmological perturbations is presented. In this framework the gauge-invariant perturbations as well as their evolution equations are obtained with minimal work, thanks to the use of a Hamilton--Jacobi technique which takes advantage of the gauge invariance of general relativity. This formalism is applied to perturbations around spatially flat and closed Friedmann--Robertson--Walker universes with the matter being given by a scalar field, both for the gauge-invariant `scalar' perturbations and gravitational waves.

Integral and differential mass formulae of four-dimensional stationary and axisymmetric Einstein--Maxwell dilaton systems are derived. The total mass (energy) of these systems are expressed in terms of other physical quantities such as electric charge of the black hole suitably modified due to the existence of the dilaton field. It is shown that when we vary the fields slightly (the metric of the spacetime , U(1)-gauge potential , and dilaton ) in such a way that they obey classical equations of motion, the variation of the dilaton does not contribute explicitly to the variation of the total mass, but contributes only through the variation of the electric charge of the black hole.

An earlier construction by the authors of sequences of globally regular, asymptotically flat initial data for the Einstein vacuum equations containing trapped surfaces for large values of the parameter is extended, from the time symmetric case considered previously, to the case of maximal slices. The resulting theorem shows rigourously that there exists a large class of initial configurations for non-time symmetric, pure gravitational waves satisfying the assumptions of the Penrose singularity theorem, and so must have a singularity to the future.

We search for apparent horizons in various kinds of analytic initial data with axisymmetry but which allow some extreme matter configurations, in order to gain some insights into the hoop conjecture proposed by Thorne. The problem of defining the circumference C of a body is also considered, and a precise definition of C is proposed. For the models considered, the necessary condition for the apparent horizon formation is found to be where M is the ADM mass. Although initial data investigated here are only of a restricted class, it is interesting to note that this criterion almost coincides with the result obtained by Barrabès et al and by Tod who investiged a convex null dust shell.

A relativistic generalization of the classical virial theorem is obtained for any stationary and asymptotically flat spacetime. This formulation is derived within the 3+1 formalism of general relativity. It may be useful as a consistency check of numerical solutions of the Einstein equations.

We investigate the causal structure of , the spacetime consisting of that portion of Schwarzschild space outside the event horizon. Two points, p and q in which do not lie on a common null geodesic are chronologically related if and only if their celestial spheres, P and Q have non-zero linking number in , the space of null geodesics of .

In this paper we study fermions interacting with an Abelian point-like vortex on a cone. In this way we obtain some induced quantum numbers of this system such as electric charge and angular momentum, and show how these quantities depend on the flux and on the parameter related to the conical geometry of the (2 + 1)-dimensional spacetime.

The possibility of atomic detection of gravitational waves on Earth is considered. The combination of extremely high lifetimes and resulting small radiative transition probabilities with rapidly growing interaction strength for Rydberg atoms having principal quantum numbers in the region might result in transition probabilities which are high enough to open up such a possibility. Transition probabilities and absorption cross sections are calculated as a function of the relevant quantum numbers of a highly excited electron. The orders of magnitude for the transition rate are evaluated for a realistic source of gravitational radiation. It is shown that no specific particle property enters the expression for the absorption cross section for gravitational waves. The only fundamental constant contained in this cross section is, apart from the fine structure constant , the Planck length .

It is shown that if a null Einstein--Maxwell spacetime admits a proper conformal vector field it must either be a (generalized type N) pp-wave or a (generalized type III) Goldberg--Kerr metric.