Abstract
We study the dynamics of a pair of extremal (half-BPS) black holes in mathcal{N} = 8 supergravity, as a potentially solvable model of gravitational dynamics. As a diagnosis of hidden symmetries, we ask whether the perihelion of the orbits precesses over time. We consider black hole charge vectors with arbitrary misalignment. First, we use scattering amplitude methods to compute the leading post-Newtonian correction for general mass ratios. This computation is greatly simplified by introducing a suitable on-shell superspace. Second, we study the probe limit to all orders in velocity and Newton’s constant through a ten-dimensional brane setup. In all cases we find no precession. We relate this to the absence of scalar triangle integrals.
Highlights
There has been a longstanding interest in applying the methods of quantum field theory and effective field theory to gravitationally bound systems — for reviews and some recent developments see [1,2,3,4,5,6,7]
We study the dynamics of a pair of extremal black holes in N = 8 supergravity, as a potentially solvable model of gravitational dynamics
We studied the precession of orbits for bound states of two extremal black holes in N = 8 supergravity
Summary
There has been a longstanding interest in applying the methods of quantum field theory and effective field theory to gravitationally bound systems — for reviews and some recent developments see [1,2,3,4,5,6,7]. Tractable models generally possess additional symmetries and conservation laws This is famously the case in the Newtonian limit, where the fact that we get closed Keplerian elliptical orbits is a consequence of the conservation of the Laplace-Runge-Lenz vector, which points in the direction of the eccentricity. Systems of supersymmetric black holes have been extensively studied, in particular, supersymmetric bound states thereof For example it is well-known that if the charge vectors of two extremal holes are aligned, the electric repulsion exactly cancels the gravitational (and scalar) attraction, leading to static solutions which experience vanishing force. We rely on the fact that closed and open (scattering) orbits are controlled by the same effective Hamiltonian It can be extracted by matching with the scattering amplitudes of black holes [27, 28]. We describe how to parametrize the charges of two such black holes, and how we will use on-shell superspace to simplify the scattering problem
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