The horizon of the McVittie black hole: on the role of the cosmic fluid modeling

Abstract

In this paper, we investigate the existence and time evolution of the cosmological and event horizons in a McVittie universe whose expansion is driven by the Redlich-Kwong, (Modified) Berthelot, Dieterici, and Peng-Robinson fluids, respectively. The equations of state of these fluids are rich enough to account for both exotic and regular, as well as ideal and non-ideal matter contents of the universe. We show that the cosmological horizon is expanding, while the event horizon is shrinking along the cosmic time evolution. The former achieves larger size for regular types of matter, contrary to the latter. The strength of interactions within the cosmic fluid are shown to play a more important role in affecting the evolution of the event horizon, rather than of the cosmological horizon in the case of a singularity-free universe. While the cosmological horizon always exists during the time evolution, the event horizon can exist only when a certain relationship between the Hawking-Hayward quasi-local mass and the Hubble function is fulfilled. In this manner, we can study the role played by the large-scale physics (cosmic evolution) on the local scale physics (evolution of a black hole).

Black holes and naked singularities from Anton–Schmidt’s fluids

“…To a first approximation, one can assume that the cosmic fluid evolves according to the Friedmann cosmology, and that the rate of increase/decrease of the mass of the black hole is directly proportional to the area of its surface and to the sum of energy and pressure of the dark fluid [51][52][53][54]. An improved treatment couples the evolution of the mass of the black hole to the evolution of the Universe adopting the McVittie metric, which does not require any ad hoc assumptions on the rate of energy exchange that is auto-matically implemented through the Einstein field equations [55].…”

The Hawking-Page-like Phase Transition from FRW Spacetime to McVittie Black Hole

“…If mH > 1/3 √ 3, the above equation ( 11) has one real negative root and another two complex roots, which are all obviously unphysical. Thus in this paper we assume that 0 < mH < 1/3 √ 3, then there are three real roots [8,12]…”

“…The McVittie spacetime usually contains a black hole horizon and a cosmological horizon, both of which are apparent horizons whose radii are time-dependent, and both can be studied from thermodynamic aspects. The geometrical properties of McVittie spacetime have already been discussed extensively [5][6][7][8][9][10][11][12][13], but on the contrary, its thermodynamic properties have rarely been studied. As far as we know, the unified first law of a dynamic and spherically symmetric spacetime was first proposed by Hayward [14] and was later applied to McVittie spacetime [15,16].…”

Searching for dynamical black holes in various theories of gravity

“…A few spherically symmetric solutions interpreted as genuine black holes embedded in Friedmann-Lemaître-Robertson-Walker (FLRW) universes are known in GR, beginning with the McVittie family 1 [19], which has been generalized [20,21] and has been the subject of much attention during the last decade [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38], also in the context of Hořava-Lifschitz and Horndeski gravity [39,40]. The phenomenology of apparent horizons can be rather bizarre and provides several surprises, such as horizons appearing and disappearing in pairs, as in the Husain-Martinez-Nuñez solution (a black hole embedded in a FLRW universe sourced by a free scalar field) [41].…”