Super-entropic black holes and the Kerr-CFT correspondence

Journal of High Energy Physics, Aug 2016

Abstract We demonstrate that Kerr-CFT duality can be extended to super-entropic black holes, which have non-compact horizons with finite area. We demonstrate that this duality is robust insofar as the ultra-spinning limit of a Kerr-AdS black hole (which yields the super-entropic class) commutes with the near-horizon limit (which yields the Kerr-CFT duality). Consequently the Bekenstein-Hawking and the CFT entropies are equivalent. We show that the duality holds for both singly-spinning super-entropic black holes in 4 dimensions and for doubly-spinning super-entropic black holes of gauged supergravity in 5 dimensions. In both cases we obtain not only the expected left/right temperatures, but also temperatures associated with electric charge and with a new thermodynamic parameter specific to super-entropic black holes.

A PDF file should load here. If you do not see its contents the file may be temporarily unavailable at the journal website or you do not have a PDF plug-in installed and enabled in your browser.

Alternatively, you can download the file locally and open with any standalone PDF reader:

https://link.springer.com/content/pdf/10.1007%2FJHEP08%282016%29148.pdf

Super-entropic black holes and the Kerr-CFT correspondence

HJE Super-entropic black holes and the Kerr-CFT Musema Sinamuli 0 1 2 3 Robert B. Mann 0 1 3 0 31 Caroline St., Waterloo , Ontario, N2L 2Y5 , Canada 1 200 University Ave., Waterloo , Ontario N2L 3G1 , Canada 2 Perimeter Institute for Theoretical Physics 3 Department of Physics and Astronomy, University of Waterloo We demonstrate that Kerr-CFT duality can be extended to super-entropic black holes, which have non-compact horizons with duality is robust insofar as the ultra-spinning limit of a Kerr-AdS black hole (which yields the super-entropic class) commutes with the near-horizon limit (which yields the Kerr-CFT duality). Consequently the Bekenstein-Hawking and the CFT entropies are equivalent. We show that the duality holds for both singly-spinning super-entropic black holes in 4 dimensions and for doubly-spinning super-entropic black holes of gauged supergravity in 5 dimensions. In both cases we obtain not only the expected left/right temperatures, but also temperatures associated with electric charge and with a new thermodynamic parameter speci c to super-entropic black holes. AdS-CFT Correspondence; Black Holes; Black Holes in String Theory; String Duality 1 Introduction 2 3 4 5 6 Super-entropic black holes of gauged supergravity Conclusion A Vanishing charge di erence between neighbouring metrics other intriguing results [2] have obtained since then. Recently a new class of rotating black hole solutions was obtained from the KerrNewman-AdS metrics [8{10]. These black holes have been called super-entropic insofar as their entropy is larger than that expected from the reverse isoperimetric inequality conjecture [15], which states that the thermodynamic volume of a black hole provides an upper bound on its entropy. The basic idea of the procedure is to transform an azimuthal coordinate of a d-dimensional Kerr-AdS metric (written in rotating-at-in nity coordinates) and then take the limit as its associated rotation parameter approaches the AdS length. The new azimuthal coordinate is then compacti ed, yielding a black hole whose horizon is topologically a (d 2)-sphere with two punctures. These black holes form a new ultraspinning limit of the Kerr-AdS class of metrics, and possess a non-compact event horizon of nite area (and hence nite entropy), the rst example of such objects in the literature to date. The purpose of this paper is to study the Kerr-CFT correspondence for super-entropic black holes. It is not a-priori obvious that the correspondence exists, given the noncompactness of their event horizons; as we shall see some but not all super-entropic black holes exhibit this correspondence. We will consider speci cally the superentropic limit of singly-spinning Kerr-Newmann-AdS black holes in d dimensions [10] as well as the ultraspinning d = 5 black holes of minimal gauged supergravity [11, 14]. Similar studies of Kerr-Newman-AdS black holes [2] found that there exists a correspondence between the { 1 { extremal versions of these black holes and a d = 2 (chiral half of a) CFT at its boundary. A key feature of these metrics is that in their near-horizon (NH) limits, the resultant metrics acquire a new form that has an extended asymptotic symmmetry group (ASG) whose generators depend strongly on the boundary conditions imposed. These boundary conditions have to be chosen in such a way that the charges associated with the di eomorphisms preserving them satisfy a number of conditions such as niteness, integrability and so on. These constraints ensure the existence of the charges (generators of di eomorphisms); indeed, the consistency of the theory relies on them. Ignoring these constraints will certainly lead to ill-de ned di eomorphism generators from which no physics can be deduced. Moreover, the boundary conditions allow us to compute the central charges that stem from the Virasoro algebra satis ed by the charges associated with the di eomorphisms preserving the boundary conditions. Once obtained, the central charges yield the CFT entropy SCFT via the Cardy formula, which is expected to be identical to the BekensteinHawking S entropy of the black hole, thereby establishing the correspondence. It is not a-priori obvious that super-entropic black holes admit such a correspondence, given their properties. It is the purpose of this paper to demonstrate that such a correspondence exists and indeed is robust. Our paper is organised as follows. In section two, we provide a brief review of the super-entropic black hole, highlighting its thermodynamic quantities and its relationship to the Smarr relation and the reverse isoperimetric inequality. In section three, we review the Kerr-CFT correspondence for Kerr-AdS black holes, along with the choice of boundary conditions. We then consider the Super-entropic-CFT correspondence, beginning with a Kerr-Newman-AdS black hole and taking both its super-entropic and near horizon limits in either order, and obtain the same results in either case. In sectio (...truncated)


This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1007%2FJHEP08%282016%29148.pdf

Musema Sinamuli, Robert B. Mann. Super-entropic black holes and the Kerr-CFT correspondence, Journal of High Energy Physics, 2016, pp. 148, Volume 2016, Issue 8, DOI: 10.1007/JHEP08(2016)148