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General Theory of Relativity
The relativistic theory of gravitation that was devised in 1915 by Albert Einstein (1879–1955). The general theory extended Einstein’s previous work on special relativity to deal with observers in accelerated frames of reference. A central postulate of the general theory is the principle of equivalence, that ‘all freely-falling, non-rotating, laboratories are fully equivalent for the performance of all physical experiments’. It follows from this that an observer in a small closed box (e.g. an elevator, or a windowless spacecraft) cannot tell whether that box is subject to uniform acceleration or is at rest in a uniform gravitational
field; both situations would give the observer a feeling of ‘weight’. Conversely, if a test particle floats freely inside a closed box, an observer cannot tell whether the box is in the depths of space, far from a gravitating body, or falling freely in the gravitational field of a massive body (for example, an observer inside an elevator falling freely down its shaft would have no sensation of weight). General relativity embodies the concept that the three dimensions of space (length, breadth, height) and the dimension of time are linked together into a four dimensional spacetime. The effect of a distribution of mass (or energy) is to induce curvature into (i.e. to bend) spacetime in its vicinity. Conversely, particles and rays of light follow paths that are determined by the curvature of spacetime in their locality. In general relativity, gravitation is regarded as a geometric property of spacetime rather than, as in Newtonian gravitation, a force acting directly between individual massive bodies. Although Newtonian theory is perfectly satisfactory
for most applications, general relativity is capable of dealing with circumstances in which Newtonian theory is inadequate. In particular, the perihelion position of the planet Mercury’s orbit advances by an amount that exceeds the Newtonian prediction by 43 arcsec per century; general relativity predicts the correct rate of advance. Other important consequences of the theory, which have been tested to a high degree of
precision by experiment and observation, include: the bending of light in a gravitational field (rays of light passing close to the edge of the Sun, for example, are deflected by an amount that is consistent with general relativity); gravitational time dilation (clocks run more slowly in strong gravitational fields than in weak ones); and gravitational redshift (light emerging from a strong
gravitational field is stretched to longer wavelengths). General relativity has important applications in many areas of astrophysics and cosmology, including describing the behavior and properties of very close binaries, binary pulsars, black holes, gravitational lensing and the universe as a whole.
General Relativity and Gravitation
The General Theory of Relativity (GR), created by Albert Einstein between 1907 and 1915, is a theory both of gravitation and of spacetime structure. It is based on the assumption that matter, via its energy-momentum, interacts with the metric of spacetime, which is considered as a dynamical field having degrees of freedom of its own ( GRAVITATIONAL RADIATION). In brief, ‘matter tells spacetime how to curve, and spacetime tells matter how to move’ (J A Wheeler). GR is a generalization of Newton’s theory of gravitation and of Special Relativity, which are both approximations to GR under appropriate conditions (see below). More generally, GR provides a common, coherent basis for classical (as opposed to quantum), macroscopic physics. Its relation to quantum physics is not yet well understood ( QUANTUM GRAVITY). While this poses an important problem of principle, it does not present a practical difficulty to astrophysics, since the atomic and subatomic scales, on which quantum laws operate, are very small compared to macroscopic scales, where gravity dominates.
According to present fundamental physics, the only one among the four basic interactions which acts between all kinds of matter is the gravitational interaction. Since it always acts as an attraction and thus cannot be shielded, and because its range is unbounded, it dominates the behavior of matter on large scales in spite of its extreme weakness. Therefore, gravity plays a significant role in nearly all parts of astronomy and astrophysics. (In the atomic and subatomic domain gravity is unmeasurably weak and totally negligible, as is highlighted by the ‘fact’ that the gravitational force between a proton and an electron is weaker than the Coulomb force by the factor 5 × 10 −38 .) Relativistic gravity is important in the following areas of research: high-precision astrometry, compact objects such as NEUTRON STARS and BLACK HOLES and systems thereof (binary PULSARS, low-mass X-RAY BINARY STARS ), active galactic nuclei and quasars, supernovae and gravitational collapse, identification of dark stars and planets ( MICROLENSING), cosmology (COSMOLOGY: STANDARD MODEL , DARK MATTER, COSMOLOGICAL CONSTANT, distribution of luminous and DARKMATTER via weak GRAVITATIONAL LENSING). In the near future a new window onto the universe is expected to open when GRAVITATIONAL WAVES become observable.
Experimental and observational tests of general relativity
Experiments and measurements supporting GR can be classified into those which test the Einstein equivalence principle and those which probe the gravitational field equation.
Tests of the Einstein equivalence principle Tests of the first kind probe the approximate local validity of Special Relativity, i.e. the existence of local inertial frames or, equivalently, the possibility to assign a unique Lorentz metric to spacetime. From the viewpoint of GR these experiments serve to identify, relative to some arbitrary reference frame, a local inertial frame. Free fall experiments and Foucault pendulum experiments carried out in a terrestrial laboratory, for example, measure the acceleration and the angular velocity of the laboratory relative to a local inertial frame. Optical experiments and quantum interference experiments with neutron waves accomplish the same, and the concordance of the results establishes, up to experimental uncertainties, the uniqueness of the spacetime metric. The experimental fact that local inertial frames are accelerated relative to each other shows that spacetime is curved.
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