Extremal Black Hole/CFT Correspondence in (Gauged) Supergravities

We extend the investigation of the recently proposed Kerr/CFT correspondence to large classes of rotating black hole solutions in gauged and ungauged supergravities. The correspondence, proposed originally for four-dimensional Kerr black holes, asserts that the quantum states in the near-horizon region of an extremal rotating black hole are holographically dual to a two-dimensional chiral theory whose Virasoro algebra arises as an asymptotic symmetry of the near-horizon geometry. In fact in dimension D there are [(D-1)/2] commuting Virasoro algebras. We consider a general canonical class of near-horizon geometries in arbitrary dimension D, and show that in any such metric, the [(D-1)/2] central charges each imply, via the Cardy formula, a microscopic entropy that agrees with the Bekenstein-Hawking entropy of the associated extremal black hole. In the remainder of the paper we show for most of the known rotating black hole solutions of gauged supergravity, and for the ungauged supergravity solutions with four charges in D=4 and three charges in D=5, that their extremal near-horizon geometries indeed lie within the canonical form. This establishes that in all these examples, the microscopic entropies of the dual CFTs agree with the Bekenstein-Hawking entropies of the extremal rotating black holes.Comment: 32 pages, references added and minor typos fixe

Characterization of critical shear stresses and bank material erosion rates on gravelly stream banks

Meandering river migration over large spatial and temporal scales has traditionally been numerically simulated using a bank erosion submodel that calculates the eroding bank migration rate as the product of the near-bank excess flow velocity and a dimensionless migration coefficient. The latter value is an empirical parameter calibrated to historical observations. In efforts to improve upon the traditional model, recent research has followed two approaches: (a) provide a means of estimating the dimensionless migration coefficient based on field measurements; and (b) discard the traditional migration coefficient approach to develop a bank erosion submodel based on the actual formulations that dictate fluvial erosion rates and mass failure which determine bank migration. The latter physics-based approach was recently implemented into the numerical model RVR Meander developed by the Ven Te Chow Hydrosystems Laboratory at the University of Illinois in Urbana-Champaign (Motta et al, 2012a); however, the governing equations used for fluvial erosion strictly apply only to banks comprised of cohesive soils. In that formulation the fluvial erosion rate is linearly dependent on the excess boundary shear stress. This study explores whether a similarly simple formulation can describe in a gross sense the migration of river banks comprised entirely of non-cohesive soil or composite banks consisting of non-cohesive soil at the base overlain by cohesive soil. Numerical modeling of both fluvial erosion and shallow avalanche mass failures that occur simultaneously during non-cohesive bank deformation reveal that the bank migration rate is strongly non-linear with respect to the boundary shear stress (exponent greater than 1) when considering non-cohesive bank materials. A methodology is described for developing a site specific non-cohesive bank erosion submodel that is valid and computationally practicable over the desired large spatial and temporal scales relevant to models such as RVR Meander. The new methodology allows issues such as flow regime modifications to be incorporated to change the model parameters, which was not possible using the traditional empirical approach. The numerical modeling performed in this study also provides fundamental insights into deformation of non-cohesive river banks: it demonstrates that high flow events tend to cause bank slope reduction, with lower flow events tending to rejuvenate the steepness of the bank; it quantifies the importance of prior erosional history in influencing bank migration rates; and it quantifies the feedback of basal armoring on deformation of the unarmored region.U.S. Department of the InteriorU.S. Geological SurveyOpe

A physically-based bank erosion model for composite river banks: Application to Mackinaw River, Illinois

