Aaron J. Amsel

No Dynamics in the Extremal Kerr Throat

Motivated by the Kerr/CFT conjecture, we explore solutions of vacuum general relativity whose asymptotic behavior agrees with that of the extremal Kerr throat, sometimes called the Near-Horizon Extreme Kerr (NHEK) geometry. We argue that all such solutions are diffeomorphic to the NHEK geometry itself. The logic proceeds in two steps. We first argue that certain charges must vanish at all times for any solution with NHEK asymptotics. We then analyze these charges in detail for linearized solutions. Though one can choose the relevant charges to vanish at any initial time, these charges are not conserved. As a result, requiring the charges to vanish at all times is a much stronger condition. We argue that all solutions satisfying this condition are diffeomorphic to the NHEK metric.

Uniqueness of extremal Kerr and Kerr-Newman black holes

We prove that the only four-dimensional, stationary, rotating, asymptotically flat (analytic) vacuum black hole with a single degenerate horizon is given by the extremal Kerr solution. We also prove a similar uniqueness theorem for the extremal Kerr-Newman solution. This closes a long-standing gap in the black hole uniqueness theorems.

On the stress tensor of Kerr/CFT

The recently-conjectured Kerr/CFT correspondence posits a field theory dual to dynamics in the near-horizon region of an extreme Kerr black hole with certain boundary conditions. We construct a boundary stress tensor for this theory via covariant phase space techniques. The structure of the stress tensor indicates that any dual theory is a discrete light cone quantum theory, in agreement with recent arguments by Balasubramanian et al. The key technical step in our construction is the addition of an appropriate counter-term to the symplectic structure, which is necessary to make the theory fully covariant and to resolve a subtle problem involving the integrability of charges.

Physical process first law for bifurcate Killing horizons

The physical process version of the first law for black holes states that the passage of energy and angular momentum through the horizon results in a change in area ({kappa}/8{pi}){delta}A={delta}E-{omega}{delta}J, so long as this passage is quasistationary. A similar physical process first law can be derived for any bifurcate Killing horizon in any spacetime dimension d{>=}3 using much the same argument. However, to make this law nontrivial, one must show that sufficiently quasistationary processes do in fact occur. In particular, one must show that processes exist for which the shear and expansion remain small, and in which no new generators are added to the horizon. Thorne, MacDonald, and Price considered related issues when an object falls across a d=4 black hole horizon. By generalizing their argument to arbitrary d{>=}3 and to any bifurcate Killing horizon, we derive a condition under which these effects are controlled and the first law applies. In particular, by providing a nontrivial first law for Rindler horizons, our work completes the parallel between the mechanics of such horizons and those of black holes for d{>=}3. We also comment on the situation for d=2.