On the backreaction of frame dragging

TL;DR

This paper investigates the backreaction effects of frame dragging in black Saturn systems, revealing how the central black hole's mass influences the system's response functions and frame dragging, with parallels to double Kerr solutions.

Contribution

It introduces a detailed analysis of backreaction effects in black Saturn systems, including response functions and phase behavior, extending understanding beyond test-object approximations.

Findings

Response functions show a correlation between black hole and ring properties.

Frame dragging decreases with increasing central black hole mass.

Fat phase exhibits super-extremal spin behavior.

Abstract

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.