Meandering river migration over large spatial and temporal scales has traditionally been numerically simulated using a bank erosion submodel that calculates the eroding bank migration rate as the product of the near-bank excess flow velocity and a dimensionless migration coefficient. The latter value is an empirical parameter calibrated to historical observations. In efforts to improve upon the traditional model, recent research has followed two approaches: (a) provide a means of estimating the dimensionless migration coefficient based on field measurements; and (b) discard the traditional migration coefficient approach to develop a bank erosion submodel based on the actual formulations that dictate fluvial erosion rates and mass failure which determine bank migration. The latter physics-based approach was recently implemented into the numerical model RVR Meander developed by the Ven Te Chow Hydrosystems Laboratory at the University of Illinois in Urbana-Champaign (Motta et al, 2012a); however, the governing equations used for fluvial erosion strictly apply only to banks comprised of cohesive soils. In that formulation the fluvial erosion rate is linearly dependent on the excess boundary shear stress. This study explores whether a similarly simple formulation can describe in a gross sense the migration of river banks comprised entirely of non-cohesive soil or composite banks consisting of non-cohesive soil at the base overlain by cohesive soil. Numerical modeling of both fluvial erosion and shallow avalanche mass failures that occur simultaneously during non-cohesive bank deformation reveal that the bank migration rate is strongly non-linear with respect to the boundary shear stress (exponent greater than 1) when considering non-cohesive bank materials. A methodology is described for developing a site specific non-cohesive bank erosion submodel that is valid and computationally practicable over the desired large spatial and temporal scales relevant to models such as RVR Meander. The new methodology allows issues such as flow regime modifications to be incorporated to change the model parameters, which was not possible using the traditional empirical approach. The numerical modeling performed in this study also provides fundamental insights into deformation of non-cohesive river banks: it demonstrates that high flow events tend to cause bank slope reduction, with lower flow events tending to rejuvenate the steepness of the bank; it quantifies the importance of prior erosional history in influencing bank migration rates; and it quantifies the feedback of basal armoring on deformation of the unarmored region.U.S. Department of the InteriorU.S. Geological SurveyOpe

Single-charge rotating black holes in four-dimensional gauged supergravity

We consider four-dimensional U(1)^4 gauged supergravity, and obtain asymptotically AdS_4, non-extremal, charged, rotating black holes with one non-zero U(1) charge. The thermodynamic quantities are computed. We obtain a generalization that includes a NUT parameter. The general solution has a discrete symmetry involving inversion of the rotation parameter, and has a string frame metric that admits a rank-2 Killing-Stackel tensor.Comment: 9 page

Symmetries of supergravity black holes

We investigate Killing tensors for various black hole solutions of supergravity theories. Rotating black holes of an ungauged theory, toroidally compactified heterotic supergravity, with NUT parameters and two U(1) gauge fields are constructed. If both charges are set equal, then the solutions simplify, and then there are concise expressions for rank-2 conformal Killing-Stackel tensors. These are induced by rank-2 Killing-Stackel tensors of a conformally related metric that possesses a separability structure. We directly verify the separation of the Hamilton-Jacobi equation on this conformally related metric, and of the null Hamilton-Jacobi and massless Klein-Gordon equations on the "physical" metric. Similar results are found for more general solutions; we mainly focus on those with certain charge combinations equal in gauged supergravity, but also consider some other solutions.Comment: 36 pages; v2: minor changes; v3: slightly shorte

Polarization speed meter for gravitational-wave detection

We propose a modified configuration of an advanced gravitational-wave detector that is a speed-meter-type interferometer with improved sensitivity with respect to quantum noise. With the addition of polarization-controlling components to the output of an arm cavity Michelson interferometer, an orthogonal polarization state of the interferometer can be used to store signal, returning it later with opposite phase to cancel position information below the storage bandwidth of the opposite mode. This modification provides an alternative to an external kilometer-scale Fabry-Pérot cavity, as presented in earlier work of Purdue and Chen [Phys. Rev. D 66, 122004 (2002)]. The new configuration requires significantly less physical infrastructure to achieve speed meter operation. The quantity of length and alignment degrees of freedom is also reduced. We present theoretical calculations to show that such a speed meter detector is capable of beating the strain sensitivity imposed by the standard quantum limit over a broad range of frequencies for Advanced Laser Interferometer Gravitational-wave Observatory-like parameters. The benefits and possible difficulties of implementing such a scheme are outlined. We also present results for tuning of the speed meter by adjusting the degree of polarization coupling, a novel possibility that does not exist in previously proposed designs, showing that there is a smooth transition from speed meter operation to that of a signal-recycling Michelson behavior

Two-Stage Rotational Disordering of a Molecular Crystal Surface: C60

We propose a two-stage mechanism for the rotational surface disordering phase transition of a molecular crystal, as realized in C$_{60}$ fullerite. Our study, based on Monte Carlo simulations, uncovers the existence of a new intermediate regime, between a low temperature ordered $(2 \times 2)$ state, and a high temperature $(1 \times 1)$ disordered phase. In the intermediate regime there is partial disorder, strongest for a subset of particularly frustrated surface molecules. These concepts and calculations provide a coherent understanding of experimental observations, with possible extension to other molecular crystal surfaces.Comment: 4 pages, 2 figure

Charged rotating black holes in six-dimensional gauged supergravity

We obtain non-extremal charged rotating black holes in six-dimensional SU(2) gauged supergravity with two independent angular momenta and one U(1) charge. These include supersymmetric black holes without naked closed timelike curves.Comment: 9 pages; v2: minor change