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GR: Fachverband Gravitation und Relativitätstheorie

GR 1: Schwarze Löcher I

GR 1.1: Talk

Monday, February 25, 2013, 14:00–14:15, HS 6

Tidally distorted black holes — •Norman Gürlebeck — ZARM, University of Bremen, Germany

Planets, stars and black holes are deformed due to an external gravitational field generated by e.g. a moon or a companion in a binary system. This deformation is in Newtonian theory characterized by the first and second Love numbers. These measure the deformation of the surface and the induced multipole moment produced by a specific external field. Similar definitions were employed in General Relativity in [T. Damour & O. M. Lecian, PRD, 80,044017 (2009); T. Binnington & E. Poisson, PRD, 80, 084018 (2009)]. However, these approaches require necessarily some linearizations and approximations. We employ here the source integrals for the asymptotic multipole moments, which we found recently in [N. Gürlebeck, gr-qc/arXiv:1207.4500], to show that the induced multipole moments and, thus, the second Love numbers for static and axially symmetric black holes always vanish, thereby corroborating existing results in the aforementioned papers without resorting to any approximations. Hence, the contributions of the distorted black hole to the asymptotic multipole moments turn out to be exactly those of an undistorted Schwarzschild black hole. This can be seen as a generalization of the no-hair theorem to the case where additional matter is present. Nonetheless, the internal geometry of the horizon changes, which is characterized by the first Love numbers.