Fast plunges into Kerr black holes

Shahar Hadar,Andrew Strominger,Achilleas P Porfyriadis

doi:10.1007/jhep07(2015)078

Shahar Hadar, Andrew Strominger + Show 1 more

Open Access

https://doi.org/10.1007/jhep07(2015)078

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Abstract

Most extreme-mass-ratio-inspirals of small compact objects into supermassive black holes end with a fast plunge from an eccentric last stable orbit. For rapidly rotating black holes such fast plunges may be studied in the context of the Kerr/CFT correspondence because they occur in the near-horizon region where dynamics are governed by the infinite dimensional conformal symmetry. In this paper we use conformal transformations to analytically solve for the radiation emitted from fast plunges into near-extreme Kerr black holes. We find perfect agreement between the gravity and CFT computations.

Highlights

JHEP07(2015)078 take place deep in the near horizon region where Kerr/CFT predicts the extra conformal symmetry
In this paper we extend the analysis of [12], where only the special post-ISCO plunge was analyzed, and compute analytically the radiative signature of a new family of trajectories we call “fast plunges”. These plunges are trajectories with arbitraryNHEK orbital energy which start at some finite time from theNHEK boundary. This is in contrast with the special post-ISCO plunge of [12] which comes in from the near-near-horizon extreme Kerr (NHEK) boundary in the infinite past
The fact that the fast plunges are soluble is again a direct consequence of the conformal symmetry: we show that they are related by conformal mapping to the circular orbit of [11]

Summary

Radiation from the fast NHEK plunge

Taking the limit → 0, keeping r, t finite. This effectively zooms into the near horizon region and yields the non-singular NHEK metric [1]: ds2 = 2M 2Γ(θ). Consider the equatorial plunging trajectories of small (test) compact objects in NHEK with energy and angular momentum (per unit rest mass) given by e = √4M , l = 2√M , 3R0 for arbitrary R0 > 0. The solution for this trajectory is a fast NHEK plunge: t(r) = 1 r φ(r). We will use the transformation (2.8) in order to solve for the radiation produced during the fast plunge (2.7)

Gravity analysis

CFT analysis

Gluing to asymptotically flat region

Radiation from the fast near-NHEK plunge

Findings