Generalization of McVittie’s model for an inhomogeneity in a cosmological spacetime

Matteo Carrera and Domenico Giulini
Phys. Rev. D 81, 043521 – Published 11 February 2010

Abstract

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 a vanishing electric charge and angular momentum in an environment that asymptotically tends to a Friedmann-Lemaître-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.

  • Received 24 August 2009

DOI:https://doi.org/10.1103/PhysRevD.81.043521

©2010 American Physical Society

Authors & Affiliations

Matteo Carrera*

  • Institute of Physics, University of Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg, Germany

Domenico Giulini

  • University of Hannover, Appelstrasse 2, D-30167 Hannover, Germany‡

  • *matteo.carrera@physik.uni-freiburg.de
  • domenico.giulini@itp.uni-hannover.de
  • Also at: ZARM, University of Bremen, Am Fallturm D-28359 Bremen, Germany.

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Issue

Vol. 81, Iss. 4 — 15 February 2010

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