Black Hole Vacua and Rotation

Recent developments suggest that the near-region of rotating black holes behaves like a CFT. To understand this better, I propose to study quantum fields in this region. An instructive approach for this might be to put a large black hole in AdS and to think of the entire geometry as a toy model for the ``near-region". Quantum field theory on rotating black holes in AdS can be well-defined (unlike in flat space), if fields are quantized in the co-rotating-with-the-horizon frame. First, some generalities of constructing Hartle-Hawking Green functions in this approach are discussed. Then as a specific example where the details are easy to handle, I turn to 2+1 dimensions (BTZ), write down the Green functions explicitly starting with the co-rotating frame, and observe some structural similarities they have with the Kerr-CFT scattering amplitudes. Finally, in BTZ, there is also an alternate construction for the Green functions: we can start from the covering AdS_3 space and use the method of images. Using a 19th century integral formula, I show the equality between the boundary correlators arising via the two constructions.Comment: 25 pages, 3 figure

Hidden Conformal Symmetries of Five-Dimensional Black Holes

Recently it was shown by Castro, Maloney and Strominger (CMS) that 4D Kerr black holes have a "hidden" conformal symmetry. Using some old results of Cvetic and Larsen, I show that this result is very likely to hold also for the most general black holes in five dimensions arising from heterotic/type II string theory. In particular, we show how the wave equation in these geometries in the "near region" can be written in terms of SL(2,R) X SL(2,R) Casimirs. For the special case when the black hole has two spins but no U(1) charges, detailed matches for entropy and absorption cross sections between CFT and geometry are found. The black holes we consider need not be close to extremality.Comment: 12 pages; preprint no. and refs added, typos fixe

A Comment on Kerr-CFT and Wald Entropy

We point out that the entropies of black holes in general diffeomorphism invariant theories, computed using the Kerr-CFT correspondence and the Wald formula (as implemented in the entropy function formalism), need not always agree. A simple way to illustrate this is to consider Einstein-Gauss-Bonnet gravity in four dimensions, where the Gauss-Bonnet term is topological. This means that the central charge of Kerr-CFT computed in the Barnich-Brandt-Compere formalism remains the same as in Einstein gravity, while the entropy computed using the entropy function gives a universal correction proportional to the Gauss-Bonnet coupling. We argue that at least in this example, the Kerr-CFT result is the physically reasonable one. The resolution to this discrepancy might lie in a better understanding of boundary terms.Comment: 11 pages, v2,3: refs added, minor change

A Kaluza-Klein Subttractor

We generalize the results of arXiv:1212.1875 and arXiv:1212.6919 on attraction basins and their boundaries to the case of a specific class of rotating black holes, namely the ergo-free branch of extremal black holes in Kaluza-Klein theory. We find that exact solutions that span the attraction basin can be found even in the rotating case by appealing to certain symmetries of the equations of motion. They are characterized by two asymptotic parameters that generalize those of the non-rotating case, and the boundaries of the basin are spinning versions of the (generalized) subttractor geometry. We also give examples to illustrate that the shape of the attraction basin can drastically change depending on the theory.Comment: 20 pages, 5 figure

Chiral Higher Spin Gravity

We construct a candidate for the most general chiral higher spin theory with AdS$_3$ boundary conditions. In the Chern-Simons language, on the left it has the Drinfeld-Sokolov reduced form, but on the right all charges and chemical potentials are turned on. Altogether (for the spin-3 case) these are $19$ functions. Despite this, we show that the resulting metric has the form of the "most general" AdS$_3$ boundary conditions discussed by Grumiller and Riegler. The asymptotic symmetry algebra is a product of a $\mathcal{W}_3$ algebra on the left and an affine $sl(3)_k$ current algebra on the right, as desired. The metric and higher spin fields depend on all the $19$ functions. We compare our work with previous results in the literature.Comment: v2: refs added, minor correction

Subttractors

We consider extremal limits of the recently constructed "subtracted geometry". We show that extremality makes the horizon attractive against scalar perturbations, but radial evolution of such perturbations changes the asymptotics: from a conical-box to flat Minkowski. Thus these are black holes that retain their near-horizon geometry under perturbations that drastically change their asymptotics. We also show that this extremal subtracted solution ("subttractor") can arise as a boundary of the basin of attraction for flat space attractors. We demonstrate this by using a fairly minimal action (that has connections with STU model) where the equations of motion are integrable and we are able to find analytic solutions that capture the flow from the horizon to the asymptotic region. The subttractor is a boundary between two qualitatively different flows. We expect that these results have generalizations for other theories with charged dilatonic black holes.Comment: 21 pages, 2 figure

Higher Spin Resolution of a Toy Big Bang

Diffeomorphisms preserve spacetime singularities, whereas higher spin symmetries need not. Since three dimensional de Sitter space has quotients that have big-bang/big-crunch singularities and since dS_3-gravity can be written as an SL(2,C) Chern-Simons theory, we investigate SL(3,C) Chern-Simons theory as a higher-spin context in which these singularities might get resolved. As in the case of higher spin black holes in AdS_3, the solutions are invariantly characterized by their holonomies. We show that the dS_3 quotient singularity can be de-singularized by an SL(3,C) gauge transformation that preserves the holonomy: this is a higher spin resolution the cosmological singularity. Our work deals exclusively with the bulk theory, and is independent of the subtleties involved in defining a CFT_2 dual to dS_3 in the sense of dS/CFT.Comment: v2-v3: typos removed, refs added. v4: minor improvements, Phys Rev D version, v5: one more typo fixed, footnote adde

A Neumann Boundary Term for Gravity

The Gibbons-Hawking-York (GHY) boundary term makes the Dirichlet problem for gravity well defined, but no such general term seems to be known for Neumann boundary conditions. In this paper, we view Neumann {\em not} as fixing the normal derivative of the metric ("velocity") at the boundary, but as fixing the functional derivative of the action with respect to the boundary metric ("momentum"). This leads directly to a new boundary term for gravity: the trace of the extrinsic curvature with a specific dimension-dependent coefficient. In three dimensions this boundary term reduces to a "one-half" GHY term noted in the literature previously, and we observe that our action translates precisely to the Chern-Simons action with no extra boundary terms. In four dimensions the boundary term vanishes, giving a natural Neumann interpretation to the standard Einstein-Hilbert action without boundary terms. We argue that in light of AdS/CFT, ours is a natural approach for defining a "microcanonical" path integral for gravity in the spirit of the (pre-AdS/CFT) work of Brown and York.Comment: v3: emphasized that a covariant notion of Neumann boundary condition inevitably leads to our boundary term. v4: more ref