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arXiv · 1810.00436

The $\Lambda$ to zero limit of spacetimes and its physical interpretation

Mark Bugden·Claudio Paganini
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Abstract

We study the $\Lambda \to 0$ behaviour of Schwarzschild-de Sitter spacetime and show, according to Geroch's notion of spacetime limits, that it converges to the Schwarzschild spacetime. We use an embedding into $AdS_3$ to illustrate and quantify this limiting behaviour. We use these quantitative observations to establish a hierarchy of validity between the Einstein-de Sitter equations and the Einstein equations (and therefore in a weak field limit also Newton's equations), analogous to the quantum-classical limit when taking $\hbar \to 0$.

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Mark Bugden, Claudio Paganini. 2018-09-30. The $\Lambda$ to zero limit of spacetimes and its physical interpretation. https://doi.org/10.1088/1361-6382/aaff0d

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