Einstein's general theory of relativity a century on

In this first talk, we first discuss the puzzles and clues in 19th century physics that set the scene for Einstein’s discovery of General Relativity. Then we move on to the principle of equivalence, and the central roles of the geodesic and the Riemann (curvature) tensor. Finally we motivate Einstein’s equations and observe that their correctness or otherwise is a matter for experiment and observation.

Deflection of light by gravity is an immediate consequence of the principle of equivalence. We obtain a first estimate by using Newtonian mechanics to compute deflection of a particle of speed v by a massive body and setting v=c. This estimate is only half the result of GR because gravity is a speed-dependent force. We are mostly interested in deflection by weak gravitational fields. If harmonic coordinates are used to represent such a field, we get the right answers by associating a non-unit refractive index with the field. Objects that lie behind a foreground galaxy can be multiply imaged. The images of galaxies that lie further away from the line of sight to a foreground galaxy are stretched perpendicular to the local gravitational field. Even HST cannot resolve multiple images of background stars caused by foreground stars. But when a star is lensed, its apparent brightness surges. This phenomenon has been observed thousands of times. It enables us to detect low-mass and otherwise invisible stars and planets.

Einstein's field equations are a tangled set of non-linear partial differential equations. A strategy for solving them is to consider space-times which have a large amount of symmetry. The space-time of the whole Universe is a notable example: it can be assumed to be homogenous and isotropic and completely characterized in terms of an overall scale factor. General Relativity predicts that the scale factor changes with time and therefore that Universe is constantly evolving. The type of evolution depends on the type of matter in the universe as well as the overall geometry of space. This simple mathematical model has been shown to work remarkably well: it explains the recession of galaxies and the overwhelming evidence that the universe was hotter and denser in the past.