Teaching General Relativity

This Resource Letter provides some guidance on issues that arise in teaching general relativity at both the undergraduate and graduate levels. Particular emphasis is placed on strategies for presenting the mathematical material needed for the formulation of general relativity.Comment: 14 pages, no figures; submitted as a "Resource Letter" to American Journal of Physic

The Formulation of Quantum Field Theory in Curved Spacetime

The usual formulations of quantum field theory in Minkowski spacetime make crucial use of Poincare symmetry, positivity of total energy, and the existence of a unique, Poincare invariant vacuum state. These and other key features of quantum field theory do not generalize straightforwardly to curved spacetime. We discuss the conceptual obstacles to formulating quantum field theory in curved spacetime and how they can be overcomeComment: 14 pages, no figures; to appear in proceedings of Beyond Einstein conferenc

The First Law of Black Hole Mechanics

A simple proof of a strengthened form of the first law of black hole mechanics is presented. The proof is based directly upon the Hamiltonian formulation of general relativity, and it shows that the the first law variational formula holds for arbitrary nonsingular, asymptotically flat perturbations of a stationary, axisymmetric black hole, not merely for perturbations to other stationary, axisymmetric black holes. As an application of this strengthened form of the first law, we prove that there cannot exist Einstein-Maxwell black holes whose ergoregion is disjoint from the horizon. This closes a gap in the black hole uniqueness theorems.Comment: 9 pages, to appear in Misner Festschrif

Black Holes and Thermodynamics

We review the remarkable relationship between the laws of black hole mechanics and the ordinary laws of thermodynamics. It is emphasized that - in analogy with the laws of thermodynamics - the validity the laws of black hole mechanics does not appear to depend upon the details of the underlying dynamical theory (i.e., upon the particular field equations of general relativity). It also is emphasized that a number of unresolved issues arise in ``ordinary thermodynamics'' in the context of general relativity. Thus, a deeper understanding of the relationship between black holes and thermodynamics may provide us with an opportunity not only to gain a better understanding of the nature of black holes in quantum gravity, but also to better understand some aspects of the fundamental nature of thermodynamics itself.Comment: 26 pages, plain LaTeX; to appear in the proceedings of the Symposium on Black Holes and Relativistic Stars (in honor of S. Chandrasekhar), December 14-15, 199

Gravitational Collapse and Cosmic Censorship

We review the status of the weak cosmic censorship conjecture, which asserts, in essence, that all singularities of gravitational collapse are hidden within black holes. Although little progress has been made toward a general proof (or disproof) of this conjecture, there has been some notable recent progress in the study of some examples and special cases related to the conjecture. These results support the view that naked singularities cannot arise generically.Comment: 21 pages, plain latex, no figures. Corresponds closely to talk given at the April, 1997 APS meeting in Washington, D.C. A few references adde

Quantum Fields in Curved Spacetimes and Semiclassical Approaches: A Workshop Summary

I briefly review some of the recent progress in quantum field theory in curved spacetime and other aspects of semiclassical gravity, as reported at the D3 Workshop at GR15.Comment: 7 pages, plain LaTeX 2.09 fil

The Arrow of Time and the Initial Conditions of the Universe

The existence of a thermodynamic arrow of time in the present universe implies that the initial state of the observable portion of our universe at (or near) the ``big bang'' must have been very ``special''. We argue that it is not plausible that these special initial conditions have a dynamical origin.Comment: 5 pages, no figures; write-up of talk given at Seven Pines "Arrows of Time" meeting, December, 200

Introduction to Gravitational Self-Force

The motion of sufficiently small body in general relativity should be accurately described by a geodesic. However, there should be ``gravitational self-force'' corrections to geodesic motion, analogous to the ``radiation reaction forces'' that occur in electrodynamics. It is of considerable importance to be able to calculate these self-force corrections in order to be able to determine such effects as inspiral motion in the extreme mass ratio limit. However, severe difficulties arise if one attempts to consider point particles in the context of general relativity. This article describes these difficulties and how they have been dealt with.Comment: 11 pages, no figures, to appear in proceedings of CNRS School on Mas

Gravitational Lensing in Inhomogeneous Universes

I describe a new approach (developed in collaboration with D.E. Holz) to calculating the statistical distributions for magnification, shear, and rotation of images of cosmological sources due to gravitational lensing by mass inhomogeneities on galactic and smaller scales. Our approach is somewhat similar to that used in ``Swiss cheese'' models, but the ``cheese'' has been completely eliminated, the matter distribution in the ``voids'' need not be spherically symmetric, the total mass in each void need equal the corresponding Robertson-Walker mass only on average, and we do not impose an ``opaque radius'' cutoff. In our approach, we integrate the geodesic deviation equation backwards in time until the desired redshift is reached, using a Monte Carlo procedure wherein each photon beam in effect ``creates its own universe'' as it propagates. Our approach fully takes into account effects of multiple encounters with gravitational lenses and is much easier to apply than ``ray shooting'' methods.Comment: 9 pages, latex 2e. To appear in proceedings of XLIXth Yamada Conference on Black Holes and High Energy Astrophysic

The Cosmological Memory Effect

The "memory effect" is the permanent change in the relative separation of test particles resulting from the passage of gravitational radiation. We investigate the memory effect for a general, spatially flat FLRW cosmology by considering the radiation associated with emission events involving particle-like sources. We find that if the resulting perturbation is decomposed into scalar, vector, and tensor parts, only the tensor part contributes to memory. Furthermore, the tensor contribution to memory depends only on the cosmological scale factor at the source and observation events, not on the detailed expansion history of the universe. In particular, for sources at the same luminosity distance, the memory effect in a spatially flat FLRW spacetime is enhanced over the Minkowski case by a factor of $(1 + z)$.Comment: 22 pages, 1 figure. Eqs (53)-(55) have been correcte