arXiv subjects

Dietmar Klemm

Publications and source records attributed to Dietmar Klemm.

At least 37 records · Page 2Linked to original sources

arXiv2013

Rotating black holes in 4d gauged supergravity

We present new results towards the construction of the most general black hole solutions in four-dimensional Fayet-Iliopoulos gauged supergravities. In these theories black holes can be asymptotically AdS and have arbitrary mass, angular momentum, electric and magnetic charges and NUT charge. Furthermore, a wide range of horizon topologies is allowed (compact and noncompact) and the complex scalar fields have a nontrivial radial and angular profile. We construct a large class of solutions in the simplest single scalar model with prepotential $F = -i X^0 X^1$ and discuss their thermodynamics. Moreover, various approaches and calculational tools for facing this problem with more general prepotentials are presented.

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arXiv2013

Supersymmetry of the C-metric and the general Plebanski-Demianski solution

We derive the necessary and sufficient conditions under which the general Plebanski-Demianski (PD) solution of Einstein-Maxwell theory with a negative cosmological constant admits Killing spinors. We consider in detail two different scaling limits of the PD metric. The first of these limits removes the acceleration parameter, and leads to the Carter-Plebanski solution. In this case, the integrability conditions for Killing spinors were obtained by Alonso-Alberca, Meessen and Ortin in hep-th/0003071, and we show that these are not only necessary, but also sufficient for the existence of Killing spinors. This fills also a gap in hep-th/9808097, where the integrability conditions for supersymmetry of the Kerr-Newman-AdS black hole were worked out, but the Killing spinor was not constructed explicitely. The second scaling limit eliminates the rotation parameter, and leads to the cosmological C-metric, which describes accelerated black holes in AdS. Also in this case, the supersymmetry conditions are obtained, and it is shown that they follow from the ones of the general PD solution by scaling the parameters appropriately. In all cases, we determine the three-dimensional base space that appears in the classification scheme of hep-th/0307022, and prove that for the 1/2-supersymmetric Reissner-Nordstrom-AdS spacetime, this base is unique. A Wick-rotation of our results leads to gravitational instantons that generalize the ones constructed recently by Martelli, Passias and Sparks in arXiv:12124618 to U(1)xU(1) symmetry. These instantons are shown to admit an integrable almost complex structure. Finally, our work may open the possibility to systematically construct generalizations of the PD metric that include scalar fields with a potential in matter-coupled gauged supergravity.

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arXiv2012

Black holes in an expanding universe from fake supergravity

In arXiv:0902.4814, a general recipe to construct fake supersymmetric solutions to fake N=2, d=4 gauged supergravity coupled to abelian vector multiplets was presented. We use these results to find new multi-centered black hole solutions in an asymptotically FLRW universe. These satisfy the weak energy condition and are maximally charged under two U(1) gauge fields coupled to a scalar, which drives the cosmic expansion while rolling down its potential. As a special subcase, our black holes include the ones constructed previously by Gibbons and Maeda in arXiv:0912.2809. The latter contain two non-negative real numbers n_S, n_T obeying the constraint n_S+n_T=4, with the cases n_T=4 and n_T=1 corresponding to the Kastor-Traschen and the Maeda-Ohta-Uzawa solution respectively. We show that n_S, n_T arise directly as exponents in the prepotential of the fake supergravity theory, and that the above constraint stems from the fact that the prepotential must be a homogeneous function of degree two. Finally, some physical properties of the black holes, like asymptotic behaviour, curvature singularities and trapping horizons, are also discussed. Similar to other solutions that appeared previously in the literature, there is a symmetry enhancement near the event horizon, which becomes therefore a Killing horizon, in spite of the highly dynamical nature of the original spacetime. The temperature associated to this Killing horizon turns out to be nonvanishing.

