Abstract
We propose a set of diffeomorphism that act non-trivially near the horizon of the Kerr black hole. We follow the recent developments of Haco-Hawking-Perry-Strominger to quantify this phase space, with the most substantial difference being our choice of vectors fields. Our gravitational charges are organized into a Virasoro-Kac-Moody algebra with non-trivial central extensions. We interpret this algebra as arising from a warped conformal field theory. Using the data we can infer from this warped CFT description, we capture the thermodynamic properties of the Kerr black hole.
Highlights
We will argue that a description of generic Kerr black holes in terms of a Warped Conformal Field Theories (WCFT) might appear as natural as a CFT2 one and, in particular, that it allows to reproduce the Bekenstein-Hawking entropy along the lines of [13]
We found evidence that a WCFT could be a suitable holographic description of the Kerr black hole
One notable aspect of our computation is that the contribution to the central extensions comes only from a component of the future horizon that is near the bifurcation surface at constant y
Summary
As we discuss physical observables in Kerr, one of our agenda points will be to exploit analytic properties of the black hole background. To motivate our later choices, we will review how analyticity, represented by monodromy data, enters in the structure of the Klein-Gordon equation [48, 49]. Equation (2.7) has two regular singular points at r = r+ and r = r−, which means that the solutions to (2.7) have branch cuts at these points. Unlike the singular points at r = r±, the singular point at r = ∞ is irregular This means that the series (2.12) is asymptotic rather than convergent. The true solution around this irregular point has a monodromy, αirr, which can be computed perturbatively in ω [49,50,51]. We will not interpret (2.18) as a basis for CFT2 energy eigenstates; instead we explore an alternative interpretation in terms of a WCFT description
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