Are ultra-spinning Kerr-Sen-AdS4 black holes always super-entropic ?
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-AdS4 solutions. We show that this ultra-spinning Kerr-Sen-AdS4 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-AdS4 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 (me ≥slant 8l/27 with l being the cosmological scale) both for the extremal ultra-spinning Kerr-Sen-AdS4 black hole and for the extremal super-entropic Kerr-Newman-AdS4 case, the former has a maximal horizon radius: r\, HP = l/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 .