arXiv subjects

Akihiro Ishibashi

Publications and source records attributed to Akihiro Ishibashi.

At least 73 records · Page 4Linked to original sources

arXiv2010

All Vacuum Near-Horizon Geometries in $D$-dimensions with $(D-3)$ Commuting Rotational Symmetries

We explicitly construct all stationary, non-static, extremal near horizon geometries in $D$ dimensions that satisfy the vacuum Einstein equations, and that have $D-3$ commuting rotational symmetries. Our work generalizes [arXiv:0806.2051] by Kunduri and Lucietti, where such a classification had been given in $D=4,5$. But our method is different from theirs and relies on a matrix formulation of the Einstein equations. Unlike their method, this matrix formulation works for any dimension. The metrics that we find come in three families, with horizon topology $S^2 \times T^{D-4}$, or $S^3 \times T^{D-5}$, or quotients thereof. Our metrics depend on two discrete parameters specifying the topology type, as well as $(D-2)(D-3)/2$ continuous parameters. Not all of our metrics in $D \ge 6$ seem to arise as the near horizon limits of known black hole solutions.

gr-qc↗

arXiv2009

Spherically symmetric black holes in minimally modified self-dual gravity

We discuss spherically symmetric black holes in the modified self-dual theory of gravity recently studied by Krasnov, obtained adding a Weyl-curvature dependent `cosmological term' to the Plebanski lagrangian for general relativity. This type of modified gravity admits two different types of singularities: one is a true singularity for the theory where the fundamental fields of the theory, as well as the (auxiliary) spacetime metric, become singular, and the other one is a milder "non-metric singularity" where the metric description of the spacetime breaks down but the fundamental fields themselves are regular. We first generalise this modified self-dual gravity to include Maxwell's field and then study basic features of spherically symmetric, charged black holes, with particular focus on whether these two types of singularities are hidden or naked. We restrict our attention to minimal forms of the modification, and find that the theory exhibits `screening' effects of the electric charge (or `anti-screening', depending upon the sign of the modification term), in the sense that it leads to the possibility of charging the black hole more (or less) than it would be possible in general relativity without exposing a naked singularity. We also find that for any (even arbitrarily large) value of charge, true singularities of the theory appear to be either achronal (non-timelike) covered by the hypersurface of a harmless non-metric singularity, or simply hidden inside at least one Killing horizon.

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arXiv2008

On the `Stationary Implies Axisymmetric' Theorem for Extremal Black Holes in Higher Dimensions

All known stationary black hole solutions in higher dimensions possess additional rotational symmetries in addition to the stationary Killing field. Also, for all known stationary solutions, the event horizon is a Killing horizon, and the surface gravity is constant. In the case of non-degenerate horizons (non-extremal black holes), a general theorem was previously established [gr-qc/0605106] proving that these statements are in fact generally true under the assumption that the spacetime is analytic, and that the metric satisfies Einstein's equation. Here, we extend the analysis to the case of degenerate (extremal) black holes. It is shown that the theorem still holds true if the vector of angular velocities of the horizon satisfies a certain "diophantine condition," which holds except for a set of measure zero.

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arXiv2008

Charged Black Holes in a Rotating Gross-Perry-Sorkin Monopole Background

We present a new class of stationary charged black hole solutions to five-dimensional Einstein-Maxwell-Chern-Simons theories. We construct the solutions by utilizing so called the squashing transformation. At infinity, our solutions behave as a four-dimensional flat spacetime plus a `circle' and hence describe a Kaluza-Klein black hole. More precisely, our solutions can be viewed as a charged rotating black hole in a rotating Gross-Perry-Sorkin monopole background with the black hole rotation induced from the background rotation.

hep-th↗

arXiv2008

Higher Dimensional Bondi Energy with a Globally Specified Background Structure

A higher (even spacetime) dimensional generalization of the Bondi energy has recently been proposed by gr-qc/0304054 within the framework of conformal infinity and Hamiltonian formalizm. The gauge condition employed in gr-qc/0304054 to derive the Bondi energy expression is, however, peculiar in the sense that cross-sections of null infinity specified by that gauge are anisotropic and in fact non-compact. For this reason, that gauge is difficult to use for explicit computations of the Bondi energy in general, asymptotically flat radiative spacetimes. Also it is not clear, under that gauge condition, whether apparent difference between the expressions of higher dimensional Bondi energy and the 4-dimensional one is due to the choice of gauges or qualitatively different nature of higher dimensional gravity from 4-dimensional gravity. In this paper, we consider instead, Gaussian null conformal gauge as one of more natural gauge conditions that admit a global specification of background structure with compact, spherical cross-sections of null infinity. Accordingly, we modify the previous definition of higher dimensional news tensor so that it becomes well-defined in the Gaussian null conformal gauge and derive, for vacuum solutions, the expression for the Bondi energy-momentum in the new gauge choice, which takes a universal form in arbitrary (even spacetime) dimensions greater than or equal to four.

