Spherically symmetric solutions in a FRW background

Abstract

We impose perfect fluid concept along with slow expansion approximation to derive new solutions which, considering non-static spherically symmetric metrics, can be treated as Black Holes (BHs). We will refer to these solutions as Quasi BHs. Mathematical and physical features such as Killing vectors, singularities, and mass have been studied. Their horizons and thermodynamic properties have also been investigated. In addition, relationship with other related works (including McVittie's) are described

Thermodynamic motivations of spherically symmetric static metrics

“…let us calculate the Gong-Wang mass for this metric which yields M gw (r) = r − M ms indicating that both of the Misner-Sharp and Gong-Wang mass definitions point to the same value if we evaluate the mass confined to the r = 2M ms radii. Once again, we see that both of these definitions estimate the same value for the mass confined to the horizon which is in agreement with attempts in which the dynamic black holes have been studied [60,61]. Therefore, as the previous case, r = 2M ms may be considered as a boundary for the system.…”

“…By using (2) one gets M ms (r) = r − M gw and thus M ms = M gw whiles r = 2M gw , telling us that both of these mass definitions lead to the same value if we evaluate the mass confined to the null hypersurface with radii r = 2M gw . This mutual consistency between the results of using either the Gong-Wang or Misner-Sharp masses in order to evaluate the energy confined to a null hypersurface is in line with the dynamic situations [60,61]. It is useful to note here that the adiabatic condition together with the Gong-Wang definition of mass helped us to get an expression for g rr leading to relations for the Gong-Wang and Misner-Sharp masses.…”

“…In addition, they proposed a new definition for mass in spherically symmetric spacetimes (Gong-Wang) which leads to the same value as that of Misner-Sharp if one evaluates the mass confined to the apparent horizon of FRW metric. It is also shown that, for non-static spherically symmetric metrics describing an object embedded in the FRW background, the Gong-Wang definition of mass may lead to the same value as that of the Misner-Sharp definition for energy [61].…”

Dynamic black holes in an FRW background: Lemaître transformations

“…Using perfect fluid concept in a non-static spherically symmetric background and and considering the universe expansion, one can find solutions including constant mass, charge and cosmological constant [14]. On one hand, the curvature scalars diverge on the redshift singularity as the Mcvittie spacetime.…”

“…Finally, like the Mcvittie spacetime and its generalizations, it seems that these solutions are not suitable for studying dynamical BHs. Indeed, these two class of solutions may contain naked singularity which attracted more attempts to itself, since it was shown that the naked singularity can be considered as a possible source for gravitational lansing in astrophysical observations [14][15][16]. More studies in which the prefect fluid concept is used to derive the dynamic spherically symmetric solutions can be found in Refs.…”