I studied different black holes in different spacetime and I also checked their differences, for example, the difference that exists in dS and AdS spaces. The question that has been created for me is whether it is possible to change the space of black holes from dS to AdS or vice versa with just one sign change in the cosmological constant Λ . For example, if I change the sign of the last term of equation (2) f(R) of the (Thermodynamics of Accelerating Black Holes), will it be transformed into dS space? https://arxiv.org/abs/1604.08812
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$\begingroup$ Related post by OP: physics.stackexchange.com/q/749667/2451 $\endgroup$– Qmechanic ♦Commented Feb 14, 2023 at 12:27
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Simply changing the sign of cosmological constant in an expression for a metric should give a solution of Einstein equations for the new value of cosmological constant (and in particular, the Plebanski–Demianski family, to which accelerating black holes belong, exists for all values of cosmological constant). However, apriori there is no guarantee that such solution represents a black hole in an asymptotically de Sitter space and if it does, what ranges the other parameters of solution can assume. There is also no guarantee that coordinate patch obtained for that new metric expression would be sufficient to do analysis (e.g. of thermodynamic properties) one intends to do.
However, we could hope that a small black hole in AdS (black hole mass is much smaller then (A)dS length scale, $M\ll \ell$) would remain a small black hole in dS through such change of sign, yet even then we can be certain that the global structure of this new spacetime would be completely different.
