The General Theory of Relativity is a major landmark in the development of classical Theoretical Physics. In 1905, Einstein presented his Special Theory of Relativity which we understand to be a theory of the relation between space and time in inertial frames of reference, which are in uniform relative motion with respect to each other with a constant velocity. The requirement that the laws of Physics be the same in all inertial frames leads to the idea that mass is a frame dependent quantity, and hence to a modification of Newton's Laws to take into account the new relations between the space and time coordinates of two inertial frames. In a strict sense it does not deal with accelerations. The General Theory appeared some ten years later in 1915 and represents not only a theory which describes frames of reference in arbitrary motion with respect to each other, but also a theory of gravitation. When two frames of reference are indeed in uniform (unaccelerated) relative motion, it is required that the relations between two such frames of reference become those of the Special Theory. The Special Theory can be thought of as a theory of a flat four dimensional space-time. The General Theory requires that the four dimensional space time be curved, with a curvature determined by any matter which is present: we then experience this curvature as gravity. The analogue in the Newtonian view of physics, is the calculation of potential and fields from mass distributions by using Poisson's equation. In General Relativity objects experiencing gravitational forces are now required to move along optimal paths, called geodesics, in this curved space-time. In this new geometrical way of looking at things, the requirement that motion occurs along an optimal path, takes the place of Newton's second law. In this course we will begin by examining the physical basis of the ideas lying behind General Relativity. These ideas are encapsulated in the Principle of Equivalence. We then need to develop the mathematics of tensor analysis in a curved space-time in order to be able to make accurate statements about the physical and geometrical ideas which lie behind the General Theory and from which predictions can be made. We then use the theory to predict phenomena such as the bending of light near massive objects, the precession of the perihelion of a planet and the gravitational redshift. These latter phenomena provided early experimental tests of the General Theory (tests which have been refined with time) and attracted much public attention at the time. The course then concludes by looking at the cosmological consequences of the General Theory and introduces the idea of Black Holes. The General Theory of Relativity contains very profound physical ideas which are expressed through an elegant geometric structure. Its understanding requires high level skills in handling tensors and differential equations. This beautiful theory is part of the mainstream of physics. In 1932 Dirac married together the Special Theory of Relativity with Quantum Mechanics, but to this day there is no accepted theory of quantum gravity. |