arXiv subjects

Carlos A. R. Herdeiro

Publications and source records attributed to Carlos A. R. Herdeiro.

142 records · Page 8Linked to original sources

arXiv2009

Relativistic Euler's 3-body problem, optical geometry and the golden ratio

A Weyl solution describing two Schwarzschild black holes is considered. We focus on the Z_2 invariant solution, with ADM mass M_{ADM}=2M_K, where M_K is the Komar mass of each black hole. For this solution the set of fixed points of the discrete symmetry is a totally geodesic sub-manifold. The existence and radii of circular photon orbits in this sub-manifold are studied, as functions of the distance 2L between the two black holes. For L-> 0 there are two such orbits, corresponding to r=3M_{ADM} and r=2M_{ADM} in Schwarzschild coordinates. As the distance increases, it is shown that the two photon orbits approach one another and merge when M_K=φL, where φis the golden ratio. Beyond this distance there exist no circular photon orbits. The two null orbits delimit a forbidden band for time-like circular orbits, which is interpreted in terms of optical geometry. For large L, time-like circular orbits are allowed everywhere, as in the analogous Newtonian problem. The analysis is generalised by considering a Z_2 invariant Weyl solution with an array of N black holes and also by charging the black holes, which connects the Weyl solution to a Majumdar-Papapetrou spacetime.

gr-qc↗

arXiv2009

Gauduchon-Tod structures, Sim holonomy and De Sitter supergravity

Solutions of five-dimensional De Sitter supergravity admitting Killing spinors are considered, using spinorial geometry techniques. It is shown that the "null" solutions are defined in terms of a one parameter family of 3-dimensional constrained Einstein-Weyl spaces called Gauduchon-Tod structures. They admit a geodesic, expansion-free, twist-free and shear-free null vector field and therefore are a particular type of Kundt geometry. When the Gauduchon-Tod structure reduces to the 3-sphere, the null vector becomes recurrent, and therefore the holonomy is contained in Sim(3), the maximal proper subgroup of the Lorentz group SO(4,1). For these geometries, all scalar invariants built from the curvature are constant. Explicit examples are discussed.

hep-th↗

arXiv2009

On the backreaction of frame dragging

The backreaction on black holes due to dragging heavy, rather than test, objects is discussed. As a case study, a regular black Saturn system where the central black hole has vanishing intrinsic angular momentum, J^{BH}=0, is considered. It is shown that there is a correlation between the sign of two response functions. One is interpreted as a moment of inertia of the black ring in the black Saturn system. The other measures the variation of the black ring horizon angular velocity with the central black hole mass, for fixed ring mass and angular momentum. The two different phases defined by these response functions collapse, for small central black hole mass, to the thin and fat ring phases. In the fat phase, the zero area limit of the black Saturn ring has reduced spin j^2>1, which is related to the behaviour of the ring angular velocity. Using the `gravitomagnetic clock effect', for which a universality property is exhibited, it is shown that frame dragging measured by an asymptotic observer decreases, in both phases, when the central black hole mass increases, for fixed ring mass and angular momentum. A close parallelism between the results for the fat phase and those obtained recently for the double Kerr solution is drawn, considering also a regular black Saturn system with J^{BH}\neq 0.

