General Relativity as a Tool for Astrophysics

Abstract

Phenomenologically the gravitational interaction may be characterized as the only (known) interaction which is both universal and long range. It affects all kinds of matter in the same way, and under quasistationary conditions its force falls off, like the Coulomb force, as r ⁻². In contrast to electrodynamics, it is then always attractive and thus cannot be shielded. Like electromagnetism it admits waves propagating with the fundamental speed c, but in contrast to electromagnetic waves which have helicity ±1, gravitational waves have helicity ±2. Moreover, gravity is by far the weakest interaction (at accessible energies) as highlighted by the “fact” that between a proton and an electron Newton’s force is weaker than Coulomb’s by a factor of 2 · 10³⁹. Because of these well-known properties, gravity — although unmeasurably weak and totally negligible compared to the strong and weak, short range nuclear forces in the atomic and subatomic regime — dominates in the realm of celestial bodies and systems thereof. This clear-cut separation of interaction ranges also insures that one can combine in astrophysics laws of GR with laws from quantum mechanics (equations of state, transition probabilities) without difficulties, although these laws are taken from theories which are, strictly speaking, incompatible. The combination of the two properties “universality” and “long range”, motivates the interpretation of gravity as a manifestation of the metric g _αβ and its associated affine connection Γ ^α _βγ and curvature R ^α _βγδ of spacetime. According to Einstein, the field g _αβ serves both as the metric, which locally defines the distinction between space and time and determines proper (clock) times and proper (ruler) distances, angles, areas and volumes, and as the gravitational potential whose derivatives, through the connection govern the equations of motion of matter and non-gravitational fields.