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arXiv2012

Nonextremal black holes in gauged supergravity and the real formulation of special geometry II

In arXiv:1207.2679 a new prescription for finding nonextremal black hole solutions to N=2, D=4 Fayet-Iliopoulos gauged supergravity was presented, and explicit solutions of various models containing one vector multiplet were constructed. Here we use the same method to find new nonextremal black holes to more complicated models. We also provide a general recipe to construct non-BPS extremal solutions for an arbitrary prepotential, as long as an axion-free condition holds. These follow from a set of first-order conditions, and are related to the corresponding supersymmetric black holes by a multiplication of the charge vector with a constant field rotation matrix S. The fake superpotential driving this first-order flow is nothing else than Hamilton's characteristic function in a Hamilton-Jacobi formalism, and coincides in the supersymmetric case (when S is plus or minus the identity) with the superpotential proposed by Dall'Agata and Gnecchi in arXiv:1012.3756. For the nonextremal black holes that asymptote to (magnetic) AdS, we compute both the mass coming from holographic renormalization and the one appearing in the superalgebra. The latter correctly vanishes in the BPS case, but also for certain values of the parameters that do not correspond to any known supersymmetric solution of N=2 gauged supergravity. We finally show that the product of all horizon areas depends only on the charges and the asymptotic value of the cosmological constant.

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arXiv2012

Nonextremal black holes in gauged supergravity and the real formulation of special geometry

We give a rather general recipe for constructing nonextremal black hole solutions to N=2, D=4 gauged supergravity coupled to abelian vector multiplets. This problem simplifies considerably if one uses the formalism developed in arXiv:1112.2876, based on dimensional reduction and the real formulation of special geometry. We use this to find new nonextremal black holes for several choices of the prepotential, that generalize the BPS solutions found in arXiv:0911.4926. Some physical properties of these black holes are also discussed.

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arXiv2012

Nut-charged black holes in matter-coupled N=2, D=4 gauged supergravity

Using the results of arXiv:0804.0009, where all timelike supersymmetric backgrounds of N=2, D=4 matter-coupled supergravity with Fayet-Iliopoulos gauging were classified, we construct genuine nut-charged BPS black holes in AdS_4 with nonconstant moduli. The calculations are exemplified for the SU(1,1)/U(1) model with prepotential F=-iX^0X^1. The resulting supersymmetric black holes have a hyperbolic horizon and carry two electric, two magnetic and one nut charge, which are however not all independent, but are given in terms of three free parameters. We find that turning on a nut charge lifts the flat directions in the effective black hole potential, such that the horizon values of the scalars are completely fixed by the charges. We also oxidize the solutions to eleven dimensions, and find that they generalize the geometry found in hep-th/0105250 corresponding to membranes wrapping holomorphic curves in a Calabi-Yau five-fold. Finally, a class of nut-charged Nernst branes is constructed as well, but these have curvature singularities at the horizon.

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arXiv2012

Conformal structure of the Schwarzschild black hole

We show that the scalar wave equation at low frequencies in the Schwarzschild geometry enjoys a hidden SL(2,R) invariance, which is not inherited from an underlying symmetry of the spacetime itself. Contrary to what happens for Kerr black holes, the vector fields generating the SL(2,R) are globally defined. Furthermore, it turns out that under an SU(2,1) Kinnersley transformation, which maps the Schwarzschild solution into the near horizon limit AdS_2 x S^2 of the extremal Reissner-Nordstr"om black hole (with the same entropy), the Schwarzschild hidden symmetry generators become exactly the isometries of the AdS_2 factor. Finally, we use the SL(2,R) symmetry to determine algebraically the quasinormal frequencies of the Schwarzschild black hole, and show that this yields the correct leading behaviour for large damping.

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arXiv2011

Rotating BPS black holes in matter-coupled AdS(4) supergravity

Using the general recipe given in arXiv:0804.0009, where all timelike supersymmetric solutions of N=2, D=4 gauged supergravity coupled to abelian vector multiplets were classified, we construct genuine rotating supersymmetric black holes in AdS(4) with nonconstant scalar fields. This is done for the SU(1,1)/U(1) model with prepotential F=-iX^0X^1. In the static case, the black holes are uplifted to eleven dimensions, and generalize the solution found in hep-th/0105250 corresponding to membranes wrapping holomorphic curves in a Calabi-Yau five-fold. The constructed rotating black holes preserve one quarter of the supersymmetry, whereas their near-horizon geometry is one half BPS. Moreover, for constant scalars, we generalize (a supersymmetric subclass of) the Plebanski-Demianski solution of cosmological Einstein-Maxwell theory to an arbitrary number of vector multiplets. Remarkably, the latter turns out to be related to the dimensionally reduced gravitational Chern-Simons action.