gr-qc↗

arXiv2009

Dynamical and Thermodynamical Aspects of Interacting Kerr Black Holes

We consider the asymptotically flat double-Kerr solution for two equal mass black holes with either the same or opposite angular momentum and with a massless strut between them. For fixed angular momentum and mass, the angular velocity of two co-rotating Kerr black holes decreases as they approach one another, from the Kerr value at infinite separation to the value of a single Kerr black hole with twice the mass and the angular momentum at the horizons merging limit. We show that the ratio J/M^2 for extremal co-rotating Kerr black holes varies from unity at infinite separation to two at the merging limit. These results are interpreted in terms of rotational dragging and compared with the case of counter-rotating Kerr black holes. We then analyse the merging of ergo-regions. In the co-rotating case the merger point occurs at an angle of π/2, in agreement with recent general arguments. In the counter-rotating case the ergo-regions never merge. We study the horizon geometry for both cases as a function of the distance and provide embedding diagrams. Finally, we study the thermodynamical evolution of the co-rotating double Kerr system, showing that, in the canonical ensemble, it is thermodynamically stable for fast spinning black holes. As for single Kerr black holes the stable and unstable phases are separated by a second order phase transition. We show that for large fixed angular momentum two Kerr black holes reach a minimum distance, before horizon merging has occurred, where the thermodynamical approximation breaks down. We also consider the micro-canonical ensemble to study the maximal energy that can be extracted from the double Kerr system as a function of the separation between the black holes.

gr-qc↗

arXiv2009

Five Dimensional Minimal Supergravities and Four Dimensional Complex Geometries

We discuss the relation between solutions admitting Killing spinors of minimal supergravities in five dimensions and four dimensional complex geometries. In the ungauged case (vanishing cosmological constant Λ=0) the solutions are determined in terms of a hyper-Kahler base space; in the gauged case (Λ<0) the complex geometry is Kahler; in the de Sitter case (Λ>0) the complex geometry is hyper-Kahler with torsion (HKT). In the latter case some details of the derivation are given. The method for constructing explicit solutions is discussed in each case.

hep-th↗

arXiv2008

On the interaction between two Kerr black holes

The double-Kerr solution is generated using both a Backlund transformation and the Belinskii-Zakharov inverse-scattering technique. We build a dictionary between the parametrisations naturally obtained in the two methods and show their equivalence. We then focus on the asymptotically flat double-Kerr system obeying the axis condition which is Z_2^ϕinvariant; for this system there is an exact formula for the force between the two black holes, in terms of their physical quantities and the coordinate distance. We then show that 1) the angular velocity of the two black holes decreases from the usual Kerr value at infinite distance to zero in the touching limit; 2) the extremal limit of the two black holes is given by |J|=cM^2, where c depends on the distance and varies from one to infinity as the distance decreases; 3) for sufficiently large angular momentum the temperature of the black holes attains a maximum at a certain finite coordinate distance. All of these results are interpreted in terms of the dragging effects of the system.

gr-qc↗

arXiv2008

Scalar Casimir Effect on a D-dimensional Einstein Static Universe

We compute the renormalised energy momentum tensor of a free scalar field coupled to gravity on an (n+1)-dimensional Einstein Static Universe (ESU), RxS^n, with arbitrary low energy effective operators (up to mass dimension n+1). A generic class of regulators is used, together with the Abel-Plana formula, leading to a manifestly regulator independent result. The general structure of the divergences is analysed to show that all the gravitational couplings (not just the cosmological constant) are renormalised for an arbitrary regulator. Various commonly used methods (damping function, point-splitting, momentum cut-off and zeta function) are shown to, effectively, belong to the given class. The final results depend strongly on the parity of n. A detailed analytical and numerical analysis is performed for the behaviours of the renormalised energy density and a quantity `sigma' which determines if the strong energy condition holds for the `quantum fluid'. We briefly discuss the quantum fluid back-reaction problem, via the higher dimensional Friedmann and Raychaudhuri equations, observe that equilibrium radii exist and unveil the possibility of a `Casimir stabilisation of Einstein Static Universes'.

hep-th↗

arXiv2008

A Double Myers-Perry Black Hole in Five Dimensions

Using the inverse scattering method we construct a six-parameter family of exact, stationary, asymptotically flat solutions of the 4+1 dimensional vacuum Einstein equations, with U(1)^2 rotational symmetry. It describes the superposition of two Myers-Perry black holes, each with a single angular momentum parameter, both in the same plane. The black holes live in a background geometry which is the Euclidean C-metric with an extra flat time direction. This background possesses conical singularities in two adjacent compact regions, each corresponding to a set of fixed points of one of the U(1) actions in the Cartan sub-algebra of SO(4). We discuss several aspects of the black holes geometry, including the conical singularities arising from force imbalance, and the torsion singularity arising from torque imbalance. The double Myers-Perry solution presented herein is considerably simpler than the four dimensional double Kerr solution and might be of interest in studying spin-spin interactions in five dimensional general relativity.

