arXiv subjects

C. N. Pope

Publications and source records attributed to C. N. Pope.

At least 145 records · Page 8Linked to original sources

arXiv2005

Bulk/Boundary Thermodynamic Equivalence, and the Bekenstein and Cosmic-Censorship Bounds for Rotating Charged AdS Black Holes

We show that one may pass from bulk to boundary thermodynamic quantities for rotating AdS black holes in arbitrary dimensions so that if the bulk quantities satisfy the first law of thermodynamics then so do the boundary CFT quantities. This corrects recent claims that boundary CFT quantities satisfying the first law may only be obtained using bulk quantities measured with respect to a certain frame rotating at infinity, and which therefore do not satisfy the first law. We show that the bulk black hole thermodynamic variables, or equivalently therefore the boundary CFT variables, do not always satisfy a Cardy-Verlinde type formula, but they do always satisfy an AdS-Bekenstein bound. The universal validity of the Bekenstein bound is a consequence of the more fundamental cosmic censorship bound, which we find to hold in all cases examined. We also find that at fixed entropy, the temperature of a rotating black hole is bounded above by that of a non-rotating black hole, in four and five dimensions, but not in six or more dimensions. We find evidence for universal upper bounds for the area of cosmological event horizons and black-hole horizons in rotating black-hole spacetimes with a positive cosmological constant.

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arXiv2005

Five-Dimensional Gauged Supergravity Black Holes with Independent Rotation Parameters

We construct new non-extremal rotating black hole solutions in SO(6) gauged five-dimensional supergravity. Our solutions are the first such examples in which the two rotation parameters are independently specifiable, rather than being set equal. The black holes carry charges for all three of the gauge fields in the U(1)^3 subgroup of SO(6), albeit with only one independent charge parameter. We discuss the BPS limits, showing in particular that these include the first examples of regular supersymmetric black holes with independent angular momenta in gauged supergravity. We also find non-singular BPS solitons. Finally, we obtain another independent class of new rotating non-extremal black hole solutions with just one non-vanishing rotation parameter, and one non-vanishing charge.

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arXiv2005

General Non-Extremal Rotating Black Holes in Minimal Five-Dimensional Gauged Supergravity

We construct the general solution for non-extremal charged rotating black holes in five-dimensional minimal gauged supergravity. They are characterised by four non-trivial parameters, namely the mass, the charge, and the two independent rotation parameters. The metrics in general describe regular rotating black holes, providing the parameters lie in appropriate ranges so that naked singularities and closed timelike curves (CTC's) are avoided. We calculate the conserved energy, angular momenta and charge for the solutions, and show how supersymmetric solutions arise in a BPS limit. These have naked CTC's in general, but for special choices of the parameters we obtain new regular supersymmetric black holes or smooth topological solitons.

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arXiv2005

New Einstein-Sasaki Spaces in Five and Higher Dimensions

We obtain infinite classes of new Einstein-Sasaki metrics on complete and non-singular manifolds. They arise, after Euclideanisation, from BPS limits of the rotating Kerr-de Sitter black hole metrics. The new Einstein-Sasaki spaces L^{p,q,r} in five dimensions have cohomogeneity 2, and U(1) x U(1) x U(1) isometry group. They are topologically S^2 x S^3. Their AdS/CFT duals will describe quiver theories on the four-dimensional boundary of AdS_5. We also obtain new Einstein-Sasaki spaces of cohomogeneity n in all odd dimensions D=2n+1 \ge 5, with U(1)^{n+1} isometry.

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arXiv2005

New Einstein-Sasaki and Einstein Spaces from Kerr-de Sitter

In this paper, which is an elaboration of our results in hep-th/0504225, we construct new Einstein-Sasaki spaces L^{p,q,r_1,...,r_{n-1}} in all odd dimensions D=2n+1\ge 5. They arise by taking certain BPS limits of the Euclideanised Kerr-de Sitter metrics. This yields local Einstein-Sasaki metrics of cohomogeneity n, with toric U(1)^{n+1} principal orbits, and n real non-trivial parameters. By studying the structure of the degenerate orbits we show that for appropriate choices of the parameters, characterised by the (n+1) coprime integers (p,q,r_1,...,r_{n-1}), the local metrics extend smoothly onto complete and non-singular compact Einstein-Sasaki manifolds L^{p,q,r_1,...,r_{n-1}}. We also construct new complete and non-singular compact Einstein spaces Λ^{p,q,r_1,...,r_n} in D=2n+1 that are not Sasakian, by choosing parameters appropriately in the Euclideanised Kerr-de Sitter metrics when no BPS limit is taken.

