Notes on Gravitational Physics

Abstract: These notes are self-contained, with the first 7 chapters used in a one-semester course with recommended texts by Wald, by Misner, Thorne and Wheeler, and by Schutz. In its treatment of topics covered in these standard texts, the presentation here typically includes steps 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 discoveries of gravitational waves from the inspiral and coalescence of binary black holes and neutron stars, advances in numerical relativity, and the expected LISA space-based observatory. The notes begin with a detailed presentation of special relativity 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 noise. Chap. 7 is a brief introduction to cosmology, deriving the metrics of homogeneous isotropic space, the equations governing a universe with matter, radiation and vacuum energy, and their solutions, and discussions of the cosmological redshift and on using gravitational waves to measure the Hubble constant. Chap. 8, on the initial value problem, has a section on the form of the equations used in numerical relativity. The Newman-Penrose formalism and the Teukolsky equation are covered in Chap. 9. 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. An appendix covers forms, densities, integration, and Cartan calculus.