On uniqueness of static spacetimes with non-trivial conformal scalar field

Tomikawa, Yoshimune; Shiromizu, Tetsuya; Izumi, Keisuke

doi:10.1088/1361-6382/aa7906

Cited by 20 publications

(21 citation statements)

References 23 publications

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“…In what follows, we shall consider very small deviations, |δx α | ≪ 1, |δẋ α | ≪ 1 and use a linear approximation. Substituting (44) into the geodesic equation (20) and the null condition (21), and expanding in powers of δx α and δẋ α , we derive in the first-order approximation…”

Section: Small Oscillationsmentioning

confidence: 99%

“…In [13], a photon sphere for an asymptotically flat, static space-time was defined as a timelike embedded hypersurface for which the lapse function is constant. Using this definition, uniqueness theorems for different types of space-times were proven in [13][14][15][16][17][18][19][20][21]. In [22], a photon surface is defined as a totally geodesic submanifold of the optical manifold in a static space-time.…”

Section: Introductionmentioning

confidence: 99%

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Metamorphoses of a photon sphere

Shoom

2017

Phys. Rev. D

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There are circular planar null geodesics at r = 3M around a Schwarzschild black hole of mass M . These geodesics form a photon sphere. Null geodesics of the Schwarzschild space-time which do not form the photon sphere are either escape to null infinity or get captured by the black hole. Thus, from the dynamical point of view, the photon sphere represents a smooth basin boundary that separates the basins of escape and capture of the dynamical system governing the null geodesics. Here we consider a Schwarzschild black hole distorted by an external, static, and axisymmetric quadrupolar gravitational field defined by a quadrupole moment q. We study null geodesics around such a black hole and show that the photon sphere does not survive the distortion. For q −0.017001 it transforms into a fractal basin boundary that indicates chaotic behavior of the null geodesics. We calculate the box-counting fractal dimension of the basin boundary and the related uncertainty exponent, which depend on the value of the quadrupole moment.

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Section: Small Oscillationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Metamorphoses of a photon sphere

Shoom

2017

Phys. Rev. D

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“…When 0 < m < 1, there will be two solutions for q ext from Eq. (5). The black hole can be extremal for these two values of the charge when 0 < m < 1.…”

Section: Case I: Extremal Static Charged Btz Black Holementioning

confidence: 90%

“…Mathematically, there are quite a few uniqueness results that either concern or involve photon orbits in one way or another [1][2][3][4][5]. In addition, photon orbits often saturate many inequalities, see, e.g.…”

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confidence: 99%

Lux in obscuro II: photon orbits of extremal AdS black holes revisited

Tang

Ong

Wang

2017

Class. Quantum Grav.

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A large class of spherically symmetric static extremal black hole spacetimes possesses a stable null photon sphere on their horizons. For the extremal Kerr-Newman family, the photon sphere only really coincides with the horizon in the sense clarified by Doran. The condition under which photon orbit is stable on an asymptotically flat extremal Kerr-Newman black hole horizon has recently been clarified; it is found that a sufficiently large angular momentum destabilizes the photon orbit, whereas electrical charge tends to stabilize it. We investigated the effect of a negative cosmological constant on this observation, and found the same behavior in the case of an extremal asymptotically Kerr-Newman-AdS black holes in (3 + 1)-dimensions. In (2 + 1)-dimensions, in the presence of electrical charge, the angular momentum never becomes large enough to destabilize the photon orbit. We comment on the instabilities of black hole spacetimes with a stable photon orbit.

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“…and q ′ , α ′ , β ′ , γ ′ satisfying the same relations as in (24). At the end of this section, let us mention briefly the case of the extreme Reissner-Nordstrom accelerated black hole, with Q = ±M, for which the radial function in (19) is…”

Section: Accelerating Charged Black Holesmentioning

confidence: 99%

Massless fermions on static general prolate metrics and their Heun solutions

Dariescu

Stelea

2019

Mod. Phys. Lett. A

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Employing a pseudo-orthonormal coordinate-free approach we write down the Dirac equation in spacetimes with static generally prolate metrics. As examples, we consider the electrically charged C-metric, the vacuum C-metric, the Reissner-Nordstrom and Schwarszchild spacetimes and the BBMB black hole and show that the solutions to the Dirac equations for particles these spacetimes can be derived in terms of Heun's general functions and their confluent and double confluent forms.

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On uniqueness of static spacetimes with non-trivial conformal scalar field

Cited by 20 publications

References 23 publications

Metamorphoses of a photon sphere

Metamorphoses of a photon sphere

Lux in obscuro II: photon orbits of extremal AdS black holes revisited

Massless fermions on static general prolate metrics and their Heun solutions

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