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arXiv2006

A Higher Dimensional Stationary Rotating Black Hole Must be Axisymmetric

A key result in the proof of black hole uniqueness in 4-dimensions is that a stationary black hole that is ``rotating''--i.e., is such that the stationary Killing field is not everywhere normal to the horizon--must be axisymmetric. The proof of this result in 4-dimensions relies on the fact that the orbits of the stationary Killing field on the horizon have the property that they must return to the same null geodesic generator of the horizon after a certain period, $P$. This latter property follows, in turn, from the fact that the cross-sections of the horizon are two-dimensional spheres. However, in spacetimes of dimension greater than 4, it is no longer true that the orbits of the stationary Killing field on the horizon must return to the same null geodesic generator. In this paper, we prove that, nevertheless, a higher dimensional stationary black hole that is rotating must be axisymmetric. No assumptions are made concerning the topology of the horizon cross-sections other than that they are compact. However, we assume that the horizon is non-degenerate and, as in the 4-dimensional proof, that the spacetime is analytic.

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arXiv2006

Asymptotically AdS brane black holes

We study the possibility of having a static, asymptotically AdS black hole localized on a braneworld with matter fields, within the framework of the Randall and Sundrum scenario. We attempt to look for such a brane black hole configuration by slicing a given bulk spacetime and taking Z_2 symmetry about the slices. We find that such configurations are possible, and as an explicit example, we provide a family of asymptotically AdS brane black hole solutions for which both the bulk and brane metrics are regular on and outside the black hole horizon and brane matter fields are realistic in the sense that the dominant energy condition is satisfied. We also find that our braneworld models exhibit signature change inside the black hole horizon.

hep-th↗

arXiv2005

Can the Acceleration of Our Universe Be Explained by the Effects of Inhomogeneities?

No. It is simply not plausible that cosmic acceleration could arise within the context of general relativity from a back-reaction effect of inhomogeneities in our universe, without the presence of a cosmological constant or ``dark energy.'' We point out that our universe appears to be described very accurately on all scales by a Newtonianly perturbed FLRW metric. (This assertion is entirely consistent with the fact that we commonly encounter $δρ/ρ> 10^{30}$.) If the universe is accurately described by a Newtonianly perturbed FLRW metric, then the back-reaction of inhomogeneities on the dynamics of the universe is negligible. If not, then it is the burden of an alternative model to account for the observed properties of our universe. We emphasize with concrete examples that it is {\it not} adequate to attempt to justify a model by merely showing that some spatially averaged quantities behave the same way as in FLRW models with acceleration. A quantity representing the ``scale factor'' may ``accelerate'' without there being any physically observable consequences of this acceleration. It also is {\it not} adequate to calculate the second-order stress energy tensor and show that it has a form similar to that of a cosmological constant of the appropriate magnitude. The second-order stress energy tensor is gauge dependent, and if it were large, contributions of higher perturbative order could not be neglected. We attempt to clear up the apparent confusion between the second-order stress energy tensor arising in perturbation theory and the ``effective stress energy tensor'' arising in the ``shortwave approximation.''

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arXiv2004

On the stability of naked singularities

We study the linearised stability of the nakedly singular negative mass Schwarzschild solution against gravitational perturbations. There is a one parameter family of possible boundary conditions at the singularity. We give a precise criterion for stability depending on the boundary condition. We show that one particular boundary condition is physically preferred and show that the spacetime is stable with this boundary condition.

hep-th↗

arXiv2004

Asymptotic flatness at null infinity in higher dimensional gravity

We give a geometrical definition of the asymptotic flatness at null infinity in spacetimes of even dimension $d$ greater than 4 within the framework of conformal infinity. Our definition is shown to be stable against perturbations to linear order. We also show that our definition is stringent enough to allow one to define the total energy of the system viewed from null infinity as the generator conjugate to an asymptotic time translation. We derive an expression for the generator conjugate within the Hamiltonian framework, and propose to take this notion of energy as the natural generalisation of the Bondi energy to higher dimensions. Our definitions of asymptotic flatness and the Bondi energy formula differ qualitatively from the corresponding definitions in $d=4$; although the asymptotic structure of null infinity in higher dimensions parallels that in 4-dimensions in some ways, the latter seems to be a rather special case on the whole compared to general $d>4$. Our definitions and constructions do not work in odd spacetime dimensions, essentially because the unphysical metric seems to have insufficient regularity properties at null infinity in that case.

