Four-force

About: Four-force is a research topic. Over the lifetime, 3459 publications have been published within this topic receiving 87308 citations.

Relativity and geometry

Abstract: General relativity university of pittsburgh. the geometry of special relativity. relativity and geometry dover books on physics roberto. geometry relativity and the fourth dimension rudolf v. spacetime and geometry sean carroll. einstein s theory of relativity. the geometry of general relativity is riemannian what is. general relativity simple english the free. lecture 37 riemannian geometry and the general relativity. quantum mechanics relativity geometry and the unity of. special relativity and conic sections hyperbolic. euler s formula geometry of relativity. general relativity spacetime and geometry. elementary general relativity. geometry and general relativity science4all. semi riemann geometry and general relativity. general relativity. the geometry of relativity geometry of relativity. mathematics of general relativity. geometry of space and relativity molwickpedia

On Experimental Tests of the General Theory of Relativity

Abstract: This paper explores the extent to which the three “crucial tests” support the full structure of the general theory of relativity, and do not merely verify the equivalence principle and the special theory of relativity, which are well established by other experimental evidence. It is shown how the first-order changes in the periods of identically constructed clocks and the lengths of identically constructed measuring rods can be found without using general relativity, and how the red shift and the deflection of light can be computed from them. Only the planetary orbit precession provides a real test of general relativity. Terrestrial or satellite experiments that would go beyond supplying corroborative evidence for the equivalence principle and special relativity would be extremely difficult to perform, and would, for example, require a frequency standard with an accuracy somewhat better than one part in 1018.

The Cauchy Problem in General Relativity

Abstract: After a brief introduction to classical relativity, we describe how to solve the Cauchy problem in general relativity. In particular, we introduce the notion of gauge source functions and explain how they can be used in order to reduce the problem to that of solving a system of hyperbolic partial differential equations. We then go on to explain how the initial value problem is formulated for the so-called Einstein-Vlasov system, and describe a recent future global non-linear stability result in this setting. In particular, this result applies to models of the universe which are consistent with observations.

On the Use of the Energy-Momentum Principle in General Relativity

Abstract: The primary purpose of this article is to obtain from the general relativity form of the energy-momentum principle certain new consequences which are needed for later work that the author has in mind. In addition, it is the intention to give at the same time a somewhat comprehensive and coherent treatment of the principle and its consequences, which it is hoped will increase the confidence and facility of physicists in the use of this important part of the general theory of relativity. In carrying out the investigation, it has seemed desirable for English readers, to take Eddington's "Mathematical Theory of Relativity" as a starting point, and this has incidentally led to a new form of deduction for certain consequences of the energy-momentum principle that were already known. After presenting the energy-momentum principle in the form discovered by Einstein and showing its application to the case of the conservation of energy in an isolated system, an important expression is derived which gives the total densities of energy and momentum in the form of a divergence. This expression is equivalent to one previously obtained by Einstein but on account of the starting point adopted is derived and expressed in terms of the quantities gμν and gαμν instead of the gμν and gαμν. Following this, the limiting values at large distances from an isolated material system are obtained for the quantities gαβ∂L/∂gγαβ and gα4∂L/∂gγα4. These values, which have considerable use, have not previously received explicit expression. This is followed by a deduction from our present starting point of Einstein's famous relation U=m between the energy and gravitational producing mass of an isolated system. An important expression is then obtained which gives the energy of a quasi-static isolated system in the form of an integral which has to be extended only over the portion of space actually occupied by matter or radiation. This expression has not previously received a satisfactory derivation. The result is used to obtain an expression for the energy of a spherical distribution of a perfect fluid, and it is then shown that this expression, in the case of a sphere of ordinary material, approaches in a sufficiently weak field to the classical expression for energy including the potential gravitational energy. This result is not only intrinsically useful, but also shows for a particular case that a higher order of approximation to the general relativity value for total energy is obtained by including the classical gravitational energy than by going at once to flat space-time as is often done. Finally, a general consideration is given to the problem of determining the conditions imposed on those changes from one static state to another which could occur in a non-isolated system forming part of a larger static system, without changing the distribution of matter and radiation outside the boundary and without contravening the energy-momentum principle as applied to the system as a whole.