Cosmological black holes and white holes with time-dependent mass

Abstract

We consider the causal structure of generalized uncharged McVittie spacetimes with increasing central mass $m(t)$ and positive Hubble factor $H(t)$. Under physically reasonable conditions, namely, a big bang singularity in the past, a positive cosmological constant and an upper limit to the central mass, we prove that the patch of the spacetime described by the cosmological time and areal radius coordinates is always geodesically incomplete, which implies the presence of event horizons in the spacetime. We also show that, depending on the asymptotic behavior of the $m$ and $H$ functions, the generalized McVittie spacetime can have a single black hole, a black-hole/white-hole pair or, differently from classic fixed-mass McVittie, a single white hole. A simple criterion is given to distinguish the different causal structures.

12 pages, 5 figures

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• Observational implications of cosmologically coupled black holes
• Black holes, white holes, and near-horizon physics
• Shadows of black holes at cosmological distances in the co-varying physical couplings framework
• A note on geodesics in inhomogeneous expanding spacetimes
• Feinberg-Horodecki States of Time-Dependent Mass Distribution Harmonic Oscillator
• Dynamical model for primordial black holes
• Dynamical black holes and accretion-induced backreaction
• Black-hole evaporation for cosmological observers
• Limits on the Inferred Hubble Constant Bias from a Local McVittie Gravitational Field