hep-th↗

arXiv2008

HKT Geometry and de Sitter Supergravity

Solutions of five dimensional minimal de Sitter supergravity admitting Killing spinors are considered. It is shown that the "timelike'' solutions are determined in terms of a four dimensional hyper-Kahler torsion (HKT) manifold. If the HKT manifold is conformally hyper-Kahler the most general solution can be obtained from a sub-class of supersymmetric solutions of minimal N=2 ungauged supergravity, by means of a simple transformation. Examples include a multi-BMPV de Sitter solution, describing multiple rotating black holes co-moving with the expansion of the universe. If the HKT manifold is not conformally hyper-Kahler, examples admitting a tri-holomorphic Killing vector field are constructed in terms of certain solutions of three dimensional Einstein-Weyl geometry.

hep-th↗

arXiv2007

A gravito-electromagnetic analogy based on tidal tensors

We propose a new approach to a physical analogy between General Relativity and Electromagnetism, based on tidal tensors of both theories. Using this approach we write a covariant form for the gravitational analogues of the Maxwell equations. The following realisations of the analogy are given. The first one matches linearised gravitational tidal tensors to exact electromagnetic tidal tensors in Minkwoski spacetime. The second one matches exact magnetic gravitational tidal tensors for ultra-stationary metrics to exact magnetic tidal tensors of electromagnetism in curved spaces. In the third we show that our approach leads to two-step exact derivation of the Papapetrou force on a gyroscope. We then establish a new proof for a class of tensor identities that define invariants of the type $\vec{E}^2-\vec{B}^2$ and $\vec{E}\cdot\vec{B}$, and we exhibit the invariants built from tidal tensors in both gravity and electromagnetism. We contrast our approach with the two gravito-electromagnetic analogies commonly found in the literature, and argue that it sheds light on the debate about the limit of validity of one of the analogies, and clarifies issues concerning the physical interpretation of the other.

gr-qc↗

arXiv2006

On a class of 4D Kahler bases and AdS_5 supersymmetric Black Holes

We construct a class of toric Kahler manifolds, M_4, of real dimension four, a subset of which corresponds to the Kahler bases of all known 5D asymptotically AdS_5 supersymmetric black-holes. In a certain limit, these Kahler spaces take the form of cones over Sasaki spaces, which, in turn, are fibrations over toric manifolds of real dimension two. The metric on M_4 is completely determined by a single function H(x), which is the conformal factor of the two dimensional space. We study the solutions of minimal five dimensional gauged supergravity having this class of Kahler spaces as base and show that in order to generate a five dimensional solution H(x) must obey a simple sixth order differential equation. We discuss the solutions in detail, which include all known asymptotically AdS_5 black holes as well as other spacetimes with non-compact horizons. Moreover we find an infinite number of supersymmetric deformations of these spacetimes with less spatial isometries than the base space. These deformations vanish at the horizon, but become relevant asymptotically.

hep-th↗

arXiv2005

Casimir energy and a cosmological bounce

We review different computation methods for the renormalised energy momentum tensor of a quantised scalar field in an Einstein Static Universe. For the extensively studied conformally coupled case we check their equivalence; for different couplings we discuss violation of different energy conditions. In particular, there is a family of masses and couplings which violate the weak and strong energy conditions but do not lead to spacelike propagation. Amongst these cases is that of a minimally coupled massless scalar field with no potential. We also point out a particular coupling for which a massless scalar field has vanishing renormalised energy momentum tensor. We discuss the backreaction problem and in particular the possibility that this Casimir energy could both source a short inflationary epoch and avoid the big bang singularity through a bounce.