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arXiv2010

Magnetic charges in the AdS(4) superalgebra osp(4|2)

We discuss the issue of how to include magnetic charges in the AdS(4) superalgebra osp(4|2). It is shown that the usual way of introducing a pseudoscalar central charge on the right hand side of the basic anticommutator does not work, because this breaks SO(2,3) covariance. We propose a way out by promoting the magnetic charge to a vector charge, which amounts to enlarge osp(4|2) to the superconformal algebra su(2,2|1). The conditions for 1/4, 1/2 and 3/4 BPS states are then analyzed. These states form the boundary of the convex cone associated with the Jordan algebra of 4x4 complex hermitian matrices. An Inonu-Wigner contraction of the constructed superalgebra yields a known extension of the Poincare' superalgebra containing electric and magnetic 0-brane charges as well as string- and space-filling 3-brane charges. As an example, we show how some supersymmetric AdS(4) black holes fit into the classification scheme of BPS states.

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arXiv2010

The timelike half-supersymmetric backgrounds of N=2, D=4 supergravity with Fayet-Iliopoulos gauging

Subject to some relatively mild assumptions, we derive the complete form of all timelike half-supersymmetric solutions to N=2, D=4 gauged supergravity coupled to an arbitrary number of abelian vector multiplets. This is done using spinorial geometry techniques. Explicit examples are given for a simple prepotential. Among the solutions, there are near-horizon geometries of extremal rotating BPS black holes still to be discovered, with a nontrivial dependence of the scalar fields on one of the horizon coordinates.

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arXiv2009

Supersymmetric AdS_4 black holes and attractors

Using the general recipe given in arXiv:0804.0009, where all timelike supersymmetric solutions of N=2, D=4 gauged supergravity coupled to abelian vector multiplets were classified, we construct the first examples of genuine supersymmetric black holes in AdS_4 with nonconstant scalar fields. This is done for various choices of the prepotential, amongst others for the STU model. These solutions permit to study the BPS attractor flow in AdS. We also determine the most general supersymmetric static near-horizon geometry and obtain the attractor equations in gauged supergravity. As a general feature we find the presence of flat directions in the black hole potential, i.e., generically the values of the moduli on the horizon are not completely specified by the charges. For one of the considered prepotentials, the resulting moduli space is determined explicitely. Still, in all cases, we find that the black hole entropy depends only on the charges, in agreement with the attractor mechanism.

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arXiv2009

Generalized instantons in N = 4 super Yang-Mills theory and spinorial geometry

Using spinorial geometry techniques, we classify the supersymmetric solutions of euclidean ${\cal N}=4$ super Yang-Mills theory. These backgrounds represent generalizations of instantons with nontrivial scalar fields turned on, and satisfy some constraints that bear a similarity with the Hitchin equations, and contain the Donaldson equations as a special subcase. It turns out that these constraints can be obtained by dimensional reduction of the octonionic instanton equations, and may be rephrased in terms of a selfduality-like condition for a complex connection. We also show that the supersymmetry conditions imply the equations of motion only partially.

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arXiv2009

All null supersymmetric backgrounds of N=2, D=4 gauged supergravity coupled to abelian vector multiplets

The lightlike supersymmetric solutions of N=2, D=4 gauged supergravity coupled to an arbitrary number of abelian vector multiplets are classified using spinorial geometry techniques. The solutions fall into two classes, depending on whether the Killing spinor is constant or not. In both cases, we give explicit examples of supersymmetric backgrounds. Among these BPS solutions, which preserve one quarter of the supersymmetry, there are gravitational waves propagating on domain walls or on bubbles of nothing that asymptote to AdS_4. Furthermore, we obtain the additional constraints obeyed by half-supersymmetric vacua. These are divided into four categories, that include bubbles of nothing which are asymptotically AdS_4, pp-waves on domain walls, AdS_3 x R, and spacetimes conformal to AdS_3 times an interval.

