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ESTIMATES FOR THE VOLUME OF A LORENTZIAN MANIFOLD

Claus Gerhardt

Open publisher page 6 citations

Abstract

Abstract. We prove new estimates for the volume of a Lorentzian manifold and show especially that cosmological spacetimes with crushing singularities have finite volume. Let N be a (n+1)-dimensional Lorentzian manifold and suppose that N can be decomposed in the form (0.1) N = N0 ∪ N − ∪ N+, where N0 has finite volume and N − resp. N+ represent the critical past

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What this paper is about

Abstract. We prove new estimates for the volume of a Lorentzian manifold and show especially that cosmological spacetimes with crushing singularities have finite volume. Let N be a (n+1)-dimensional Lorentzian manifold and suppose that N can be decomposed in the form (0.1) N = N0 ∪ N − ∪ N+, where N0 has finite volume and N − resp. N+ represent the critical past

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Available abstract

Abstract. We prove new estimates for the volume of a Lorentzian manifold and show especially that cosmological spacetimes with crushing singularities have finite volume. Let N be a (n+1)-dimensional Lorentzian manifold and suppose that N can be decomposed in the form (0.1) N = N0 ∪ N − ∪ N+, where N0 has finite volume and N − resp. N+ represent the critical past

Key concepts: Physics, Manifold (fluid mechanics), Gravitational singularity, Differential geometry, Volume (thermodynamics), Finite volume method, Mathematical physics, Theoretical physics

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