hep-th↗

arXiv2005

Hagedorn transition and chronology protection in string theory

We conjecture chronology is protected in string theory due to the condensation of light winding strings near closed null curves. This condensation triggers a Hagedorn phase transition, whose end-point target space geometry should be chronological. Contrary to conventional arguments, chronology is protected by an infrared effect. We support this conjecture by studying strings in the O-plane orbifold, where we show that some winding string states are unstable and condense in the non-causal region of spacetime. The one-loop string partition function has infrared divergences associated to the condensation of these states.

hep-th↗

arXiv2003

Classical and Quantum Strings in compactified pp-waves and Godel type Universes

We consider Neveu-Schwarz pp-waves with spacetime supersymmetry. Upon compactification of a spacelike direction, these backgrounds develop Closed Null Curves (CNCs) and Closed Timelike Curves (CTCs), and are U-dual to supersymmetric Godel type universes. We study classical and quantum strings in this background, with emphasis on the strings winding around the compact direction. We consider two types of strings: long strings stabilized by NS flux and rotating strings which are stabilized against collapse by angular momentum. Some of the latter strings wrap around CNCs and CTCs, and are thus a potential source of pathology. We analyze the partition function, and in particular discuss the effects of these string states. Although our results are not conclusive, the partition function seems to be dramatically altered due to the presence of CNCs and CTCs. We discuss some interpretations of our results, including a possible sign of unitary violation.

hep-th↗

arXiv2003

Spinning deformations of the D1-D5 system and a geometric resolution of Closed Timelike Curves

The SO(4) isometry of the extreme Reissner-Nordstrom black hole of N=1, D=5 supergravity can be partly broken, without breaking any supersymmetry, in two different ways. The ``right'' solution is a rotating black hole (BMPV); the ``left'' is interpreted as a black hole in a Godel universe. In ten dimensions, both spacetimes are described by deformations of the D1-D5-pp-wave system with the property that the non-trivial Closed Timelike Curves of the five dimensional manifold are absent in the universal covering space of the ten dimensional manifold. In the decoupling limit, the BMPV deformation is normalizable. It corresponds to the vev of an IR relevant operator of dimension Δ=1. The Godel deformation is sub-leading in α' unless we take an infinite vorticity limit; in such case it is a non-normalizable perturbation. It corresponds to the insertion of a vector operator of dimension Δ=5. Thus we conclude that from the dual (1+1)-CFT viewpoint the SO(4) R-symmetry is broken `spontaneously' in the BMPV case and explicitly in the Godel case.

hep-th↗

arXiv2001

Flux-branes and the Dielectric Effect in String Theory

We consider the generalization to String and M-theory of the Melvin solution. These are flux p-branes which have (p+1)-dimensional Poincare invariance and are associated to an electric (p+1)-form field strength along their worldvolume. When a stack of Dp-branes is placed along the worldvolume of a flux (p+3)-brane it will expand to a spherical D(p+2)-brane due to the dielectric effect. This provides a new setup to consider the gauge theory/gravity duality. Compactifying M-theory on a circle we find the exact gravity solution of the type IIA theory describing the dielectric expansion of N D4-branes into a spherical bound state of D4-D6-branes, due to the presence of a flux 7-brane. In the decoupling limit, the deformation of the dual field theory associated with the presence of the flux brane is irrelevant in the UV. We calculate the gravitational radius and energy of the dielectric brane which give, respectively, a prediction for the VEV of scalars and vacuum energy of the dual field theory. Consideration of a spherical D6-brane probe with n units of D4-brane charge in the dielectric brane geometry suggests that the dual theory arises as the Scherk-Schwarz reduction of the M5-branes (2,0) conformal field theory. The probe potential has one minimum placed at the locus of the bulk dielectric brane and another associated to an inner dielectric brane shell.

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