Evolution of scalar perturbations near the Cauchy horizon of a charged black hole

Yekta Gürsel; Vernon D. Sandberg; Igor D. Novikov; A. A. Starobinsky

doi:10.1103/PhysRevD.19.413

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Evolution of scalar perturbations near the Cauchy horizon of a charged black hole

Yekta Gürsel and Vernon D. Sandberg

Igor D. Novikov

A. A. Starobinsky

W.K. Kellogg Radiation Laboratory, California Institute of Technology, Pasadena, California 91125

Space Research Institute Academy of Science, Profsoyuznaja 88, Moscow, 117810, Union of Soviet Socialist Republics

The Landau Institute for Theoretical Physics, Academy of Sciences of the USSR, Moscow, Union of Soviet Socialist Republics

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Phys. Rev. D 19, 413 – Published 15 January, 1979

DOI: https://doi.org/10.1103/PhysRevD.19.413

Abstract

We describe the evolution of a scalar test field on the interior of a Reissner-Nordström black hole. For a wide variety of initial field configurations the energy density in the scalar field is shown to develop singularities in a neighborhood of the geometry's Cauchy horizon, suggesting that for a stellar collapse curvature singularities will develop prior to encountering the Cauchy horizon. The extension to the interior of stationary perturbations due to exterior sources is shown not to disrupt the Cauchy horizon.

References (18)

H. Reissner, Ann. Phys. (Leipzig) 50, 106 (1916) G. Nordström, Proc. Kon. Ned. Akad. Wet. 20, 1238 (1918)
W. Israel, Commun. Math. Phys. 8, 245 (1968)
S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space Time (Cambridge Univ. Press, Cambridge, 1973)
J. C. Graves and D. Brill, Phys. Rev. 120, 1507 (1960)
R. Penrose, in 1968 Battelles Rencontres, edited by B. S. DeWitt and J. A. Wheeler (Benjamin, New York, 1968)
K. Kuchař, Czech, J. Phys. B18, 435 (1968)
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M. Simpson and R. Penrose, Int. J. Theor. Phys. 7, 183 (1973)
J. M. McNamara, Proc. R. Soc. London A358, 499 (1978)
Y. Gürsel, I. D. Novikov, V. D. Sandberg, and A. A. Starobinsky (unpublished)
J. Bičák, Gen. Relativ. Gravit. 3, 331 (1972)
N. R. Sibgatullin and G. A. Alekseev, Zh. Eksp. Teor. Fiz. 67, 1233 (1974) [Sov. Phys.-JETP 40, 613 (1975)]
V. Moncrief, Phys. Rev. D 9, 2707 (1974) ibid.10, 1057 (1974)
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J. M. McNamara, Mathematics Division, University of Sussex, Falmer, Brighton, United Kingdom, report (unpublished)
A. Erdélyi et al., Higher Transcendental Functions (McGraw-Hill, New York, 1953), Vol. I I. S. Gradshteyn and I. W. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1965), 4th edition M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965)

[c1] H. Reissner, Ann. Phys. (Leipzig) 50, 106 (1916) G. Nordström, Proc. Kon. Ned. Akad. Wet. 20, 1238 (1918)

[c2] W. Israel, Commun. Math. Phys. 8, 245 (1968)

[c3] S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space Time (Cambridge Univ. Press, Cambridge, 1973)

[c4] J. C. Graves and D. Brill, Phys. Rev. 120, 1507 (1960)

[c5] R. Penrose, in 1968 Battelles Rencontres, edited by B. S. DeWitt and J. A. Wheeler (Benjamin, New York, 1968)

[c6] K. Kuchař, Czech, J. Phys. B18, 435 (1968)

[c7] J. D. Bekenstein, Phys. Rev. D 4, 2185 (1971)

[c8] D. G. Boulware, Phys. Rev. D 8, 2363 (1973)

[c9] M. Simpson and R. Penrose, Int. J. Theor. Phys. 7, 183 (1973)

[c10] J. M. McNamara, Proc. R. Soc. London A358, 499 (1978)

[c11] Y. Gürsel, I. D. Novikov, V. D. Sandberg, and A. A. Starobinsky (unpublished)

[c12] J. Bičák, Gen. Relativ. Gravit. 3, 331 (1972)

[c13] N. R. Sibgatullin and G. A. Alekseev, Zh. Eksp. Teor. Fiz. 67, 1233 (1974) [Sov. Phys.-JETP 40, 613 (1975)]

[c14] V. Moncrief, Phys. Rev. D 9, 2707 (1974) ibid.10, 1057 (1974)

[c15] F. Zerilli, Phys. Rev. D 9, 860 (1974)

[c16] R. H. Price, Phys. Rev. D 5, 2419 (1972)

[c17] J. M. McNamara, Mathematics Division, University of Sussex, Falmer, Brighton, United Kingdom, report (unpublished)

[c18] A. Erdélyi et al., Higher Transcendental Functions (McGraw-Hill, New York, 1953), Vol. I I. S. Gradshteyn and I. W. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1965), 4th edition M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965)

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Evolution of scalar perturbations near the Cauchy horizon of a charged black hole

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