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arXiv2005

Non-extremal Charged Rotating Black Holes in Seven-Dimensional Gauged Supergravity

We obtain the solution for non-extremal charged rotating black holes in seven-dimensional gauged supergravity, in the case where the three rotation parameters are set equal. There are two independent charges, corresponding to gauge fields in the U(1)xU(1) abelian subgroup of the SO(5) gauge group. A new feature in these solutions, not seen previously in lower-dimensional examples, is that the first-order "odd-dimensional self-duality" equation for the 4-form field strength plays a non-trivial role. We also study the BPS limit of our solutions where the black holes become supersymmetric. Our results are of significance for the AdS_7/CFT_6 correspondence in M-theory.

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arXiv2005

String and M-theory Deformations of Manifolds with Special Holonomy

The R^4-type corrections to ten and eleven dimensional supergravity required by string and M-theory imply corrections to supersymmetric supergravity compactifications on manifolds of special holonomy, which deform the metric away from the original holonomy. Nevertheless, in many such cases, including Calabi-Yau compactifications of string theory and G_2-compactifications of M-theory, it has been shown that the deformation preserves supersymmetry because of associated corrections to the supersymmetry transformation rules, Here, we consider Spin(7) compactifications in string theory and M-theory, and a class of non-compact SU(5) backgrounds in M-theory. Supersymmetry survives in all these cases too, despite the fact that the original special holonomy is perturbed into general holonomy in each case.

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arXiv2005

Horava-Witten Stability: eppur si muove

We construct exact time-dependent solutions of the supergravity equations of motion in which two initially non-singular branes, one with positive and the other with negative tension, move together and annihilate each other in an all-enveloping spacetime singularity. Among our solutions are the Horava-Witten solution of heterotic M-theory and a Randall-Sundrum I type solution, both of which are supersymmetric, i.e. BPS, in the time-independent case. In the absence of branes our solutions are of Kasner type, and the source of instability may ascribed to a failure to stabilise some of the modulus fields of the compactification. It also raises questions about the viability of models based on some sorts of negative tension brane.

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arXiv2004

BPS Geometries and AdS Bubbles

Recently, 1/2-BPS AdS bubble solutions have been obtained by Lin, Lunin and Maldacena, which correspond to Fermi droplets in phase space in the dual CFT picture. They can be thought of as generalisations of 1/2-BPS AdS black hole solutions in five or seven dimensional gauged supergravity. In this paper, we extend these solutions by invoking additional gauge fields and scalar fields in the supergravity Lagrangians, thereby obtaining AdS bubble generalisations of the previously-known multi-charge AdS black solutions of gauged supergravity. We also obtain analogous AdS bubble solutions in four-dimensional gauged supergravity. Our solutions generically preserve supersymmetry fractions 1/4, 1/8 and 1/8 in seven, five and four dimensions respectively. They can be lifted to M-theory or type IIB string theory, using previously known formulae for the consistent Pauli sphere reductions that yield the gauged supergravities. We also find similar solutions in six-dimensional gauged supergravity, and discuss their lift to the massive type IIA theory.

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arXiv2004

Supergravities with Minkowski x Sphere Vacua

Recently the authors have introduced a new gauged supergravity theory with a positive definite potential in D=6, obtained through a generalised Kaluza-Klein reduction from D=7. Of particular interest is the fact that this theory admits certain Minkowski x Sphere vacua. In this paper we extend the previous results by constructing gauged supergravities with positive definitive potentials in diverse dimensions, together with their vacuum solutions. In addition, we prove the supersymmetry of the generalised reduction ansatz. We obtain a supersymmetric solution with no form-field fluxes in the new gauged theory in D=9. This solution may be lifted to D=10, where it acquires an interpretation as a time-dependent supersymmetric cosmological solution supported purely by the dilaton. A further uplift to D=11 yields a solution describing a pp-wave.

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arXiv2004

A Note on Einstein Sasaki Metrics in D \ge 7

In this paper, we obtain new non-singular Einstein-Sasaki spaces in dimensions D\ge 7. The local construction involves taking a circle bundle over a (D-1)-dimensional Einstein-Kahler metric that is itself constructed as a complex line bundle over a product of Einstein-Kahler spaces. In general the resulting Einstein-Sasaki spaces are singular, but if parameters in the local solutions satisfy appropriate rationality conditions, the metrics extend smoothly onto complete and non-singular compact manifolds.

