Introduction to the mathematics of general relativity

About: Introduction to the mathematics of general relativity is a research topic. Over the lifetime, 2583 publications have been published within this topic receiving 73295 citations.

Static Axisymmetric Interior Solution in General Relativity

Abstract: A class of static, axisymmetric, interior solutions of Einstein's field equations in general relativity is obtained. The solutions are physically reasonable, and can be interpreted as sources for Weyl and Levi-Civita's general exterior solution that is flat at infinity, by making the metric components and their derivatives continuous at the boundary of the matter. For a particular model, a correlation is exhibited between the structure of the source material and the exterior field, which resembles closely, but not exactly, that of the corresponding Newtonian model.

Scalar plane waves in general relativity

Abstract: A number of exact solutions of Einstein's equations are obtained, which describe the collisions between one scalar plane wave and one scalar, neutrino, electromagnetic or gravitational plane wave.

The fluctuation spectra around a Gaussian classical solution of a tensor model and the general relativity

Abstract: Tensor models can be interpreted as theory of dynamical fuzzy spaces. In this paper, I study numerically the fluctuation spectra around a Gaussian classical solution of a tensor model, which represents a fuzzy flat space in arbitrary dimensions. It is found that the momentum distribution of the low-lying low-momentum spectra is in agreement with that of the metric tensor modulo the general coordinate transformation in the general relativity at least in the dimensions studied numerically, i.e. one to four dimensions. This result suggests that the effective field theory around the solution is described in a similar manner as the general relativity.

Mysteries of R ik = 0: A novel paradigm in Einstein's theory of gravitation

Abstract: Despite a century-long effort, a proper energy-stress tensor of the gravitational field, could not have been discovered. Furthermore, it has been discovered recently that the standard formulation of the energy-stress tensor of matter, suffers from various inconsistencies and paradoxes, concluding that the tensor is not consistent with the geometric formulation of gravitation [Astrophys. Space Sci., 2009, 321: 151; Astrophys. Space Sci., 2012, 340: 373]. This perhaps hints that a consistent theory of gravitation should not have any bearing on the energy-stress tensor. It is shown here that the so-called “vacuum” field equations R ik = 0 do not represent an empty spacetime, and the energy, momenta and angular momenta of the gravitational and the matter fields are revealed through the geometry, without including any formulation thereof in the field equations. Though, this novel discovery appears baffling and orthogonal to the usual understanding, is consistent with the observations at all scales, without requiring the hypothetical dark matter, dark energy or inflation. Moreover, the resulting theory circumvents the long-standing problems of the standard cosmology, besides explaining some unexplained puzzles.

A New Perspective on Relativity: An Odyssey in Non-Euclidean Geometries

Abstract: A Brief History of Relativity, Light, and Gravity Which Geometry? The Origins of Mass Relativity of Thermodynamics The 'General' Theory Short-Circuited Relativity of Hyperbolic Space Nonequivalence of Gravitation and Acceleration Aberration and Radiation Pressure in the Klein and Poincare Models The Inertia of Polarization.