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Stationary spacetime
About: Stationary spacetime is a research topic. Over the lifetime, 1385 publications have been published within this topic receiving 29671 citations.
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TL;DR: The Einstein equation is derived from the form of black hole entropy together with the fundamental relation $\delta Q=TdS$ connecting heat, entropy, and temperature, and its validity is seen to depend on the existence of local equilibrium conditions.
Abstract: The Einstein equation is derived from the proportionality of entropy and the horizon area together with the fundamental relation $\ensuremath{\delta}Q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}T\mathrm{dS}$. The key idea is to demand that this relation hold for all the local Rindler causal horizons through each spacetime point, with $\ensuremath{\delta}Q$ and $T$ interpreted as the energy flux and Unruh temperature seen by an accelerated observer just inside the horizon. This requires that gravitational lensing by matter energy distorts the causal structure of spacetime so that the Einstein equation holds. Viewed in this way, the Einstein equation is an equation of state.
2,363 citations
TL;DR: In this article, the authors propose spacetime uncertainty relations motivated by Heisenberg's uncertainty principle and by Einstein's theory of classical gravity, which is described by a non-commutative algebra whose commutation relations do imply our uncertainty relations.
826 citations
TL;DR: In this paper, a method is described for constructing, from any source-free solution of Einstein's equations which possesses a Killing vector, a one-parameter family of new solutions.
Abstract: A method is described for constructing, from any source‐free solution of Einstein's equations which possesses a Killing vector, a one‐parameter family of new solutions. The group properties of this transformation are discussed. A new formalism is given for treating space‐times having a Killing vector.
682 citations
TL;DR: In this paper, the authors study the quantization of free massive fields with spin 1 and 2 in the expanding part of de Sitter spacetime and find that the square of the mass M2 cannot be between 0 (linearized gravity) and 23 × (cosmological constant) in the spin-2 case.
576 citations
TL;DR: The results suggest that AdS space is unstable under arbitrarily small generic perturbations, and it is conjecture that this instability is triggered by a resonant mode mixing which gives rise to diffusion of energy from low to high frequencies.
Abstract: We study the nonlinear evolution of a weakly perturbed anti-de Sitter (AdS) space by solving numerically the four-dimensional spherically symmetric Einstein-massless-scalar field equations with negative cosmological constant. Our results suggest that AdS space is unstable under arbitrarily small generic perturbations. We conjecture that this instability is triggered by a resonant mode mixing which gives rise to diffusion of energy from low to high frequencies.
533 citations