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)