An analysis of the Sultana-Dyer cosmological black hole solution of the Einstein equations

Charged black holes in expanding Einstein-de Sitter universes

Inspired in a previous work by McClure and Dyer (Classical Quantum Gravity 23, 1971 (2006)), we analyze some solutions of the Einstein-Maxwell equations which were originally written to describe charged black holes in cosmological backgrounds. A detailed analysis of the electromagnetic sources for a sufficiently general metric is performed, and then we focus on deriving the electromagnetic four-current as well as the conserved electric charge of each metric. The charged McVittie solution is revisited and a brief study of its causal structure is performed, showing that it may represent a charge…

Conformally Schwarzschild cosmological black holes

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 $p=wρ$ 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 coor…

The curious case of the Buchdahl-Land-Sultana-Wyman-Ibañez-Sanz spacetime

We revisit Wyman's "other" scalar field solution of the Einstein equations and its Sultana generalization to positive cosmological constant, which has a finite 3-space and corresponds to a special case of a stiff fluid solution proposed by Buchdahl and Land and, later, by Ibañez and Sanz to model relativistic stars. However, there is a hidden cosmological constant and the peculiar geometry prevents the use of this spacetime to model relativistic stars.

Wyman's "other" scalar field solution, Sultana's generalization, and their Brans-Dicke and $R^2$ relatives

Wyman's less known static and spherically symmetric solution of the Einstein-Klein-Gordon equations and its recent generalization for positive cosmological constant are discussed, showing that they contain central naked singularities. By mapping back to the Jordan frame, we obtain the conformal cousins of these geometries that solve the vacuum Brans-Dicke field equations and are time-dependent and spherical. Their physical nature is discussed and the geometry is shown to be also a solution of purely quadratic gravity.

Cosmological Effects on Black Hole Formation

The formation of cosmological black holes is investigated using the functional Schroedinger equation as observed by an asymptotic observer, assuming a spherical domain wall collapse process. The mass formula of the Sultana-Dyer black hole is derived using Israel's domain wall mathematical framework. This is used to examine the semi-classical and quantum nature of the collapsing domain wall in the general scale of an arbitrary scale factor, while ignoring evaporation and back reaction mass losses. Particular FLRW scale factors are then explored for black hole horizon formation times, all yieldi…

非最小耦合电磁场及其对原初黑洞的可观测效应

Non-minimally coupled electromagnetic fields and observable implications for primordial black holes

本文通过研究非最小耦合电磁场在Sultana–Dyer型原初黑洞与施瓦西黑洞中的传播特性，发现原初黑洞可用于约束非最小耦合参数，且特定质量原初黑洞的光子球存在高偏振可观测特征。

Temperature and thermodynamic structure of Einstein's equations for a cosmological black hole

It is expected that the cosmological black holes are the closest realistic solutions of gravitational theories and they evolve with time. Moreover, the natural way of defining thermodynamic entities for the stationary ones is not applicable in the case of a time dependent spacetime. Here we confine our discussion within the Sultana-Dyer metric which is a cosmological black hole solution of Einstein's gravity. In literature, there exists two expressions of horizon temperature -- one is time dependent and the other does not depend on time. To single out the correct one we find the temperature by…

Conformal Transformation, Near Horizon Symmetry, Virasoro Algebra and Entropy

There are certain black hole solutions in general relativity (GR) which are conformally related to the stationary solutions in GR. It is not obvious that the horizon entropy of these spacetimes is also one quarter of the area of horizon, like the stationary ones. Here I study this topic in the context of Virasoro algebra and Cardy formula. Using the fact that the conformal spacetime admits conformal Killing vector and the horizon is determined by the vanishing of the norm of it, the diffemorphisms are obtained which keep the near horizon structure invariant. The Noether charge and a bracket am…

Black Hole Evaporation in an Expanding Universe

We calculate the quantum radiation power of black holes which are asymptotic to the Einstein-de Sitter universe at spatial and null infinities. We consider two limiting mass accretion scenarios, no accretion and significant accretion. We find that the radiation power strongly depends on not only the asymptotic condition but also the mass accretion scenario. For the no accretion case, we consider the Einstein-Straus solution, where a black hole of constant mass resides in the dust Friedmann universe. We find negative cosmological correction besides the expected redshift factor. This is given in…

The theory of stochastic cosmological lensing

On the scale of the light beams subtended by small sources, e.g. supernovae, matter cannot be accurately described as a fluid, which questions the applicability of standard cosmic lensing to those cases. In this article, we propose a new formalism to deal with small-scale lensing as a diffusion process: the Sachs and Jacobi equations governing the propagation of narrow light beams are treated as Langevin equations. We derive the associated Fokker-Planck-Kolmogorov equations, and use them to deduce general analytical results on the mean and dispersion of the angular distance. This formalism is …