Are ultra-spinning Kerr-Sen-AdS$_4$ black holes always super-entropic ?

TL;DR

This paper investigates the thermodynamics of ultra-spinning Kerr-Sen-AdS4 black holes, revealing that unlike super-entropic Kerr-Newman-AdS4 black holes, their isoperimetric ratio can vary around unity, indicating diverse entropic properties.

Contribution

It derives new mass formulae and shows that ultra-spinning Kerr-Sen-AdS4 black holes do not always violate the Reverse Isoperimetric Inequality, unlike their super-entropic counterparts.

Findings

Ultra-spinning Kerr-Sen-AdS4 black holes can satisfy or violate the RII depending on parameters.

Both black holes share similar horizon geometry but differ in entropic properties.

Extremal ultra-spinning Kerr-Sen-AdS4 black holes have a maximum horizon radius, unlike super-entropic cases.

Abstract

We study thermodynamics of the four-dimensional Kerr-Sen-AdS black hole and its ultra-spinning counterpart, and verify that both black holes fullfil the first law and Bekenstein-Smarr mass formulae of black hole thermodynamics. Furthermore, we derive new Christodoulou-Ruffini-like squared-mass formulae for the usual and ultra-spinning Kerr-Sen-AdS$_4$ solutions. We show that this ultra-spinning Kerr-Sen-AdS$_4$ black hole does not always violate the Reverse Isoperimetric Inequality (RII) since the value of the isoperimetric ratio can be larger/smaller than, or equal to unity, depending upon where the solution parameters lie in the parameters space. This property is obviously different from that of the Kerr-Newman-AdS$_4$ super-entropic black hole, which always strictly violates the RII, although both of them have some similar properties in other aspects, such as horizon geometry and conformal boundary. In addition, it is found that while there exists the same lower bound on mass ($m_e \geqslant 8l/\sqrt{27}$ with $l$ being the cosmological scale) both for the extremal ultra-spinning Kerr-Sen-AdS$_4$ black hole and for the extremal super-entropic Kerr-Newman-AdS$_4$ case, the former has a maximal horizon radius: $r_{\rm\, HP} = l/\sqrt{3}$ which is the minimum of the latter. Therefore, these two different kinds of four-dimensional ultra-spinning charged AdS black holes exhibit some significant physical differences .