Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-08-21
Phys.Rev.D81:043521,2010
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
LaTeX (RevTeX), 15 pages, no figure
Scientific paper
10.1103/PhysRevD.81.043521
McVittie's spacetime is a spherically symmetric solution to Einstein's equation with an energy-momentum tensor of a perfect fluid. It describes the external field of a single quasi-isolated object with vanishing electric charge and angular momentum in an environment that asymptotically tends to a Friedmann--Lemaitre--Robertson--Walker universe. We critically discuss some recently proposed generalizations of this solution, in which radial matter accretion as well as heat currents are allowed. We clarify the hitherto unexplained constraints between these two generalizing aspects as being due to a geometric property, here called spatial Ricci-isotropy, which forces solutions covered by the McVittie ansatz to be rather special. We also clarify other aspects of these solutions, like whether they include geometries which are in the same conformal equivalence class as the exterior Schwarzschild solution, which leads us to contradict some of the statements in the recent literature.
Carrera Matteo
Giulini Domenico
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