D-bound and Bekenstein bound for McVittie solution surrounded by dark energy cosmological fields

Abstract

The cosmological candidate fields for dark energy as quintessence, phantom and cosmological constant are studied in terms of an entropic hypothesis imposed on the McVittie solution surrounded by dark energy. We certify this hypothesis as "D-bound-Bekenstein bound identification" for dilute systems and use it as a criterion to determine which candidate of dark energy can satisfy this criterion for a dilute McVittie solution. It turns out that only the cosmological constant can pass this criterion successfully while the quintessence and phantom fields fail, as non-viable dark energy fields for this particular black hole solution. Moreover, assuming this black hole to possess the saturated entropy, the entropy-area law and the holographic principle can put two constraints on the radius R of the cosmological horizon. The first one shows that the Hubble radius is discrete such that for any arbitrary value of the black hole mass m 0 , the value of R is determined up to an integer number. The latter one shows that when a black hole is immersed in a cosmological background, the radius of the cosmological horizon is constrained as R < 1 H .

D-bound and the Bekenstein bound for the surrounded Vaidya black hole

“…It seems that by implementation of a thermodynamical criterion, namely the identification of the D-bound and the Bekenstein bound, on the Vaidya black hole solution surrounded by cosmological fields, one may exclude the quintessence and phantom fields and just keep the cosmological constant as the single field for which the D-bound and the Bekenstein bound are exactly identified. 2 We have studied the same thermodynamical criterion on the other known dynamical black hole solutions surrounded by cosmological fields and observed that the cosmological constant is preferred as the viable cosmological field rather than the other known cosmological fields [61,62]. In [62], the hypothesis of the "D-bound-Bekenstein bound identification" has been applied for the McVittie solution surrounded by cosmological fields in the dilute limit and it has been indicated that this criterion is only true for the cosmological constant field as a candidate for the dark energy, and the other cosmological fields, such as phantom and quintessence fields, do not satisfy this criterion.…”

“…2 We have studied the same thermodynamical criterion on the other known dynamical black hole solutions surrounded by cosmological fields and observed that the cosmological constant is preferred as the viable cosmological field rather than the other known cosmological fields [61,62]. In [62], the hypothesis of the "D-bound-Bekenstein bound identification" has been applied for the McVittie solution surrounded by cosmological fields in the dilute limit and it has been indicated that this criterion is only true for the cosmological constant field as a candidate for the dark energy, and the other cosmological fields, such as phantom and quintessence fields, do not satisfy this criterion. Also in [61] the same criterion is applied for the universe system and the universe-black hole system, which is dominated by quintessence, phantom or cosmological constant fields.…”

A study of McVittie Spacetime in Stationary and Dynamical Regime

“…The study of the dark energy era in the McVittie universe has also brought the interest to researchers. [ 40 ] If in Equation () it is found that $$\dot{r}_{0}&gt;0$$, then w must be greater than −1 and it indicates that the regime is dark energy dominated as in the present universe. Therefore, it may be said that the dark energy dominated era arises when the stationary point moves away of the black hole, or in other words, when the r 0 is shifted towards the cosmological horizon.…”