Introduction

The principles of General Relativity

The construction of a quantum theory of gravity is a major ambition of modern physics research. However, the absence of any direct experimental evidence implies that we do not have any empirical point of reference about the principles that will underlie this theory. We therefore have to proceed mainly by theoretical arguments, trying to uncover such principles from the structure of the theories we already possess.

Clearly, the most relevant theory for this purpose is General Relativity, which provides the classical description of the gravitational field. General Relativity is essentially based on two principles, uncovered by Einstein after the continuous effort of seven years. The first one asserts the importance of the spacetime description: all gravitational phenomena can be expressed in terms of a Lorentzian metric on a four-dimensional manifold. The second one is the principle of general covariance: the Lorentzian metric is a dynamical variable, its equations of motion preserve their form in all coordinate systems of the underlying manifold.

The first principle defines the kinematics of General Relativity. It identifies the basic variables that are employed in the theory's mathematical description, and determines their relation to physical quantities measured in experiments. This principle implies that General Relativity is a geometric theory. It refers primarily to the relations between spacetime events: the metric determines their distance and causal relation.