arXiv subjects

B. F. Whiting

Publications and source records attributed to B. F. Whiting.

8 recordsLinked to original sources

arXiv2025

Perturbations of Black Holes in Einstein-Maxwell-Dilaton-Axion (EMDA) Theories

We extend our earlier work on the linearised perturbations of static black holes in Einstein-Maxwell-Dilaton (EMD) theories to the case where the black holes are solutions in an enlarged theory including also an axion. We study the perturbations in a 3-parameter family of such EMDA theories. The systems of equations describing the linearised perturbations can always be separated, but they can only be decoupled when the three parameters are restricted to a 1-parameter family of EMDA theories, characterised by a parameter $b$ that determines the coupling of the axion to the $\epsilon^{\mu\nu\rho\sigma}\, F_{\mu\nu}\, F_{\rho\sigma}$ term. In the specific case when $b=1$, the theory is related to an ${\cal N}=2$ supergravity. In this one case we find that the perturbations in the axial and the polar sectors are related by a remarkable transformation, which generalises one found by Chandrasekhar for the perturbations of Reissner-Nordstr\"om in Einstein-Maxwell theory. This transformation is of a form found in supersymmetric quantum mechanical models. The existence of such mappings between the axial and polar perturbations appears to correlate with those cases where there is an underlying supergravity supporting the solution, even though the black hole backgrounds are non-extremal and therefore not supersymmetric. We prove the mode stability of the static black hole solutions in the supersymmetric EMDA theory. For other values of the parameter $b$ in the EMDA theories that allow decoupling of the modes, we find that one of the radial potentials can be negative outside the horizon if $b$ is sufficiently large, raising the possibility of there being perturbative mode instabilities in such a case.

hep-th↗

arXiv2024

On The Perturbations of Gibbons-Maeda Black Holes in Einstein-Maxwell-Dilaton Theories

The study of perturbations around black hole backgrounds in general relativity and Einstein-Maxwell theory has a long history, going back to the work of Regge and Wheeler in the 1950s. As part of a broader investigation of perturbations around black holes in supergravity, we describe here our results for the perturbations around the Gibbons-Maeda static charged black holes in a class of Einstein-Maxwell-Dilaton theories. Our analysis follows the general strategy developed by Chandrasekhar and Xanthopoulos for the perturbations of the Reissner-Nordström black hole. Here, the analysis is considerably more involved, because of the presence of the dilaton field, which couples to the other polar modes. We nonetheless find that the problem is completely solvable, in the sense that one can separate variables and eventually describe all the perturbations in terms of diagonalised second-order radial equations. We are able to prove the mode stability of all the Gibbons-Maeda black hole solutions.

hep-th↗

arXiv2022

Mode Stability For Massless Scalars In Five-Dimensional Black Hole Backgrounds

The mode stability of the Kerr black hole in four dimensions was demonstrated by Whiting in 1989, by separating the Teukolsky equation that describes gravitational perturbations and then transforming the radial and angular equations in such a way that the problem can be reformulated as a wave equation in an auxiliary spacetime in which the proof of stability is greatly simplified, owing to the absence of an ergoregion. As a preliminary step towards extending these ideas to higher-dimensional black holes, we study the mode stability of the massless scalar wave equation in the five-dimensional black hole solutions of Einstein gravity and supergravity. We show how the wave equation can again be mapped into one in an auxiliary spacetime in which there is no ergoregion, allowing us to give a proof of the mode stability of the solutions of the scalar wave equation.

gr-qc↗

arXiv2021

Supergravity Black Holes, Love Numbers and Harmonic Coordinates

To perform realistic tests of theories of gravity, we need to be able to look beyond general relativity and evaluate the consistency of alternative theories with observational data from, especially, gravitational wave detections using, for example, an agnostic Bayesian approach. In this paper we further examine properties of one class of such viable, alternative theories, based on metrics arising from ungauged supergravity. In particular, we examine the massless, neutral, minimally coupled scalar wave equation in a general stationary, axisymmetric background metric such as that of a charged rotating black hole, when the scalar field is either time independent or in the low-frequency, near-zone limit, with a view to calculating the Love numbers of tidal perturbations, and of obtaining harmonic coordinates for the background metric. For a four-parameter family of charged asymptotically flat rotating black hole solutions of ungauged supergravity theory known as STU black holes, which includes Kaluza-Klein black holes and the Kerr-Sen black hole as special cases, we find that all time-independent solutions, and hence the harmonic coordinates of the metrics, are identical to those of the Kerr solution. In the low-frequency limit we find the scalar fields exhibit the same $SL(2,R)$ symmetry as holds in the case of the Kerr solution. We point out extensions of our results to a wider class of metrics, which includes solutions of Einstein-Maxwell-Dilaton theory.

gr-qc↗

arXiv2020

Positive Energy Functional for Massless Scalars in Rotating Black Hole Backgrounds of Maximal Ungauged Supergravity

We outline a proof of the stability of a massless neutral scalar field $ψ$ in the background of a wide class of four dimensional asymptotically flat rotating and ``electrically charged'' solutions of supergravity, and the low energy limit of string theory, known as STU metrics. Despite their complexity, we find it possible to circumvent the difficulties presented by the existence of ergo-regions and the related phenomenon of super-radiance in the original metrics by following a strategy due to Whiting, and passing to an auxiliary metric admitting an everywhere lightlike Killing field and constructing a scalar field $Ψ$ (related to a possible unstable mode $ψ$ by a non-local transformation) which satisfies the massless wave equation with respect to the auxiliary metric. By contrast with the case for $ψ$, the associated energy density of $Ψ$ is not only conserved but is also non-negative.

gr-qc↗

arXiv2007

Analytic approximations, perturbation methods, and their applications

The paper summarizes the parallel session B3 {\em Analytic approximations, perturbation methods, and their applications} of the GR18 conference. The talks in the session reported notably recent advances in black hole perturbations and post-Newtonian approximations as applied to sources of gravitational waves.

gr-qc↗

arXiv2004

Optimal combination of signals from co-located gravitational wave interferometers for use in searches for a stochastic background

This article derives an optimal (i.e., unbiased, minimum variance) estimator for the pseudo-detector strain for a pair of co-located gravitational wave interferometers (such as the pair of LIGO interferometers at its Hanford Observatory), allowing for possible instrumental correlations between the two detectors. The technique is robust and does not involve any assumptions or approximations regarding the relative strength of gravitational wave signals in the detector pair with respect to other sources of correlated instrumental or environmental noise. An expression is given for the effective power spectral density of the combined noise in the pseudo-detector. This can then be introduced into the standard optimal Wiener filter used to cross-correlate detector data streams in order to obtain an optimal estimate of the stochastic gravitational wave background. In addition, a dual to the optimal estimate of strain is derived. This dual is constructed to contain no gravitational wave signature and can thus be used as on "off-source" measurement to test algorithms used in the "on-source" observation.

gr-qc↗

arXiv1993

Black Hole Evaporation without Information Loss

An approach to black hole quantization is proposed wherein it is assumed that quantum coherence is preserved. A consequence of this is that the Penrose diagram describing gravitational collapse will show the same topological structure as flat Minkowski space. After giving our motivations for such a quantization procedure we formulate the background field approximation, in which particles are divided into "hard" particles and "soft" particles. The background space-time metric depends both on the in-states and on the out-states. We present some model calculations and extensive discussions. In particular, we show, in the context of a toy model, that the $S$-matrix describing soft particles in the hard particle background of a collapsing star is unitary, nevertheless, the spectrum of particles is shown to be approximately thermal. We also conclude that there is an important topological constraint on functional integrals.

gr-qc↗