Abstract
Using on-shell amplitude methods, we derive a rotating black hole solution in a generic theory of Einstein gravity with additional terms cubic in the Riemann tensor. We give an explicit expression for the metric in Einsteinian Cubic Gravity (ECG) and low energy effective string theory, which correctly reproduces the previously discovered solutions in the zero angular-momentum limit. We show that at first order in the coupling, the classical potential can be written to all orders in spin as a differential operator acting on the non-rotating potential, and we comment on the relation to the Janis-Newman algorithm. Furthermore, we derive the classical impulse and scattering angle for such a black hole and comment on the phenomenological interest of such quantities.
Highlights
We have recently entered the era of gravitational wave astronomy, where one of the key subjects of observation will be black holes [1,2]
We give an explicit expression for the metric in Einsteinian cubic gravity and low-energy effective string theory, which correctly reproduces the previously discovered solutions in the zero-angular-momentum limit
Since we want to compare with the nondispersive Kerr black hole solution we at this point restrict the potential to the nondispersive terms (i.e., w 1⁄4 0) and taking the Fourier transform, we find that the all-order in spin potential is given by κ2 32π mAmB
Summary
We have recently entered the era of gravitational wave astronomy, where one of the key subjects of observation will be black holes [1,2]. We shall study the effects of adding cubic curvature contributions to the EinsteinHilbert action, considering rotating black hole solutions to the field equations. Such analyses are important in order to test the validity of GR in the strong gravity regime of black holes, and further, to identify if such modifications to GR are necessary. Two of the present authors used modern amplitude methods to derive nonrotating black hole solutions in cubic theories of gravity [3]. We should note that while we have kept the generic form of P for generality, it has been shown that the terms involving the Ricci curvature tensor do not contribute to on-shell amplitudes [39].1 the terms proportional to β3 and β4 in P will play no role in the following discussion
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