Uniform Energy Bound and Morawetz Estimate for Extreme Components of Spin Fields in the Exterior of a Slowly Rotating Kerr Black Hole II: Linearized Gravity

We consider the Maxwell equation in the exterior of a very slowly rotating Kerr black hole. For this system, we prove the boundedness of a positive definite energy on each hypersurface of constant [Formula: see text]. We also prove the convergence of each solution to a stationary Coulomb solution. We separate a general solution into the charged, Coulomb part and the uncharged part. Convergence to the Coulomb solutions follows from the fact that the uncharged part satisfies a Morawetz estimate, i.e. that a spatially localized energy density is integrable in time. For the unchanged part, we study both the full Maxwell equation and the Fackerell–Ipser equation for one component. To treat the Fackerell–Ipser equation, we use a Fourier transform in [Formula: see text]. For the Fackerell–Ipser equation, we prove a refined Morawetz estimate that controls 3/2 derivatives with no loss near the orbiting null geodesics.

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Spinning test body orbiting around a Kerr black hole: Eccentric equatorial orbits and their asymptotic gravitational-wave fluxes

Physical Review D ◽

10.1103/physrevd.103.104045 ◽

2021 ◽

Vol 103 (10) ◽

Author(s):

Viktor Skoupý ◽

Georgios Lukes-Gerakopoulos

Keyword(s):

Black Hole ◽

Gravitational Wave ◽

Kerr Black Hole ◽

Test Body

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Spherical orbits around a Kerr black hole

General Relativity and Gravitation ◽

10.1007/s10714-020-02782-z ◽

2021 ◽

Vol 53 (1) ◽

Author(s):

Edward Teo

Keyword(s):

Black Hole ◽

Kerr Black Hole

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Choked accretion onto a Kerr black hole

Physical Review D ◽

10.1103/physrevd.103.023003 ◽

2021 ◽

Vol 103 (2) ◽

Author(s):

Alejandro Aguayo-Ortiz ◽

Olivier Sarbach ◽

Emilio Tejeda

Keyword(s):

Black Hole ◽

Kerr Black Hole

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Influence of the geometric configuration of accretion flow on the black hole spin dependence of relativistic acoustic geometry

International Journal of Modern Physics D ◽

10.1142/s0218271818500232 ◽

2018 ◽

Vol 27 (03) ◽

pp. 1850023 ◽

Cited By ~ 2

Author(s):

Pratik Tarafdar ◽

Tapas K. Das

Keyword(s):

Black Hole ◽

Kerr Black Hole ◽

Geometric Configuration ◽

Surface Gravity ◽

Linear Perturbation ◽

Flow Profile ◽

White Hole ◽

Accretion Flow ◽

Black Hole Spin ◽

General Relativistic

Linear perturbation of general relativistic accretion of low angular momentum hydrodynamic fluid onto a Kerr black hole leads to the formation of curved acoustic geometry embedded within the background flow. Characteristic features of such sonic geometry depend on the black hole spin. Such dependence can be probed by studying the correlation of the acoustic surface gravity [Formula: see text] with the Kerr parameter [Formula: see text]. The [Formula: see text]–[Formula: see text] relationship further gets influenced by the geometric configuration of the accretion flow structure. In this work, such influence has been studied for multitransonic shocked accretion where linear perturbation of general relativistic flow profile leads to the formation of two analogue black hole-type horizons formed at the sonic points and one analogue white hole-type horizon which is formed at the shock location producing divergent acoustic surface gravity. Dependence of the [Formula: see text]–[Formula: see text] relationship on the geometric configuration has also been studied for monotransonic accretion, over the entire span of the Kerr parameter including retrograde flow. For accreting astrophysical black holes, the present work thus investigates how the salient features of the embedded relativistic sonic geometry may be determined not only by the background spacetime, but also by the flow configuration of the embedding matter.

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