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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.
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TL;DR: In this article, the positive energy argument of Geroch for time-symmetric initial data sets can be generalized to general initial data set and shown to be applicable to general data sets.
Abstract: We show that the positive energy argument of Geroch for time‐symmetric initial data sets can be generalized to general initial data sets
101 citations
TL;DR: In this article, the authors extend the validity of Dain's angularmomentum inequality to maximal, asymptotically flat, initial data sets on a simply connected manifold with several invariant under a U(1) action and which admit a twist potential.
101 citations
TL;DR: A nonlocal form of the effective gravitational action could cure the unboundedness of euclidean gravity with Einstein action as mentioned in this paper, which is compatible with all present tests of general relativity and post-Newtonian gravity.
Abstract: A nonlocal form of the effective gravitational action could cure the unboundedness of euclidean gravity with Einstein action. On sub-horizon length scales the modified gravitational field equations seem compatible with all present tests of general relativity and post-Newtonian gravity. They induce a difference in the effective Newtonian constant between regions of space with vanishing or nonvanishing curvature scalar (or Ricci tensor). In cosmology they may lead to a value Ω < 1 for the critical density after inflation. The simplest model considered here appears to be in conflict with nucleosynthesis, but generalizations consistent with all cosmological observations seem conceivable.
100 citations
01 Jan 1951
TL;DR: In this paper, the authors introduce a formula for the force density representing the action of the field on each body, i.e., force density is defined as a function of the influence of the interaction between two objects.
Abstract: A field theory has to describe quantitatively a certain type of interaction between material bodies The field equations alone will in general not be sufficient for this purpose Besides the field equations we have to postulate also the equations of motion of the material bodies under the influence of the interaction, ie we have to introduce a formula for the force density representing the action of the field on each body
99 citations
TL;DR: In this paper, it was shown that for generic static spacetimes with horizons, this highly symmetric form of the Einstein tensor leads quite naturally and generically to the interpretation of the near-horizon field equations as a thermodynamic identity.
Abstract: It is well known that, for a wide class of spacetimes with horizons, Einstein equations near the horizon can be written as a thermodynamic identity. It is also known that the Einstein tensor acquires a highly symmetric form near static, as well as stationary, horizons. We show that, for generic static spacetimes, this highly symmetric form of the Einstein tensor leads quite naturally and generically to the interpretation of the near-horizon field equations as a thermodynamic identity. We further extend this result to generic static spacetimes in Lanczos-Lovelock gravity, and show that the near-horizon field equations again represent a thermodynamic identity in all these models. These results confirm the conjecture that this thermodynamic perspective of gravity extends far beyond Einstein's theory.
99 citations