Effects of cosmic acceleration on black hole thermodynamics

Direct local impacts of cosmic acceleration upon a black hole are matters of interest. Babichev et al. had published before that the Friedmann equations which are prevailing the part of fluid filled up in the universe to lead (or to be very specific, 'dominate') the other constituents of universe and are forcing the universe to undergo present-day accelerating phase (or to lead to violate the strong energy condition and latter the week energy condition), will themselves tell that the rate of change of mass of the central black hole due to such exotic fluid's accretion will essentially shrink the mass of the black hole. But this is a global impact indeed. The local changes in the space time geometry next to the black hole can be analysed from a modified metric governing the surrounding space time of a black hole. A charged de Sitter black hole solution encircled by quintessence field is chosen for this purpose. Different thermodynamic quantities are analysed for different values of quintessence equation of state parameter, omega(q). Specific jumps in the nature of the thermodynamic space near to the quintessence or phantom barrier are noted and physically interpreted as far as possible. Nature of phase transitions and the situations at which these transitions are taking place are also explored. It is determined that before quintessence starts to work (omega(q) = -0.33 > -1/3) it was preferable to have a small unstable black hole followed by a large stable one. But in quintessence (-1/3 > omega(q) > -1), black holes are des-tined to be unstable large ones pre-quelled by stable/unstable small/intermediate mass black holes.