The "universal property" of Horizon Entropy Sum of Black Holes in Four Dimensional Asymptotical (anti-)de-Sitter Spacetime Background

Understand

We present a new ``universal property'' of entropy, that is the ``entropy sum'' relation of black holes in four dimensional (anti-)de-Sitter asymptotical background.

• They depend only on the cosmological constant with the necessary effect of the un-physical ``virtual'' horizon included in the spacetime where only the cosmological constant, mass of black hole, rotation parameter and Maxwell field exist.
• When there is more extra matter field in the spacetime, one will find the ``entropy sum'' is also dependent of the strength of these extra matter field.
• For both cases, we conclude that the ``entropy sum'' does not depend on the conserved charges $M$, $Q$ and $J$, while it does depend on the property of background spacetime.