Notes on Gravitational Physics

Abstract

These notes are self-contained, with the first six chapters used for a one-semester course with recommended texts by Wald, Misner, Thorne, and Wheeler (MTW), and, particularly for gravitational waves, by Schutz and by Thorne and Blandford. In its treatment of topics covered in these standard texts, the presentation here typically includes steps between equations that are skipped in Wald or MTW. Treatments of gravitational waves, particle orbits in black-hole backgrounds, the Teukolsky equation, and the initial value equations are motivated in part by the dramatic discoveries of gravitational waves from the inspiral and coalescence of binary black holes and neutron stars, advances in numerical relativity, and the expected launch of the LISA space-based observatory. Students are assumed to have encountered special relativity, but these notes give a detailed presentation with a geometrical orientation, starting with with time dilation and length contraction and including relativistic particles, fluids, electromagnetism, and curvilinear coordinates. Chaps. 2-5 cover curvature, the Einstein equation, relativistic stars, and black holes. Chap. 6, on gravitational waves, includes a discussion of detection and of noise in interferometric detectors. Chap. 7, on the initial value problem, has a section on the form of the equations used in numerical relativity. Its notation is that used, for example, in Baumgarte and Shapiro and Shibata; the presentation here is taken in part from the text by Friedman and Stergioulas. The notes also have a chapter on the Newman-Penrose formalism and the Teukolsky equation. Following that is a chapter on black-hole thermodynamics and a final chapter on the gravitational action and on conserved quantities for asymptotically flat spacetimes, using Noether’s theorem.