Gravitational perturbations in a cavity: Nonlinearities

Menon, Dhanya S.; Suneeta, Vardarajan

doi:10.1103/physrevd.100.044060

Cited by 3 publications

(4 citation statements)

References 45 publications

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“…The axisymmetric, steady-state, force-free magnetosphere around Kerr BHs is governed 1 A few families of exact solutions (e.g. Menon & Dermer 2005Brennan et al 2013;Menon 2015;Compère et al 2016) to the equations of force-free electrodynamics in the Kerr spacetime have been found in the past decade. But these solutions have various limitations, e.g., not allowing energy extraction from the BH, being electrically dominated instead of magnetically dominated, lacking clear physical interpretation, or being time-dependent and not axisymmetric, which make it difficult to compare these exact solutions with simulations and numerical solutions.…”

Section: Introductionmentioning

confidence: 99%

Analytic Properties of Force-free Jets in the Kerr Spacetime. III. Uniform Field Solution

Pan

Huang

2017

ApJ

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The structure of steady axisymmetric force-free magnetosphere of a Kerr black hole (BH) is governed by a second-order partial differential equation of A φ depending on two "free" functions Ω(A φ ) and I(A φ ), where A φ is the φ component of the vector potential of the electromagnetic field, Ω is the angular velocity of the magnetic field lines and I is the poloidal electric current. In this paper, we investigate the solution uniqueness. Taking asymptotically uniform field as an example, analytic studies imply that there are infinitely many solutions approaching uniform field at infinity, while only a unique one is found in general relativistic magnetohydrodynamic simulations. To settle down the disagreement, we reinvestigate the structure of the governing equation and numerically solve it with given constraint condition and boundary condition. We find that the constraint condition (field lines smoothly crossing the light surface (LS)) and boundary conditions at horizon and at infinity are connected via radiation conditions at horizon and at infinity, rather than being independent. With appropriate constraint condition and boundary condition, we numerically solve the governing equation and find a unique solution. Contrary to naive expectation, our numerical solution yields a discontinuity in the angular velocity of the field lines and a current sheet along the last field line crossing the event horizon. We also briefly discuss the applicability of the perturbation approach to solving the governing equation.

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Section: Introductionmentioning

confidence: 99%

Analytic Properties of Force-free Jets in the Kerr Spacetime. III. Uniform Field Solution

Pan

Huang

2017

ApJ

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“…After doing the necessary projections, one gets the following equations (see [38] for more details): The higher order tensor sector takes the form:…”

Section: Linear and Higher Order Equationsmentioning

confidence: 99%

“…The above replacement of (2) S ij with (2) A ij is possible because of the traceless property, T i i = 0 satisfied by the tensor harmonics. The explicit form of (2) A ij , in case we start out only with tensor type perturbations, at linear level is given by (see appendix C of [38])…”

Section: Special Modesmentioning

confidence: 99%

“…Geons were also constructed in [30], [31], [32], [33], [34], [35], [36] and [37]. Nonlinear perturbation theory was employed to study pure gravitational perturbations in a cavity in Minkowski, in general dimensions [38]. Very recently, the resonant system was derived in five dimensions, within cohomogenity-two biaxial Bianchi IX ansatz [39].…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear perturbations of higher dimensional anti-de Sitter spacetime

Menon,

Suneeta

2020

Preprint

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We study nonlinear gravitational perturbations of vacuum Einstein equations, with Λ < 0 in (n + 2) dimensions, with n > 2, the n = 2 case already having been done before. We follow the formalism by Ishibashi, Kodama and Seto to decompose the metric perturbations into tensor, vector and scalar sectors, and simplify the Einstein equations. We render the metric perturbations asymptotically anti-de Sitter by employing a suitable gauge choice for each of the sectors. Finally, we analyze the resonant structure of the perturbed equations at second order for the five dimensional case, by starting out with tensor-type perturbations at the linear level. We find evidence for resonances at second order.

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Nonlinear perturbations of higher dimensional anti–de Sitter spacetime

Menon

Suneeta

2020

Phys. Rev. D

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Gravitational perturbations in a cavity: Nonlinearities

Cited by 3 publications

References 45 publications

Analytic Properties of Force-free Jets in the Kerr Spacetime. III. Uniform Field Solution

Analytic Properties of Force-free Jets in the Kerr Spacetime. III. Uniform Field Solution

Nonlinear perturbations of higher dimensional anti-de Sitter spacetime

Nonlinear perturbations of higher dimensional anti–de Sitter spacetime

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