The general theory of relativity represents a further modification of classical concepts of space and time that goes far beyond those implicit in the special theory. The special theory does away with the absolute character of time and with the absolute distance between two objects that are at rest relative to each other. The geometric concepts appropriate to the special theory are the four-dimensional space-time continuum, in which events that are fixed in space and in time are represented by points, often referred to as world points (to distinguish them from the points of ordinary three-dimensional space), and the histories of particles moving through space in the course of time by curves (world curves); the representations of particles that are not accelerated by forces are straight lines.

Minkowski's space-time is a rigidly flat continuum, as is the three-dimensional space of Euclid's geometry. Distances between world points are measured by the invariant intervals, whose magnitudes do not depend on the particular coordinate system, or frame of reference, used. The Minkowski universe is homogeneous; that is to say, geometric figures constructed at any site may be transferred to another site without distortion. Finally, among all the possible frames of reference there is a special set, the inertial frames of reference, just as in ordinary space the rectilinear coordinate systems are distinguished by their simplicity among all conceivable coordinate systems. Space-time serves as the immutable backdrop of all physical processes, without being affected by them.

In general relativity, space-time also is a four-dimensional continuum, with invariant intervals being defined at least locally between events taking place close to each other. But only small regions of space-time resemble the continuum envisaged by Minkowski, just as small bits of a spherical surface appear nearly planar. In the broad sense, according to general relativity, space-time is curved, and this curvature is equivalent to the presence of a gravitational field. Far from being rigid and homogeneous, the general-relativistic space-time continuum has geometric properties that vary from point to point and that are affected by local physical processes. Space-time ceases to be a stage, or scaffolding, for the dynamics of nature; it becomes an integral part of the dynamic process. General relativity, it has been said, makes physics part of geometry. It may also be claimed that general relativity makes geometry part of physics, that is to say, of a natural science. Not only are the properties of space and time subject to scientific investigation, to a study by means of experiments, but specific properties, such as the amount of curvature in a particular location at a specified time, are to be measured with the help of physical instruments.

Though the general theory of relativity is universally accepted as the most satisfactory basis of the gravitational force now known, it has not been completely fused with quantum mechanics, of which the central concept is that energy and angular momentum exist only in finite and discrete lumps, called quanta. Since the 1920s quantum mechanics has been the sole rationale of the forces that act between subatomic particles; gravitation doubtless is one of these forces, but its effects are unobservably small in comparison to electromagnetic and nuclear forces. Relativistic phenomena in the subatomic realm have been adequately dealt with by merging quantum mechanics with the special, not the general, theory.

Many physicists, foremost among them Einstein himself, tried during the first half of the 20th century to enrich the geometric structure of space-time so as to encompass all known physical interactions. Their goal, a unified field theory, remained elusive but was brought nearer during the late 1960s by the successful unification of the electromagnetic and the so-called weak nuclear force.

Immediately on publication of Einstein's paper on general relativity, the German astronomer Karl Schwarzschild found a mathematical solution to the new field equations, which corresponds to the gravitational field of a compact massive body, such as a star or planet, and which is now referred to as Schwarzschild's field. If the mass that serves as the source of the field is fairly diffuse, so that the gravitational field on the surface of the astronomical body is fairly weak, Schwarzschild's field will exhibit physical properties similar to those described by Newton. Gross deviations will be found if the mass is so highly concentrated that the field on the surface is strong. At the time of Schwarzschild's work, in 1916, this appeared to be a theoretical speculation; but with the discovery of pulsars and their interpretation as probable neutron stars composed of matter that has the same density as atomic nuclei (so-called nuclear matter), the possibility exists that strong fields may soon be accessible to astronomical observation.

The most conspicuous feature of the Schwarzschild field is that if the total mass is thought of as concentrated at the very centre, a point called a singularity, then at a finite distance from that centre, the Schwarzschild radius, the geometry of space-time changes drastically from that to which we are accustomed. Particles and even light rays cannot penetrate from inside the Schwarzschild radius to the outside and be detected. Conversely, to an outside observer any objects approaching the Schwarzschild radius appear to take an infinite time to penetrate toward the inside. There cannot be any effective communication between the inside and the outside, and the boundary between them is called an event horizon.

The exterior and the interior of the Schwarzschild radius are not cut off from each other entirely, however. Suppose an observer were to attach himself to a particle that is falling freely straight toward the centre and that this observer is equipped with a clock that reads its own proper time. This observer would penetrate the Schwarzschild radius within a finite proper time; moreover, he would find no abnormalities in his environment as he did so. The reason is that his clock would deviate from one permanently kept outside and at a constant distance from the centre, so grossly that the same event that seen from the outside takes forever occurs within a finite time to the free-falling observer.

These peculiarities of the Schwarzschild field may well have practical applications in astronomy. In 1931 the Indian-born U.S. astrophysicist Subrahmanyan Chandrasekhar, and in 1939 the U.S. physicist J. Robert Oppenheimer, established that a star whose mass exceeds the mass of the Sun by an appreciable factor is bound to contract and, eventually, to collapse under the influence of its own gravity, no matter how resistant its constituent matter. As many stars are believed to have such large masses, it is likely that there already exist some collapsed stars, so-called black holes. Though continuing to make its presence known by the gravitational attraction it exerts on other stars, a black hole would not emit light, and thus be invisible, hence its name.