Dynamics of a self-gravitating shell of matter

Details Dynamics of a self-gravitating shell of matter Dynamics of a self-gravitating shell of matter

2005-07-18

arxiv.org/abs/gr-qc/0507074v2

Phys. Rev. D 72, 084015 (2005)

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

published

Scientific paper

10.1103/PhysRevD.72.084015

Dynamics of a self-gravitating shell of matter is derived from the Hilbert variational principle and then described as an (infinite dimensional, constrained) Hamiltonian system. A method used here enables us to define singular Riemann tensor of a non-continuous connection {\em via} standard formulae of differential geometry, with derivatives understood in the sense of distributions. Bianchi identities for the singular curvature are proved. They match the conservation laws for the singular energy-momentum tensor of matter. Rosenfed-Belinfante and Noether theorems are proved to be still valid in case of these singular objects. Assumption about continuity of the four-dimensional spacetime metric is widely discussed.

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