Instability of an “approximate black hole”

Matthew W. Choptuik; Eric W. Hirschmann; Steven L. Liebling

doi:10.1103/PhysRevD.55.6014

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Instability of an “approximate black hole”

Matthew W. Choptuik, Eric W. Hirschmann, and Steven L. Liebling

Center for Relativity, The University of Texas at Austin, Austin, Texas 78712-1081

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Phys. Rev. D 55, 6014 – Published 15 May, 1997

DOI: https://doi.org/10.1103/PhysRevD.55.6014

Abstract

We investigate the stability of a family of spherically symmetric static solutions in vacuum Brans-Dicke theory (with $ω = 0)$ recently described by van Putten. Using linear perturbation theory, we find one exponentially growing mode for every member of the family of solutions, and thus conclude that the solutions are not stable. Using a previously constructed code for spherically symmetric Brans-Dicke theory, additional evidence for instability is provided by directly evolving the static solutions with perturbations. The full nonlinear evolutions also suggest that the solutions are black-hole-threshold critical solutions.

References (13)

M. H. P. M. van Putten, Phys. Rev. D 54, R5931 (1996).
C. Brans and R. H. Dicke, Phys. Rev. 124, 925 (1961).
S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1972).
In general, we have tried to follow van Putten’s notation fairly closely. However, we found the field $ψ (r, t)$ to be a useful quantity in the perturbation and use it instead of van Putten’s $γ (r, t)$ . Note too that at one point in his derivation van Putten uses $ψ$ , but for a quantity different from what we have defined above.
S. L. Liebling and M. W. Choptuik, Phys. Rev. Lett. 77, 1424 (1996).
What it means for a solution with a naked singularity at the origin to disperse is perhaps not well defined at the moment. However, the evolution clearly indicates that the energy content is moving toward large radius.
T. Hara, T. Koike, and S. Adachi, LANLReport No. , 1996 (unpublished).
R. Bartnik and J. McKinnon, Phys. Rev. Lett. 61, 141 (1988).
M. W. Choptuik, T. Chmaj, and P. Bizon, Phys. Rev. Lett. 77, 424 (1996).
H. A. Buchdahl, Phys. Rev. 115, 1325 (1959).
M. Wyman, Phys. Rev. D 24, 839 (1981).
P. Jetzer and D. Scialom, Phys. Lett. A 169, 12 (1992).
A. I. Janis, E. T. Newman, and J. Winicour, Phys. Rev. Lett. 20, 878 (1968).

[c1] M. H. P. M. van Putten, Phys. Rev. D 54, R5931 (1996).

[c2] C. Brans and R. H. Dicke, Phys. Rev. 124, 925 (1961).

[c3] S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1972).

[c4] In general, we have tried to follow van Putten’s notation fairly closely. However, we found the field $ψ (r, t)$ to be a useful quantity in the perturbation and use it instead of van Putten’s $γ (r, t)$ . Note too that at one point in his derivation van Putten uses $ψ$ , but for a quantity different from what we have defined above.

[c5] S. L. Liebling and M. W. Choptuik, Phys. Rev. Lett. 77, 1424 (1996).

[c6] What it means for a solution with a naked singularity at the origin to disperse is perhaps not well defined at the moment. However, the evolution clearly indicates that the energy content is moving toward large radius.

[c7] T. Hara, T. Koike, and S. Adachi, LANLReport No. , 1996 (unpublished).

[c8] R. Bartnik and J. McKinnon, Phys. Rev. Lett. 61, 141 (1988).

[c9] M. W. Choptuik, T. Chmaj, and P. Bizon, Phys. Rev. Lett. 77, 424 (1996).

[c10] H. A. Buchdahl, Phys. Rev. 115, 1325 (1959).

[c11] M. Wyman, Phys. Rev. D 24, 839 (1981).

[c12] P. Jetzer and D. Scialom, Phys. Lett. A 169, 12 (1992).

[c13] A. I. Janis, E. T. Newman, and J. Winicour, Phys. Rev. Lett. 20, 878 (1968).

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