Near Extremal Kerr Entropy from AdS_2 Quantum Gravity

We analyze the asymptotic symmetries of near extremal Kerr black holes in four dimensions using the AdS_2/CFT_1 correspondence. We find a Virasoro algebra with central charge c_R=12J that is independent from the Virasoro algebra (with the same central charge) that acts on the degenerate ground state. The energy of the excitations is computed as well, and we can use Cardy's formula to determine the near extremal entropy. Our result is consistent with the Bekenstein-Hawking area law for near extremal Kerr black holes.Comment: 28 pages. v2: references added, typos correcte

Off the track: A profile of non-tenure track faculty at McGill University

A survey conducted at McGill University suggests that non-tenure track faculty are a diverse group of highly-qualified individuals whose employment status involves a high degree of uncertainty. In accordance with other Canadian and American studies, the survey also found that a disproportionate number of women occupy non-tenure track as opposed to tenured or tenure track positions. Since the 1980s, North American universities have responded to increasing student enrollments and con- tinued cuts to government funding by appointing significant numbers of faculty to full-time and part-time non-tenure track positions. Due to the precariousness of their employment status, non-tenure track faculty rep- resent an attractive buffer in times of financial restraint. Despite their increasing numbers, however, little is known about the composition and concerns of non-tenure track faculty as a group. This article describes this group at one university and puts into question the structural and power relations that have led to their increased use and abuse.Une étude faite à l'université McGill suggère que le corps enseignant dont le statut ne donne pas accès à la permanence est fortement diversifié et composé d'individus très qualifiés, mais que ce même statut implique une grande incertitude d'emploi. A l'instar des études canadiennes et américaines, cette étude montre également qu'à l'université McGill, un nombre disproportionné de femmes occupent des postes qui ne donnent pas accès à la permanence par opposition à des postes permanents ou qui donnent accès à la permanence. Depuis les années 1980, les universités Nord-américaines ont réagi à l'accroissement de la clientèle étudiante et aux compressions répétées des subventions de l'État en embauchant un nombre important d'enseignants à des postes à temps partiel ou plein temps qui ne donnent pas accès à la permanence. La précarité inhérente à ce statut d'emploi est une solution attrayante en période de restriction budgétaire. Quoique le nombre de postes soit en croissance constante, on connait peu de choses sur la composition de ce groupe et leurs préoccupations à propos de leur statut. Cet article décrit un groupe dans une université et soulève des questions de relations structurales et de pouvoir qui ont mené à accroître et à abuser de cette forme d'emploi

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.Comment: 19 page

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.Comment: 42 pages, 3 figures. v3: minor clarifications and correction

Multitrace deformations, Gamow states, and Stability of AdS/CFT

We analyze the effect of multitrace deformations in conformal field theories at leading order in a large N approximation. These theories admit a description in terms of a weakly coupled gravity dual. We show how the deformations can be mapped into boundary terms of the gravity theory and how to reproduce the RG equations found in field theory. In the case of doubletrace deformations, and for bulk scalars with masses in the range $-d^2/4<m^2<-d^2/4+1$, the deformed theory flows between two fixed points of the renormalization group, manifesting a resonant behavior at the scale characterizing the transition between the two CFT's. On the gravity side the resonance is mapped into an IR non-normalizable mode (Gamow state) whose overlap with the UV region increases as the dual operator approaches the free field limit. We argue that this resonant behavior is a generic property of large N theories in the conformal window, and associate it to a remnant of the Nambu-Goldstone mode of dilatation invariance. We emphasize the role of nonminimal couplings to gravity and establish a stability theorem for scalar/gravity systems with AdS boundary conditions in the presence of arbitrary boundary potentials and nonminimal coupling.Comment: 14 pages, references added, introduction change

Particle dynamics near extreme Kerr throat and supersymmetry

The extreme Kerr throat solution is believed to be non-supersymmetric. However, its isometry group SO(2,1) x U(1) matches precisely the bosonic subgroup of N=2 superconformal group in one dimension. In this paper we construct N=2 supersymmetric extension of a massive particle moving near the horizon of the extreme Kerr black hole. Bosonic conserved charges are related to Killing vectors in a conventional way. Geometric interpretation of supersymmetry charges remains a challenge.Comment: V2: 10 pages; discussion in sect. 4 and 5 extended, acknowledgements and references adde

From Unruh temperature to generalized Bousso bound

In a classical spacetime satisfying Einstein's equation and the null convergence condition, the same quantum mechanical effects that cause black holes to have a temperature are found to imply, if joined to the macroscopic nature of entropy, the covariant entropy bound in its generalized form. This is obtained from thermodynamics, as applied across the local Rindler causal horizon through every point p of the null hypersurfaces L the covariant entropy bound refers to, in the direction of the null geodesics generating L.Comment: 5 pages. v2: some changes to clarify the path to the obtained results; two (final) paragraphs, the acknowledgments and a reference adde

On the CFT duals for near-extremal black holes

We consider Kerr-Newman-AdS-dS black holes near extremality and work out the near-horizon geometry of these near-extremal black holes. We identify the exact U(1)_L x U(1)_R isometries of the near-horizon geometry and provide boundary conditions enhancing them to a pair of commuting Virasoro algebras. The conserved charges of the corresponding asymptotic symmetries are found to be well defined and non-vanishing and to yield central charges c_L\neq0 and c_R=0. The Cardy formula subsequently reproduces the Bekenstein-Hawking entropy of the black hole. This suggests that the near-extremal Kerr-Newman-AdS-dS black hole is holographically dual to a non-chiral two-dimensional conformal field theory.Comment: 11 page

Conformal mechanics inspired by extremal black holes in d=4

A canonical transformation which relates the model of a massive relativistic particle moving near the horizon of an extremal black hole in four dimensions and the conventional conformal mechanics is constructed in two different ways. The first approach makes use of the action-angle variables in the angular sector. The second scheme relies upon integrability of the system in the sense of Liouville.Comment: V2: presentation improved, new material and references added; the version to appear in JHE