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arXiv2009

Dyonic AdS black holes from magnetohydrodynamics

We use the AdS/CFT correspondence to argue that large dyonic black holes in anti-de Sitter spacetime are dual to stationary solutions of the equations of relativistic magnetohydrodynamics on the conformal boundary of AdS. The dyonic Kerr-Newman-AdS_4 solution corresponds to a charged diamagnetic fluid not subject to any net Lorentz force, due to orthogonal magnetic and electric fields compensating each other. The conserved charges, stress tensor and R-current of the fluid are shown to be in exact agreement with the corresponding quantities of the black hole. Furthermore, we obtain stationary solutions of the Navier-Stokes equations in four dimensions, which yield predictions for (yet to be constructed) charged rotating black strings in AdS_5 carrying nonvanishing momentum along the string. Finally, we consider Scherk-Schwarz reduced AdS gravity on a circle. In this theory, large black holes and black strings are dual to lumps of deconfined plasma of the associated CFT. We analyze the effects that a magnetic field introduces in the Rayleigh-Plateau instability of a plasma tube, which is holographically dual to the Gregory-Laflamme instability of a magnetically charged black string.

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arXiv2009

Black Holes as Lumps of Fluid

The old suggestive observation that black holes often resemble lumps of fluid has recently been taken beyond the level of an analogy to a precise duality. We investigate aspects of this duality, and in particular clarify the relation between area minimization of the fluid vs. area maximization of the black hole horizon, and the connection between surface tension and curvature of the fluid, and surface gravity of the black hole. We also argue that the Rayleigh-Plateau instability in a fluid tube is the holographic dual of the Gregory-Laflamme instability of a black string. Associated with this fluid instability there is a rich variety of phases of fluid solutions that we study in detail, including in particular the effects of rotation. We compare them against the known results for asymptotically flat black holes finding remarkable agreement. Furthermore, we use our fluid results to discuss the unknown features of the gravitational system. Finally, we make some observations that suggest that asymptotically flat black holes may admit a fluid description in the limit of large number of dimensions.

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arXiv2008

All timelike supersymmetric solutions of N=2, D=4 gauged supergravity coupled to abelian vector multiplets

The timelike supersymmetric solutions of N=2, D=4 gauged supergravity coupled to an arbitrary number of abelian vector multiplets are classified using spinorial geometry techniques. We show that the generalized holonomy group for vacua preserving N supersymmetries is GL((8-N)/2,C) $\ltimes$ N/2 C^((8-N)/2) $\subseteq$ GL(8,R), where N=0,2,4,6,8. The spacetime turns out to be a fibration over a three-dimensional base manifold with U(1) holonomy and nontrivial torsion. Our results can be used to construct new supersymmetric AdS black holes with nontrivial scalar fields turned on.

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arXiv2008

Black strings in AdS_5

We present non-extremal magnetic black string solutions in five-dimensional gauged supergravity. The conformal infinity is the product of time and S^1xS_h, where S_h denotes a compact Riemann surface of genus h. The construction is based on both analytical and numerical techniques. We compute the holographic stress tensor, the Euclidean action and the conserved charges of the solutions and show that the latter satisfy a Smarr-type formula. The phase structure is determined in the canonical ensemble, and it is shown that there is a first order phase transition from small to large black strings, which disappears above a certain critical magnetic charge that is obtained numerically. For another particular value of the magnetic charge, that corresponds to a twisting of the dual super Yang-Mills theory, the conformal anomalies coming from the background curvature and those arising from the coupling to external gauge fields exactly cancel. We also obtain supersymmetric solutions describing waves propagating on extremal BPS magnetic black strings, and show that they possess a Siklos-Virasoro reparametrization invariance.

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arXiv2007

The CFT dual of AdS gravity with torsion

We consider the Mielke-Baekler model of three-dimensional AdS gravity with torsion, which has gravitational and translational Chern-Simons terms in addition to the usual Einstein-Hilbert action with cosmological constant. It is shown that the topological nature of the model leads to a finite Fefferman-Graham expansion. We derive the holographic stress tensor and the associated Ward identities and show that, due to the asymmetry of the left- and right-moving central charges, a Lorentz anomaly appears in the dual conformal field theory. Both the consistent and the covariant Weyl and Lorentz anomaly are determined, and the Wess-Zumino consistency conditions for the former are verified. Moreover we consider the most general solution with flat boundary geometry, which describes left-and right-moving gravitational waves on AdS_3 with torsion, and shew that in this case the holographic energy-momentum tensor is given by the wave profiles. The anomalous transformation laws of the wave profiles under diffeomorphisms preserving the asymptotic form of the bulk solution yield the central charges of the dual CFT and confirm the results that appeared earlier on in the literature. We finally comment on some points concerning the microstate counting for the Riemann-Cartan black hole.

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