http://arxiv.org/abs/2103.05490
We analyze the Post-Newtonian orbit of stars around a deformed Kerr black hole. The deformation we consider is a class of disformal transformations of a non-trivial Kerr solution in scalar-tensor theory which are labeled via the disformal parameter $D$. We study different limits of the disformal parameter, and compare the trajectories of stars orbiting a black hole to the case of the Kerr spacetime in general relativity, up to 2PN order. Our findings show that for generic non-zero $D$, the no-hair theorem of general relativity is violated, in the sense that the black hole’s quadrupole Q is not determined by its mass $M$ and angular momentum $J$ through the relation $Q=-J^2/M$. Limiting values of $D$ provide examples of simple and exact non-circular metric solutions, whereas in a particular limit, where $1+D$ is small but finite, we obtain a leading correction to the Schwarzschild precession due to disformality. In this case, the disformal parameter is constrained using the recent measurement of the pericenter precession of the star S2 by the GRAVITY collaboration.
T. Anson, E. Babichev and C. Charmousis
Wed, 10 Mar 21
54/56
Comments: 23 pages, 1 figure
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