The characteristic initial value problem for plane symmetric spacetimes with weak regularity - General Relativity and Quantum CosmologyReportar como inadecuado




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Abstract: We investigate the existence and the global causal structure of planesymmetric spacetimes with weak regularity when the matter consists of anirrotational perfect fluid with pressure equal to its mass-energy density. Ourtheory encompasses the class of weakly regular spacetimes whose metriccoefficients have square-integrable first-order derivatives and whose curvaturemust be understood in the sense of distributions. We formulate thecharacteristic initial value problem with data posed on two null hypersurfacesintersecting along a two-plane. Relying on Newman-Penrose-s formalism andexpressing our weak regularity conditions in terms of the Newman-Penrosescalars, we arrive at a fully geometrical formulation in which, along eachinitial hypersurface, two scalar fields describing the incoming radiation mustbe prescribed. To analyze the future boundary of such a spacetime and identifyits global causal structure, we introduce a gauge that reduces the Einsteinequations to a coupled system of wave equations and ordinary differentialequations for well-chosen unknowns. We prove that, within the weak regularityclass under consideration and for generic initial data, a true spacetimesingularity forms in finite proper time. Our formulation is robust enough sothat propagating discontinuities in the curvature or in the matter variables donot prevent us from constructing a spacetime whose curvature genericallyblows-up on the future boundary. Earlier work on the problem studied here wasrestricted to sufficiently regular and vacuum spacetimes.



Autor: Philippe G. LeFloch, John M. Stewart

Fuente: https://arxiv.org/







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