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).
Highlights
Neglecting the presence of matter in its proximity, the Kerr solution cannot provide any possible mechanism for the formation of an accretion disk around the central massive source [1,2], whose existence instead has been established from the study of active galactic nuclei [3] and of the jets emitted by the particles falling into it [4]
The Kerr solution does not take into account that the black hole should live inside a Universe which, according to the current standard model of cosmology ( -Cold Dark Matter model or CDM in short), expand in time and it is not empty but dominated by some form of dark energy which is taken to be a cosmological constant in the simplest scenario [12]
The physics accounting for the existence of black holes and the one explaining the global evolution of the Universe may seem unrelated at first sight because the former involves physics at relatively small scale, while the latter focuses on large scale effects
Summary
Neglecting the presence of matter in its proximity, the Kerr solution cannot provide any possible mechanism for the formation of an accretion disk around the central massive source [1,2], whose existence instead has been established from the study of active galactic nuclei [3] and of the jets emitted by the particles falling into it [4]. The Kerr solution does not take into account that the black hole should live inside a Universe which, according to the current standard model of cosmology ( -Cold Dark Matter model or CDM in short), expand in time and it is not empty but dominated by some form of dark energy which is taken to be a cosmological constant in the simplest scenario [12] Along this line of thinking, one can adopt the Schwarzschild-(anti-)de Sitter metric for describing a spherically symmetric black hole embedded in a spacetime whose matter–energy is given by the cosmological constant [13].
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