Speaker
Description
The bound-to-boundary (B2B) correspondence allows for the translation of results obtained for scattering encounters to bound orbits and vice versa. To the uninitiated this relationship sometimes appears almost magical. In this talk we seek to understand the B2B correspondence by examining the case of a test particle interacting with a Kerr black hole. This has the distinct advantage of having access to analytic solutions that are valid to all orders in $G$, $c$, and $a$, at cost the cost of having access to only the leading order terms in the mass-ratio.
Taking a more geometric view of the correspondence we find it illustrative to distinguish two separate dualities that together make up the B2B correspondence. The first relates bound geodesics around a Kerr black hole through analytic continuation to a series of scattering orbits that alternate the between the original Kerr spacetime and its negative mass counterpart. The second duality relates the scattering in the positive mass spacetime to that in the negative mass counterpart.
Together the two dualities allow one to start with knowledge of just one type of scattering and recover knowledge of bound orbit dynamics.
We discuss several equivalent formulations of the second duality, including as a positive/negative angular momentum duality (as in the original B2B proposal), a positive/negative eccentricity duality, and as a positive/negative gravitational coupling duality.
The new found formulation of the B2B correspondence applies to fully generic (i.e. with precessing spins) binaries, and applies to both orbit averaged and local quantities.