hep-th↗

arXiv2004

Asymptotic Flatness and Bondi Energy in Higher Dimensional Gravity

We give a general geometric definition of asymptotic flatness at null infinity in $d$-dimensional general relativity ($d$ even) within the framework of conformal infinity. Our definition is arrived at via an analysis of linear perturbations near null infinity and shown to be stable under such perturbations. The detailed fall off properties of the perturbations, as well as the gauge conditions that need to be imposed to make the perturbations regular at infinity, are qualitatively different in higher dimensions; in particular, the decay rate of a radiating solution at null infinity differs from that of a static solution in higher dimensions. The definition of asymptotic flatness in higher dimensions consequently also differs qualitatively from that in $d=4$. We then derive an expression for the generator conjugate to an asymptotic time translation symmetry for asymptotically flat spacetimes in $d$-dimensional general relativity ($d$ even) within the Hamiltonian framework, making use especially of a formalism developed by Wald and Zoupas. This generator is given by an integral over a cross section at null infinity of a certain local expression and is taken to be the definition of the Bondi energy in $d$ dimensions. Our definition yields a manifestly positive flux of radiated energy. Our definitions and constructions fail in odd spacetime dimensions, essentially because the regularity properties of the metric at null infinity seem to be insufficient in that case. We also find that there is no direct analog of the well-known infinite set of angle dependent translational symmetries in more than 4 dimensions.

gr-qc↗

arXiv2004

Topology and Signature Changes in Braneworlds

It has been believed that topology and signature change of the universe can only happen accompanied by singularities, in classical, or instantons, in quantum, gravity. In this note, we point out however that in the braneworld context, such an event can be understood as a classical, smooth event. We supply some explicit examples of such cases, starting from the Dirac-Born-Infeld action. Topology change of the brane universe can be realised by allowing self-intersecting branes. Signature change in a braneworld is made possible in an everywhere Lorentzian bulk spacetime. In our examples, the boundary of the signature change is a curvature singularity from the brane point of view, but nevertheless that event can be described in a completely smooth manner from the bulk point of view.

hep-th↗

arXiv2004

Dynamics in Non-Globally-Hyperbolic Static Spacetimes III: Anti-de Sitter Spacetime

In recent years, there has been considerable interest in theories formulated in anti-de Sitter (AdS) spacetime. However, AdS spacetime fails to be globally hyperbolic, so a classical field satisfying a hyperbolic wave equation on AdS spacetime need not have a well defined dynamics. Nevertheless, AdS spacetime is static, so the possible rules of dynamics for a field satisfying a linear wave equation are constrained by our previous general analysis--given in paper II--where it was shown that the possible choices of dynamics correspond to choices of positive, self-adjoint extensions of a certain differential operator, $A$. In the present paper, we reduce the analysis of electromagnetic, and gravitational perturbations in AdS spacetime to scalar wave equations. We then apply our general results to analyse the possible dynamics of scalar, electromagnetic, and gravitational perturbations in AdS spacetime. In AdS spacetime, the freedom (if any) in choosing self-adjoint extensions of $A$ corresponds to the freedom (if any) in choosing suitable boundary conditions at infinity, so our analysis determines all of the possible boundary conditions that can be imposed at infinity. In particular, we show that other boundary conditions besides the Dirichlet and Neumann conditions may be possible, depending on the value of the effective mass for scalar field perturbations, and depending on the number of spacetime dimensions and type of mode for electromagnetic and gravitational perturbations.

hep-th↗

arXiv2004

Master equations for perturbations of generalised static black holes with charge in higher dimensions

We extend the formulation for perturbations of maximally symmetric black holes in higher dimensions developed by the present authors in a previous paper (hep-th/0305147) to a charged black hole background whose horizon is described by an Einstein manifold. For charged black holes, perturbations of electromagnetic fields are coupled to the vector and scalar modes of metric perturbations non-trivially. We show that by taking appropriate combinations of gauge-invariant variables for these perturbations, the perturbation equations for the Einstein-Maxwell system are reduced to two decoupled second-order wave equations describing the behaviour of the electromagnetic mode and the gravitational mode, for any value of the cosmological constant. These wave equations are transformed into Schrödinger-type ODEs through a Fourier transformation with respect to time. Using these equations, we investigate the stability of generalised black holes with charge. We also give explicit expressions for the source terms of these master equations with application to the emission problem of gravitational waves in mind.

