Smooth non-zero rest-mass evolution across time-like infinity

Friedrich, Helmut

doi:10.1007/s00023-014-0368-7

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Smooth non-zero rest-mass evolution across time-like infinity

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Friedrich, Helmut
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Friedrich, H. (2015). Smooth non-zero rest-mass evolution across time-like infinity. Annales Henri Poincare, 16, 2215-2238. doi:10.1007/s00023-014-0368-7.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0027-9F9F-6

Abstract

It is shown that solutions to Einstein's field equations with positive cosmological constant can include non-zero rest-mass fields which coexist with and travel unimpeded across a smooth conformal boundary. This is exemplified by the coupled Einstein-massive-scalar field equations for which the mass $m$ is related to the cosmological constant $\lambda$ by the relation $3\,m^2 = 2\,\lambda$. Cauchy data for the conformal field equations can in this case be prescribed on the (compact, space-like) conformal boundary ${\cal J}^+$. Their developments backwards in time induce a set of standard Cauchy data on space-like slices for the Einstein-massive-scalar field equations which is open in the set of all Cauchy data for this system.