Cardy-Verlinde Formula and asymptotically flat rotating Charged black holes

TL;DR

This paper extends the Cardy-Verlinde formula to various asymptotically flat rotating charged black holes in Einstein-Maxwell and string theories, analyzing their entropy bounds and revealing tighter bounds than Bekenstein's in some cases.

Contribution

It generalizes the Cardy-Verlinde formula to several black hole solutions and explores their entropy bounds, including new unified expressions and tighter bounds than Bekenstein's.

Findings

The Cardy-Verlinde formula is adapted to Kerr-Newman, EMDA, Kaluza-Klein, and Sen black holes.

The entropy bounds for Kaluza-Klein and Sen black holes are tighter than Bekenstein's bound.

Unified entropy bounds are derived for EMDA, Kaluza-Klein, and Sen black holes.

Abstract

The Cardy-Verlinde formula is generalized to the asymptotically flat rotating charged black holes in the Einstein-Maxwell theory and low-energy effective field theory describing string by using some typical spacetimes, such as the Kerr-Newman, Einstein-Maxwell-dilaton-axion, Kaluza-Klein, and Sen black holes. For the Kerr-Newman black hole, the definition of the Casimir energy takes the same form as that of the Kerr-Newman-AdS$_4$ and Kerr-Newman-dS$_4$ black holes, while the Cardy-Verlinde formula possesses different from since the Casimir energy does not appear in the extensive energy. The Einstein-Maxwell-dilaton-axion, Kaluza-Klein, and Sen black holes have special property: The definition of the Casimir energy for these black holes is similar to that of the Kerr-Newman black hole, but the Cardy-Verlinde formula takes the same form as that of the Kerr black hole. Furthermore, we also study the entropy bounds for the systems in which the matters surrounds these black holes. We find that the bound for the case of the Kerr-Newman black hole is related to its charge, and the bound for the cases of the EMDA, Kaluza-Klein, and Sen black holes can be expressed as a unified form. A surprising result is that the entropy bounds for the Kaluza-Klein and Sen black holes are tighter than the Bekenstein one.