Cauchy horizon stability in self-similar collapse: Scalar radiation

Nolan, Brien C.; Waters, Thomas J.

doi:10.1103/physrevd.66.104012

Cited by 17 publications

(38 citation statements)

References 13 publications

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“…We note that Re(ν 2 ) > Re(1 − t), and so the earlier restriction Re(t) < 0 implies that Re(ν 2 ) > 1, and so both solutions p C i , i = 1, 2 are finite at the Cauchy horizon. (This applies quite generally in self-similar collapse to a naked singularity when the dominant energy condition holds: see [9].) As these solutions can be written as different C−linear combinations of p N i , i = 1, 2, this implies that the series representations of p N i , i = 1, 2 must both converge at x = x c .…”

Section: Lemma 65 Ifmentioning

confidence: 99%

“…If we form the general solution 9) and from this solutions for A, B, C and K, we find to leading order near x = −∞ (r = 0),…”

Section: Minkowski Regionmentioning

confidence: 99%

“…In a previous paper [9], the authors have shown that all self-similar spherically symmetric space-times which admit a Cauchy horizon, and thus a naked singularity, are stable when we inject a scalar field; that is, the flux of the scalar field as measured by a timelike observer crossing the Cauchy horizon remains finite. This paper extends on that work by considering metric and matter perturbations of SSSS space-times.…”

Section: Introductionmentioning

confidence: 99%

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Even perturbations of the self-similar Vaidya space-time

Nolan

Waters

2005

Phys. Rev. D

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We study even parity metric and matter perturbations of all angular modes in self-similar Vaidya space-time. We focus on the case where the background contains a naked singularity. Initial conditions are imposed describing a finite perturbation emerging from the portion of flat space-time preceding the matter-filled region of space-time. The most general perturbation satisfying the initial conditions is allowed impinge upon the Cauchy horizon (CH), whereat the perturbation remains finite: there is no "blue-sheet" instability. However when the perturbation evolves through the CH and onto the second future similarity horizon of the naked singularity, divergence necessarily occurs: this surface is found to be unstable. The analysis is based on the study of individual modes following a Mellin transform of the perturbation. We present an argument that the full perturbation remains finite after resummation of the (possibly infinite number of) modes.

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Section: Lemma 65 Ifmentioning

confidence: 99%

“…If we form the general solution 9) and from this solutions for A, B, C and K, we find to leading order near x = −∞ (r = 0),…”

Section: Minkowski Regionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Even perturbations of the self-similar Vaidya space-time

Nolan

Waters

2005

Phys. Rev. D

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“…One of such discrete values of D is D F ≡ 2/3(1 + α) 2 , for which we can find the solution for Eqs. (3.10), (3.11) and (3.12) written by…”

Section: Background Self-similar Spacetimesmentioning

confidence: 99%

Stability analysis of self-similar behaviors in perfect fluid gravitational collapse

Mitsuda

Tomimatsu

2006

Phys. Rev. D

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Stability of self-similar solutions for gravitational collapse is an important problem to be investigated from the perspectives of their nature as an attractor, critical phenomena and instability of a naked singularity. In this paper we study spherically symmetric non-self-similar perturbations of matter and metrics in spherically symmetric self-similar backgrounds. The collapsing matter is assumed to be a perfect fluid with the equation of state P = αρ. We construct a single wave equation governing the perturbations, which makes their time evolution in arbitrary self-similar backgrounds analytically tractable. Further we propose an analytical application of this master wave equation to the stability problem by means of the normal mode analysis for the perturbations having the time dependence given by exp (iω log |t|), and present some sufficient conditions for the absence of nonoscillatory unstable normal modes with purely imaginary ω.

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“…Though we use a standard Fourier decomposition of the Green's function by the function expi! logjtj (in an analogous way to the Mellin transformation in [17]), we reveal a time evolution of perturbations by integrating the Fourier components with respect to the spectral parameter !, which will allow us to find new features missed in [17].…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic radiation due to naked singularity formation in self-similar gravitational collapse

2005

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Dynamical evolution of test fields in background geometry with a naked singularity is an important problem relevant to the Cauchy horizon instability and the observational signatures different from black hole formation. In this paper we study electromagnetic perturbations generated by a given current distribution in collapsing matter under a spherically symmetric self-similar background. Using the Green's function method, we construct the formula to evaluate the outgoing energy flux observed at the future null infinity. The contributions from ''quasinormal'' modes of the self-similar system as well as ''high-frequency'' waves are clarified. We find a characteristic power-law time evolution of the outgoing energy flux which appears just before naked singularity formation and give the criteria as to whether or not the outgoing energy flux diverges at the future Cauchy horizon.

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Cauchy horizon stability in self-similar collapse: Scalar radiation

Abstract: The stability of the Cauchy horizon in spherically symmetric self-similar collapse is studied by determining the flux of scalar radiation impinging on the horizon. This flux is found to be finite.

Cited by 17 publications

References 13 publications

Even perturbations of the self-similar Vaidya space-time

Even perturbations of the self-similar Vaidya space-time

Stability analysis of self-similar behaviors in perfect fluid gravitational collapse

Electromagnetic radiation due to naked singularity formation in self-similar gravitational collapse

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