Positive Energy Theorems in General Relativity

Abstract

At the end of the nineteenth century light was regarded as an electromagnetic wave propagating in a material medium called ether. The speed c appearing in Maxwell’s wave equations was the speed of light with respect to the ether. Therefore, according to the Galilean addition of velocities, the speed of light in the laboratory would differ from c. The measure of such a difference would reveal the motion of the laboratory (the Earth) relative to the ether (a sort of absolute motion). However, the Earth’s absolute motion was never evidenced. Galileo addition of velocities is based on the assumption that lengths and time intervals are invariant (independent of the state of motion). In this way of thinking, the spacetime emanates from our daily experience and lies at the heart of Newton’s classical mechanics. Nevertheless, in 1905 Einstein defied Galileo addition of velocities by postulating that light travels at the same speed c in any inertial frame. In doing so, Einstein extended the principle of relativity to the electromagnetic phenomena described by Maxwell’s laws. In Einstein’s special relativity the ether does not exist and the absolute motion is devoid of meaning. The invariance of the speed of light forced the replacement of Galileo transformations with Lorentz transformations. Thus, relativistic length contractions and time dilations entered our understanding of spacetime. Newtonian mechanics had to be reformulated, which led to the discovery of the mass–energy equivalence.