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arXiv2004

Charged Rotating Black Holes in Four-Dimensional Gauged and Ungauged Supergravities

We study four-dimensional non-extremal charged rotating black holes in ungauged and gauged supergravity. In the ungauged case, we obtain rotating black holes with four independent charges, as solutions of N=2 supergravity coupled to three abelian vector multiplets. This is done by reducing the theory along the time direction to three dimensions, where it has an O(4,4) global symmetry. Applied to the reduction of the uncharged Kerr metric, O(1,1)^4\subset O(4,4) transformations generate new solutions that correspond, after lifting back to four dimensions, to the introduction of four independent electromagnetic charges. In the case where these charges are set pairwise equal, we then generalise the four-dimensional rotating black holes to solutions of gauged N=4 supergravity, with mass, angular momentum and two independent electromagnetic charges. The dilaton and axion fields are non-constant. We also find generalisations of the gauged and ungauged solutions to include the NUT parameter, and for the ungauged solutions, the acceleration parameter too. The solutions in gauged supergravity provide new gravitational backgrounds for a further study of the AdS_4/CFT_3 correspondence at non-zero temperature.

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arXiv2004

Supersymmetric Deformations of G_2 Manifolds from Higher-Order Corrections to String and M-Theory

The equations of 10 or 11 dimensional supergravity admit supersymmetric compactifications on 7-manifolds of $G_2$ holonomy, but these supergravity vacua are deformed away from special holonomy by the higher-order corrections of string or M-theory. We find simple expressions for the first-order corrections to the Einstein and Killing spinor equations in terms of the calibrating 3-form of the leading-order G_2-holonomy background. We thus obtain, and solve explicitly, systems of first-order equations describing the corrected metrics for most of the known classes of cohomogeneity-one 7-metrics with G_2 structures

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arXiv2004

Charged Kerr-de Sitter Black Holes in Five Dimensions

We construct a general class of non-extremal charged Kerr-de Sitter black holes in five dimensions, in which the two rotation parameters are set equal. There are three non-trivial parameters, namely the mass, charge and angular momentum. All previously-known cases, supersymmetric and non-supersymmetric, that have equal angular momenta are encompassed as special cases.

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arXiv2004

Charged Rotating Black Holes in Five Dimensional U(1)^3 Gauged N=2 Supergravity

We obtain the general solution for non-extremal 3-charge dilatonic rotating black holes in the U(1)^3 gauged five-dimensional N=2 supergravity coupled to two vector multiplets, in the case where the two rotation parameters are set equal. These solutions encompass all the previously-known extremal solutions, and, by setting the three charges equal, the recently-obtained non-extremal solutions of N=2 gauged five-dimensional pure supergravity.

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arXiv2004

Rotating Black Holes in Higher Dimensions with a Cosmological Constant

We present the metric for a rotating black hole with a cosmological constant and with arbitrary angular momenta in all higher dimensions. The metric is given in both Kerr-Schild and Boyer-Lindquist form. In the Euclidean-signature case, we also obtain smooth compact Einstein spaces on associated S^{D-2} bundles over S^2, infinitely many for each odd D\ge 5. Applications to string theory and M-theory are indicated.

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arXiv2004

The General Kerr-de Sitter Metrics in All Dimensions

We give the general Kerr-de Sitter metric in arbitrary spacetime dimension D\ge 4, with the maximal number [(D-1)/2] of independent rotation parameters. We obtain the metric in Kerr-Schild form, where it is written as the sum of a de Sitter metric plus the square of a null geodesic vector, and in generalised Boyer-Lindquist coordinates. The Kerr-Schild form is simpler for verifying that the Einstein equations are satisfied, and we have explicitly checked our results for all dimensions D\le 11. We discuss the global structure of the metrics, and obtain formulae for the surface gravities and areas of the event horizons. We also obtain the Euclidean-signature solutions, and we construct complete non-singular compact Einstein spaces on associated S^{D-2} bundles over S^2, infinitely many for each odd D \ge 5.

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arXiv2004

Variant N=(1,1) Supergravity and (Minkowski)_4 x S^2 Vacua

We construct the fermionic sector and supersymmetry transformation rules of a variant N=(1,1) supergravity theory obtained by generalized Kaluza-Klein reduction from seven dimensions. We show that this model admits both (Minkowski)_4 x S^2 and (Minkowski)_3 x S^3 vacua. We perform a consistent Kaluza-Klein reduction on S^2 and obtain D=4, N=2 supergravity coupled to a vector multiplet, which can be consistently truncated to give rise to D=4, N=1 supergravity with a chiral multiplet.

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