Topic
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.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper, a new algorithm was developed to find the exact solutions of the Einstein's field equations, and the singularities of the time-periodic solutions were investigated and some new physical phenomena, such as degenerate event horizon and time periodic event horizon, were found.
Abstract: In this paper, we develop a new algorithm to find the exact solutions of the Einstein’s field equations. Time-periodic solutions are constructed by using the new algorithm. The singularities of the time-periodic solutions are investigated and some new physical phenomena, such as degenerate event horizon and time-periodic event horizon, are found. The applications of these solutions in modern cosmology and general relativity are expected.
17 citations
TL;DR: The main idea is to include the spin as a thermodynamic variable in the theory to derive the equations of motion for a spinning fluid in the Einstein-Cartan theory.
Abstract: Methods used earlier to derive the equations of motion for a spinning fluid in the Einstein-Cartan theory are specialized to the case of general relativity. The main idea is to include the spin as a thermodynamic variable in the theory.
17 citations
17 citations
TL;DR: In this article, it was shown that the standard ADM form, as well as some of its variations (including the most recent conformally-decomposed version), suffers from a certain but standard type of ill-posedness.
Abstract: It is shown that the formulation of the Einstein equations widely in use in numerical relativity, namely, the standard ADM form, as well as some of its variations (including the most recent conformally-decomposed version), suffers from a certain but standard type of ill-posedness. Specifically, the norm of the solution is not bounded by the norm of the initial data irrespective of the data. A long-running numerical experiment is performed as well, showing that the type of ill-posedness observed may not be serious in specific practical applications, as is known from many numerical simulations.
17 citations
Abstract: Positive energy density tends to limit the size of space. This effect is studied within several contexts. We obtain sufficient conditions (which involve the energy density in a crucial way) for the compactness of spatial hypersurfaces in space‐time. We then obtain some results concerning static or, more generally, stationary space‐times. The Schwarzchild solution puts an upper bound on the size of a static spherically symmetric fluid with density bounded from below. We derive a result of roughly the same nature which, however, requires no symmetry and allows for rotation. Also, we show that static or rotating universes with Λ = 0 require that the density along some spatial geodesic must fall off rapidly with distance from a point.
17 citations