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arXiv2003

Stability of Generalised Static Black Holes in Higher Dimensions

We discuss the stability of (charged) static black holes in higher-dimensional spacetimes with and without cosmological constant by using gauge-invariant master equations of the Schroedinger equation type for black hole perturbations derived by the authors recently. In particular, we show that the stability of higher-dimensional Schwarzschild black holes can be proved with the help of a technique called S-deformation of the master equations. We also point out that higher-dimensional static black holes might be unstable only against scalar-type perturbations in the neutral case and in the charged case with spherically symmetric or flat horizons.

gr-qc↗

arXiv2003

Stability of Higher-Dimensional Schwarzschild Black Holes

We investigate the classical stability of the higher-dimensional Schwarzschild black holes against linear perturbations, in the framework of a gauge-invariant formalism for gravitational perturbations of maximally symmetric black holes, recently developed by the authors. The perturbations are classified into the tensor, vector, and scalar-type modes according to their tensorial behaviour on the spherical section of the background metric, where the last two modes correspond respectively to the axial- and the polar-mode in the four-dimensional situation. We show that, for each mode of the perturbations, the spatial derivative part of the master equation is a positive, self-adjoint operator in the $L^2$-Hilbert space, hence that the master equation for each tensorial type of perturbations does not admit normalisable negative-modes which would describe unstable solutions. On the same Schwarzschild background, we also analyse the static perturbation of the scalar mode, and show that there exists no static perturbation which is regular everywhere outside the event horizon and well-behaved at spatial infinity. This checks the uniqueness of the higher-dimensional spherically symmetric, static, vacuum black hole, within the perturbation framework. Our strategy for the stability problem is also applicable to the other higher-dimensional maximally symmetric black holes with non-vanishing cosmological constant. We show that all possible types of maximally symmetric black holes (thus, including the higher-dimensional Schwarzschild-de Sitter and Schwarzschild-anti-de Sitter black holes) are stable against the tensor and the vector perturbations.

hep-th↗

arXiv2003

A master equation for gravitational perturbations of maximally symmetric black holes in higher dimensions

We show that in four or more spacetime dimensions, the Einstein equations for gravitational perturbations of maximally symmetric vacuum black holes can be reduced to a single 2nd-order wave equation in a two-dimensional static spacetime for a gauge-invariant master variable, irrespective of the mode of perturbations. Our formulation applies to the case of vanishing as well as non-vanishing cosmological constant Lambda. The sign of the sectional curvature K of each spatial section of equipotential surfaces is also kept general. In the four-dimensional Schwarzschild background, this master equation for a scalar perturbation is identical to the Zerilli equation for the polar mode and the master equation for a vector perturbation is identical to the Regge-Wheeler equation for the axial mode. Furthermore, in the four-dimensional Schwarzschild-anti-de Sitter background with K=0,1, our equation coincides with those derived by Cardoso and Lemos recently. As a simple application, we prove the perturbative stability and uniqueness of four-dimensional non-extremal spherically symmetric black holes for any Lambda. We also point out that there exists no simple relation between scalar-type and vector-type perturbations in higher dimensions, unlike in four dimensions. Although we only treat maximally symmetric black holes in the present paper, the final master equations are valid even when the hirozon geometry is described by a generic Einstein manifold.

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arXiv2003

Dynamics in Non-Globally-Hyperbolic Static Spacetimes II: General Analysis of Prescriptions for Dynamics

It was previously shown by one of us that in any static, non-globally-hyperbolic, spacetime it is always possible to define a sensible dynamics for a Klein-Gordon scalar field. The prescription proposed for doing so involved viewing the spatial derivative part, $A$, of the wave operator as an operator on a certain $L^2$ Hilbert space $\mathcal H$ and then defining a positive, self-adjoint operator on $\mathcal H$ by taking the Friedrichs extension (or other positive extension) of $A$. However, this analysis left open the possibility that there could be other inequivalent prescriptions of a completely different nature that might also yield satisfactory definitions of the dynamics of a scalar field. We show here that this is not the case. Specifically, we show that if the dynamics agrees locally with the dynamics defined by the wave equation, if it admits a suitable conserved energy, and if it satisfies certain other specified conditions, then it must correspond to the dynamics defined by choosing some positive, self-adjoint extension of $A$ on $\mathcal H$. Thus, subject to our requirements, the previously given prescription is the only possible way of defining the dynamics of a scalar field in a static, non-globally-hyperbolic, spacetime. In a subsequent paper, this result will be applied to the analysis of scalar, electromagnetic, and gravitational perturbations of anti-de Sitter spacetime. By doing so, we will determine all possible choices of boundary conditions at infinity in anti-de Sitter spacetime that give rise to sensible dynamics.

gr-qc↗