Static Kerr Green’s function in closed form and an analytic derivation of the self-force for a static scalar charge in Kerr space-time

Ottewill, Adrian C.; Taylor, PM

doi:10.1103/physrevd.86.024036

Cited by 18 publications

(13 citation statements)

References 32 publications

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“…However, neither Konno and Takahashi nor the present author have found general expressions for the radial indefinite integrals. Yet another analytic approach is to try to integrate the source term against the analytically known Green's function [25]. However, the Green's function is written in terms of a complete elliptic integral of the first kind [26], and the present author has not had any success integrating the source against the Green's function.…”

Section: Numerical Scheme and Solutionsmentioning

confidence: 99%

Rapidly rotating black holes in dynamical Chern-Simons gravity: Decoupling limit solutions and breakdown

Stein

2014

Phys. Rev. D

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Rapidly rotating black holes are a prime arena for understanding corrections to Einstein's theory of general relativity (GR). We construct solutions for rapidly rotating black holes in dynamical Chern-Simons (dCS) gravity, a useful and motivated example of a post-GR correction. We treat dCS as an effective theory and thus work in the decoupling limit, where we apply a perturbation scheme using the Kerr metric as the background solution. Using the solutions to the scalar field and the trace of the metric perturbation, we determine the regime of validity of our perturbative approach. We find that the maximal spin limit may be divergent, and the decoupling limit is strongly restricted for rapid rotation. Rapidly-rotating stellar-mass BHs can potentially be used to place strong bounds on the coupling parameter of dCS. In order for the black hole observed in GRO J1655-40 to be within the decoupling limit we need 22 km, a value 7 orders of magnitude smaller than present Solar System bounds on dynamical Chern-Simons gravity.

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Section: Numerical Scheme and Solutionsmentioning

confidence: 99%

Rapidly rotating black holes in dynamical Chern-Simons gravity: Decoupling limit solutions and breakdown

Stein

2014

Phys. Rev. D

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“…The generalization of this solution to the case of a scalar charge was found in [9]. Further generalizations to the Reissner-Nordström and Kerr black holes can be found in [3,4,10]. Exact higher-dimensional solutions for a field of a static point charge near extremely charged black holes (or a set of such black holes) described by Majumdar-Papapetrou metrics were found in [11].…”

Section: Jhep04(2015)014mentioning

confidence: 88%

Bi-conformal symmetry and static Green functions in the Schwarzschild-Tangherlini spacetimes

Frolov

Zelnikov

2015

J. High Energ. Phys.

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We study a static massless minimally coupled scalar field created by a source in a static D-dimensional spacetime. We demonstrate that the corresponding equation for this field is invariant under a special transformation of the background metric. This transformation consists of the static conformal transformation of the spatial part of the metric accompanied by a properly chosen transformation of the red-shift factor. Both transformations are determined by one function Ω of the spatial coordinates. We show that in a case of higher dimensional spherically symmetric black holes one can find such a bi-conformal transformation that the symmetry of the D-dimensional metric is enhanced after its application. Namely, the metric becomes a direct sum of the metric on a unit sphere and the metric of 2D anti-de Sitter space. The method of the heat kernels is used to find the Green function in this new space, which allows one, after dimensional reduction, to obtain a static Green function in the original space of the static black hole. The general useful representation of static Green functions is obtained in the Schwarzschild-Tangherlini spacetimes of arbitrary dimension. The exact explicit expressions for the static Green functions are obtained in such metrics for D < 6. It is shown that in the four dimensional case the corresponding Green function coincides with the Copson solution.

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“…Havingλ d sit at a fixed point implies -from eq. (3.28) -the quantity λ d evolves as 31) and so from (3.23) h 0 ( ) at the fixed point evolves as To gain some intuition, let us focus on the Klein-Gordon case s = 0 for a moment. Using (2.32) to eliminate ξ,…”

Section: Fixed Points As Perfect Absorbers/emittersmentioning

confidence: 99%

Effective field theory of black hole echoes

Burgess

Plestid

Rummel

2018

J. High Energ. Phys.

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Gravitational wave 'echoes' during black-hole merging events have been advocated as possible signals of modifications to gravity in the strong-field (but semiclassical) regime. In these proposals the observable effect comes entirely from the appearance of nonzero reflection probability at the horizon, which vanishes for a standard black hole. We show how to apply EFT reasoning to these arguments, using and extending earlier work for localized systems that relates choices of boundary condition to the action for the physics responsible for these boundary conditions. EFT reasoning applied to this action argues that linear 'Robin' boundary conditions dominate at low energies, and we determine the relationship between the corresponding effective coupling (whose value is the one relevant low-energy prediction of particular modifications to General Relativity for these systems) and the phenomenologically measurable near-horizon reflection coefficient. Because this connection involves only near-horizon physics it is comparatively simple to establish, and we do so for perturbations in both the Schwarzschild geometry (which is the one most often studied theoretically) and the Kerr geometry (which is the one of observational interest for post-merger ring down). In passing we identify the renormalization-group evolution of the effective couplings as a function of a regularization distance from the horizon, that enforces how physics does not depend on the precise position where the boundary conditions are imposed. We show that the perfect-absorber/perfectemitter boundary conditions of General Relativity correspond to the only fixed points of this evolution. Nontrivial running of all other RG evolution reflects how modifications to gravity necessarily introduce new physics near the horizon. arXiv:1808.00847v2 [gr-qc]

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Static Kerr Green’s function in closed form and an analytic derivation of the self-force for a static scalar charge in Kerr space-time

Cited by 18 publications

References 32 publications

Rapidly rotating black holes in dynamical Chern-Simons gravity: Decoupling limit solutions and breakdown

Rapidly rotating black holes in dynamical Chern-Simons gravity: Decoupling limit solutions and breakdown

Bi-conformal symmetry and static Green functions in the Schwarzschild-Tangherlini spacetimes

Effective field theory of black hole echoes

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