Tidally Distorted Black Holes
According to the no-hair theorem, static black holes are described by a Schwarzschild spacetime provided there are no other sources of the gravitational field. This requirement, however, is in astrophysical realistic scenarios often violated, e.g., if the black hole is part of a binary system or if they are surrounded by an accretion disk. In these cases, the black hole is distorted due to tidal forces. We show that the subsequent formulation of the no-hair theorem holds nonetheless: The contribution of the distorted black hole to the multipole moments that describe the gravitational field close to infinity is that of a Schwarzschild black hole. This implies that there is no multipole moment induced in the black hole and that its second Love numbers, which measure the distortion, vanish as was already shown in approximations to general relativity. But here we proof this property of black holes in full general relativity.
I thank Abhay Ashtekar for pointing out this interesting question. I also thank J. Steinhoff for fruitful discussions. Furthermore, I gratefully acknowledge support from the DFG within the Research Training Group 1620 “Models of Gravity”.
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