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Register a new userOn non-uniform black branes
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Authors
Steven S. Gubser
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Certain black branes are unstable toward fluctuations that lead to non-uniform mass distributions. We study static, non-uniform solutions that differ only perturbatively from uniform ones. For uncharged black strings in five dimensions, we find evidence of a first order transition from uniform to non-uniform solutions.
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We study extremal non-BPS black holes and strings arising in M-theory compactifications on Calabi-Yau threefolds, obtained by wrapping M2 branes on non-holomorphic 2-cycles and M5 branes on non-holomorphic 4-cycles. Using the attractor mechanism we compute the black hole mass and black string tension, leading to a conjectural formula for the asymptotic volumes of connected, locally volume-minimizing representatives of non-holomorphic, even-dimensional homology classes in the threefold, without knowledge of an explicit metric. In the case of divisors we find examples where the volume of the representative corresponding to the black string is less than the volume of the minimal piecewise-holomorphic representative, predicting recombination for those homology classes and leading to stable, non-BPS strings. We also compute the central charges of non-BPS strings in F-theory via a near-horizon $AdS_3$ limit in 6d which, upon compactification on a circle, account for the asymptotic entropy of extremal non-supersymmetric 5d black holes (i.e., the asymptotic count of non-holomorphic minimal 2-cycles).
We study the equations of black strings in spacetimes of arbitrary dimensions with a negative cosmological constant and construct numerically non uniform black strings solutions. Our results suggest the existence of a localised black hole in asymptotically locally $AdS$ spacetime. We also present evidences for a dependence of the critical dimension on the horizon radius.The critical dimension represents the dimension where the order of the phase transition between uniform and non uniform black string changes. Finally, we argue that both, the regular asymptotically locally $AdS$ solution and $AdS$ black string solutions with a very small horizon radius, present a negative tension. This turns out to be an unexpected feature of the solutions.
The non-commutative geometry of deformation quantization appears in string theory through the effect of a B-field background on the dynamics of D-branes in the topological limit. For arbitrary backgrounds, associativity of the star product is lost, but only cyclicity is necessary for a description of the effective action in terms of a generalized product. In previous work we showed that this property indeed emerges for a non-associative product that we extracted from open string amplitudes in curved background fields. In the present note we extend our investigation through second order in a complete derivative expansion. We establish cyclicity with respect to the Born--Infeld measure and find a logarithmic correction that modifies the Kontsevich formula in an arbitrary background satisfying the generalized Maxwell equation. This equation is the physical equivalent of a divergence-free non-commutative parameter, which is required for cyclicity already in the associative case.
We extend the recent work on fluid-gravity correspondence to charged black-branes by determining the metric duals to arbitrary charged fluid configuration up to second order in the boundary derivative expansion. We also derive the energy-momentum tensor and the charge current for these configurations up to second order in the boundary derivative expansion. We find a new term in the charge current when there is a bulk Chern-Simons interaction thus resolving an earlier discrepancy between thermodynamics of charged rotating black holes and boundary hydrodynamics. We have also confirmed that all our expressions are covariant under boundary Weyl-transformations as expected.
We consider black $p$-brane solutions of the low energy string action, computing scalar perturbations. Using standard methods, we derive the wave equations obeyed by the perturbations and treat them analytically and numerically. We have found that tensorial perturbations obtained via a gauge-invariant formalism leads to the same results as scalar perturbations. No instability has been found. Asymptotically, these solutions typically reduce to a $AdS_{(p+2)}times S^{(8-p)}$ space, which, in the framework of Maldacenas conjecture, can be regarded as a gravitational dual to a conformal field theory defined in a $(p+1)$-dimensional flat space-time. The results presented open the possibility of a better understanding the AdS/CFT correspondence, as originally formulated in terms of the relation among brane structures and gauge theories.
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