Deformed black hole in Sagittarius A. (arXiv:2103.05490v2 [gr-qc] UPDATED)
<a href="http://arxiv.org/find/gr-qc/1/au:+Anson_T/0/1/0/all/0/1">Timothy Anson</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Babichev_E/0/1/0/all/0/1">Eugeny Babichev</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Charmousis_C/0/1/0/all/0/1">Christos Charmousis</a>
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.
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.
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