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Cynthia Keeler

Publications and source records attributed to Cynthia Keeler.

41 records · Page 3Linked to original sources
arXiv2012

Separability of Black Holes in String Theory

We analyze the origin of separability for rotating black holes in string theory, considering both massless and massive geodesic equations as well as the corresponding wave equations. We construct a conformal Killing-Stackel tensor for a general class of black holes with four independent charges, then identify two-charge configurations where enhancement to an exact Killing-Stackel tensor is possible. We show that further enhancement to a conserved Killing-Yano tensor is possible only for the special case of Kerr-Newman black holes. We construct natural null congruences for all these black holes and use the results to show that only the Kerr-Newman black holes are algebraically special in the sense of Petrov. Modifying the asymptotic behavior by the subtraction procedure that induces an exact SL(2)^2 also preserves only the conformal Killing-Stackel tensor. Similarly, we find that a rotating Kaluza-Klein black hole possesses a conformal Killing-Stackel tensor but has no further enhancements.

hep-th↗
arXiv2011

Wilsonian Approach to Fluid/Gravity Duality

The problem of gravitational fluctuations confined inside a finite cutoff at radius $r=r_c$ outside the horizon in a general class of black hole geometries is considered. Consistent boundary conditions at both the cutoff surface and the horizon are found and the resulting modes analyzed. For general cutoff $r_c$ the dispersion relation is shown at long wavelengths to be that of a linearized Navier-Stokes fluid living on the cutoff surface. A cutoff-dependent line-integral formula for the diffusion constant $D(r_c)$ is derived. The dependence on $r_c$ is interpreted as renormalization group (RG) flow in the fluid. Taking the cutoff to infinity in an asymptotically AdS context, the formula for $D(\infty)$ reproduces as a special case well-known results derived using AdS/CFT. Taking the cutoff to the horizon, the effective speed of sound goes to infinity, the fluid becomes incompressible and the Navier-Stokes dispersion relation becomes exact. The resulting universal formula for the diffusion constant $D(horizon)$ reproduces old results from the membrane paradigm. Hence the old membrane paradigm results and new AdS/CFT results are related by RG flow. RG flow-invariance of the viscosity to entropy ratio $η/s$ is shown to follow from the first law of thermodynamics together with isentropy of radial evolution in classical gravity. The ratio is expected to run when quantum gravitational corrections are included.

hep-th↗
arXiv2011

From Navier-Stokes To Einstein

We show by explicit construction that for every solution of the incompressible Navier-Stokes equation in $p+1$ dimensions, there is a uniquely associated "dual" solution of the vacuum Einstein equations in $p+2$ dimensions. The dual geometry has an intrinsically flat timelike boundary segment $Σ_c$ whose extrinsic curvature is given by the stress tensor of the Navier-Stokes fluid. We consider a "near-horizon" limit in which $Σ_c$ becomes highly accelerated. The near-horizon expansion in gravity is shown to be mathematically equivalent to the hydrodynamic expansion in fluid dynamics, and the Einstein equation reduces to the incompressible Navier-Stokes equation. For $p=2$, we show that the full dual geometry is algebraically special Petrov type II. The construction is a mathematically precise realization of suggestions of a holographic duality relating fluids and horizons which began with the membrane paradigm in the 70's and resurfaced recently in studies of the AdS/CFT correspondence.

hep-th↗
arXiv2010

Three Dimensional Origin of AdS_2 Quantum Gravity

We study AdS_2 quantum gravity with emphasis on consistency with results from AdS_3. We lift AdS_2 black holes to three dimensions and map fluctuations around the solutions. Comparison with near extremal BTZ are discussed, with due emphasis on global aspects. The results confirm that parameters like central charges and conformal weights computed directly in 2D are consistent with standard results in 3D. Applying our results to the thermodynamics of near extreme Kerr black holes, we show that AdS_2 quantum gravity gives the correct central charge c=12J, and the entropy of excitations above the extremal limit is captured correctly.

hep-th↗