## On the backreaction of frame dragging

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Herdeiro, Carlos A. R.

Rebelo, Carmen

Warnick, Claude M.

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##### Abstract

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The backreaction on black holes due to dragging heavy, rather than test,
objects is discussed. As a case study, a regular black Saturn system where the
central black hole has vanishing intrinsic angular momentum, J^{BH}=0, is
considered. It is shown that there is a correlation between the sign of two
response functions. One is interpreted as a moment of inertia of the black ring
in the black Saturn system. The other measures the variation of the black ring
horizon angular velocity with the central black hole mass, for fixed ring mass
and angular momentum. The two different phases defined by these response
functions collapse, for small central black hole mass, to the thin and fat ring
phases. In the fat phase, the zero area limit of the black Saturn ring has
reduced spin j^2>1, which is related to the behaviour of the ring angular
velocity. Using the `gravitomagnetic clock effect', for which a universality
property is exhibited, it is shown that frame dragging measured by an
asymptotic observer decreases, in both phases, when the central black hole mass
increases, for fixed ring mass and angular momentum. A close parallelism
between the results for the fat phase and those obtained recently for the
double Kerr solution is drawn, considering also a regular black Saturn system
with J^{BH}\neq 0.

Comment: 18 pages, 8 figures

Comment: 18 pages, 8 figures

##### Keywords

General Relativity and Quantum Cosmology, High Energy Physics - Theory