213 research outputs found
Stationary black holes: Large analysis
We consider the effective theory of the large D stationary black hole. By
solving Einstein equation with a cosmological constant using the 1/D expansion
in near zone of a black hole we obtain the effective equation for the
stationary black hole. The effective equation describes the Myers-Perry black
hole, bumpy black holes and, possibly, the black ring solution as its
solutions. In this effective theory the black hole is represented as the
embedded membrane in the background, i.e., Minkowski or Anti-de Sitter
spacetime and its mean curvature is given by the redshifted surface gravity by
the background geometry and the local Lorentz boost. The local Lorentz boost
property of the effective equation is observed also in the metric. In fact we
show that the leading order metric of the Einstein equation in the 1/D
expansion is generically regarded as the Lorentz boosted Schwarzschild black
hole. We apply this Lorentz boost property of the stationary black hole
solution to solve the perturbation equation. As a result we obtain the analytic
formula for the quasinormal mode of the singly rotating Myers-Perry black hole
in the 1/D expansion.Comment: 45 pages, 6 figures, published version in JHE
Holographic superconductivity in the large D expansion
We study holographic superconductivity by expanding the equations in the
inverse of the number of spacetime dimensions D. We obtain an analytic
expression for the critical temperature as a function of the conformal
dimension of the condensate operator. Its accuracy for 3+1-dimensional
superconductors is better than 15%. The analysis reveals a simple, and
quantitative, explanation for the onset of the superconducting instability, as
well as universal features of holographic superconductivity in the large D
limit. In particular, this allows to easily compute the effects of backreaction
on the critical temperature.Comment: 21 pages, 7 figures. v2: minor clarifications, refs added, lighter
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Non-uniform black strings and the critical dimension in the expansion
Non-uniform black strings (NUBS) are studied by the large effective
theory approach. By solving the near-horizon geometry in the expansion,
we obtain the effective equation for the deformed horizon up to the
next-to-next-to-leading order (NNLO) in . We also solve the far-zone
geometry by the Newtonian approximation. Matching the near and far zones, the
thermodynamic variables are computed in the expansion. As the result, the
large analysis gives a critical dimension at which the
translation-symmetry-breaking phase transition changes between first and second
order. This value of agrees perfectly, within the precision of the
expansion, with the result previously obtained by E. Sorkin through the
numerical resolution. We also compare our NNLO results for the thermodynamics
of NUBS to earlier numerical calculations, and find good agreement within the
expected precision.Comment: 33 pages, 8 figures, Ancillary Mathematica notebook contains details
of NNLO results; v2: Published versio
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