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arXiv · 1610.02519

Boundedness of the total energy of relativistic membranes evolving in a curved spacetime

Philippe G. LeFloch·Changhua Wei
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Abstract

We establish a global existence theory for the equation governing the evolution of a relativistic membrane in a (possibly curved) Lorentzian manifold, when the spacetime metric is a perturbation of the Minkowski metric. Relying on the Hyperboloidal Foliation Method introduced by LeFloch and Ma in 2014, we revisit a theorem established earlier by Lindblad (who treated membranes in the flat Minkowski spacetime) and we provide a simpler proof of existence, which is also valid in a curved spacetime and, most importantly, leads to the important property that the total energy of the membrane is globally bounded in time.

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Philippe G. LeFloch, Changhua Wei. 2016-10-08. Boundedness of the total energy of relativistic membranes evolving in a curved spacetime. https://arxiv.org/abs/1610.02519

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