Conformally Schwarzschild cosmological black holes

Abstract

We thoroughly investigate conformally Schwarzschild spacetimes in different coordinate systems to seek for physically reasonable models of a cosmological black hole. We assume that a conformal factor depends only on the time coordinate and that the spacetime is asymptotically flat Friedmann-Lema\^ıtre-Robertson-Walker universe filled by a perfect fluid obeying a linear equation state $p=w\rho$ with $w>-1/3$. In this class of spacetimes, the McClure-Dyer spacetime, constructed in terms of the isotropic coordinates, and the Thakurta spacetime, constructed in terms of the standard Schwarzschild coordinates, are identical and do not describe a cosmological black hole. In contrast, the Sultana-Dyer and Culetu classes of spacetimes, constructed in terms of the Kerr-Schild and Painlevé-Gullstrand coordinates, respectively, describe a cosmological black hole. In the Sultana-Dyer case, the corresponding matter field in general relativity can be interpreted as a combination of a homogeneous perfect fluid and an inhomogeneous null fluid, which is valid everywhere in the spacetime unlike Sultana and Dyer's interpretation. In the Culetu case, the matter field can be interpreted as a combination of a homogeneous perfect fluid and an inhomogeneous anisotropic fluid. However, in both cases, the total energy-momentum tensor violates all the standard energy conditions at a finite value of the radial coordinate in late times. As a consequence, the Sultana-Dyer and Culetu black holes for $-1/3<w\le 1$ cannot describe the evolution of a primordial black hole after its horizon entry.

58 pages, 10 figures, 8 tables; v3, this version corrects the published version according to the corrigendum (2023 Class. Quantum Grav. 40, 079501). The main results remain unchanged

References in corpus (8)

• Cosmological expansion and local physics
• McVittie's Legacy: Black Holes in an Expanding Universe
• Generalized Misner-Sharp quasi-local mass in Einstein-Gauss-Bonnet gravity
• Black Hole Evaporation in an Expanding Universe
• Foliation dependence of black hole apparent horizons in spherical symmetry
• Dynamical black holes with symmetry in Einstein-Gauss-Bonnet gravity
• The Hawking temperature of expanding cosmological black holes
• Conformal time dependent Painleve-Gullstrand spacetime

Cited by in corpus (3)

• Physical Features of Geometrically Deformed Anisotropic Charged Three-dimensional BTZ Black Holes
• Magnetized dynamical black holes
• Dynamical axisymmetric compact objects in General Relativity