Yukawa potential in a Schwarzschild background

Gottlieb, Daniel Henry; Hojman, R.; H., Rodríguez, L.; Zamorano, Nelson

doi:10.1007/bf02899373

Cited by 12 publications

(20 citation statements)

References 4 publications

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“…Already the early investigations [19,20] of the models with the simplest possible MAG Lagrangians, which include only a linear Hilbert term, quadratic segmental curvature invariant, and a single trace torsion or Weyl nonmetricity square term, have shown that an effective Einstein-Proca theory arises naturally from the vacuum MAG field equations (cf. also [12,21]). This result was subsequently extended to a very general family of MAG Lagrangians [22][23][24].…”

Section: Introductionmentioning

confidence: 88%

“…Qualitative analysis of the self-consistent Einstein-Proca system revealed the absence of black hole type solutions (possessing a regular horizon) with an external vec-tor meson "hair" [8][9][10]. At the same time several exact spherically symmetric solutions of the Proca wave equation on the classical Schwarzschild background spacetime were obtained [11][12][13]. Assuming that a massive vector field source was located on a thin spherical shell outside the Schwarzschild horizon, it was demonstrated in [11] that the meson field may change the structure of the spacetime near the central singularity.…”

Section: Introductionmentioning

confidence: 99%

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Einstein-Proca model: spherically symmetric solutions

Obukhov¹,

Vlachynsky²

1999

Ann. Phys.

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The Proca wave equation describes a classical massive spin 1 particle. We analyze the gravitational interaction of this vector field. In particular, the spherically symmetric solutions of the Einstein-Proca coupled system are obtained numerically. Although at infinity the metric field approaches the usual Schwarzschild (Reissner-Nordstro È m) limit, we demonstrate the absence of black hole type configurations.

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Section: Introductionmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Einstein-Proca model: spherically symmetric solutions

Obukhov¹,

Vlachynsky²

1999

Ann. Phys.

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“…Contributions of the solution (6) into the field strength E ≡ ∂ r A t = − √ I 1 and the invariant I 2 are finite at the horizon, but grow without bound at r → ∞. On the other hand, as we approach the gravitational radius, the contribution of the solution (7) to the field strength diverges logarithmically and the invariant I 2 grows infinitely according to the law 1/ h(r ). Considered at spatial infinity this solution vanishes quasi exponentially.…”

Section: Static Solution Of the Proca Equationmentioning

confidence: 97%

“…An exact static solution of the Proca equation on the Schwarzschild background was obtained in one form or a e-mail: andrikola@yandex.ru (corresponding author) another in early works [6][7][8]. An analysis [8,9] demonstrated a non-trivial dependence of the Proca static field created by a uniformly charged spherical shell surrounding the BH on the distance between the shell surface and the horizon.…”

Section: Introductionmentioning

confidence: 99%

On dynamic aspects of the Proca field screening by a black hole

Erofeev

2020

Eur. Phys. J. C

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Classical black holes are known for almost half a century to nullify exterior classical massive vector field associated with a charge crossing the event horizon. This implies that, from the point of view of an external observer, the Proca field of the charge is screened with the strength gradually increasing as the charge adiabatically approaches the event horizon. In this paper we reject the adiabaticity constraint and calculate analytically the field evolution with respect to a distant observer in the frame of the simplest model of a contracting charged spherical shell concentrically surrounding a Schwarzschild black hole. We show that a time scale of the screening is determined by a mass of the black hole and, moreover, loss of Proca hair during the collapse of charged matter has the same temporal character. Due to existence of the event horizon, there is discontinuous jump between massive and massless electrodynamics. This means that presence of an arbitrarily small mass of the photon induces observable effects, which include generation of electric asymmetry of the Universe and galactic magnetic fields.

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“…Then, the Proca equations on a Schwarzschild background -i.e. taking the line element (3.6) with σ(r) = 1, N (r) = 1 − 2M/r, -can be solved in closed form by taking the ansatz [70]…”

Section: A Modified Peña-sudarsky Theoremmentioning

confidence: 99%

Kerr black holes with Proca hair

Herdeiro

Radu

Rúnarsson

2016

Class. Quantum Grav.

251

289

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Bekenstein proved that in Einstein's gravity minimally coupled to one (or many) real, Abelian, Proca field, stationary black holes (BHs) cannot have Proca hair. Dropping Bekenstein's assumption that matter inherits spacetime symmetries, we show this model admits asymptotically flat, stationary, axisymmetric, regular on and outside an event horizon BHs with Proca hair, for an even number of real (or an arbitrary number of complex) Proca fields. To establish it, we start by showing that a test, complex Proca field can form bound states, with real frequency, around Kerr BHs: stationary Proca clouds. These states exist at the threshold of superradiance. It was conjectured in [1,2], that the existence of such clouds at the linear level implies the existence of a new family of BH solutions at the non-linear level. We confirm this expectation and explicitly construct examples of such Kerr black holes with Proca hair (KBHsPH). For a single complex Proca field, these BHs form a countable number of families with three continuous parameters (ADM mass, ADM angular momentum and Noether charge). They branch off from the Kerr solutions that can support stationary Proca clouds and reduce to Proca stars [3] when the horizon size vanishes. We present the domain of existence of one family of KBHsPH, as well as its phase space in terms of ADM quantities. Some physical properties of the solutions are discussed; in particular, and in contrast with Kerr BHs with scalar hair, some spacetime regions can be counter-rotating with respect to the horizon. We further establish a no-Proca-hair theorem for static, spherically symmetric BHs but allowing the complex Proca field to have a harmonic time dependence, which shows BHs with Proca hair in this model require rotation and have no static limit. KBHsPH are also disconnected from Kerr-Newman BHs with a real, massless vector field. * herdeiro@ua.pt

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Yukawa potential in a Schwarzschild background

Cited by 12 publications

References 4 publications

Einstein-Proca model: spherically symmetric solutions

Einstein-Proca model: spherically symmetric solutions

On dynamic aspects of the Proca field screening by a black hole

Kerr black holes with Proca hair

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