Null infinity at the edge of a black hole

Abstract: Null hypersurfaces are lightlike surfaces that naturally emerge when asking questions like “what is an asymptotically flat spacetime?” or “what is a black hole?”. This gives rise to the concepts of “null infinities” and “event horizons”. In this talk, I will highlight the observation that all spacetimes that are asymptotically flat near null infinity can be mapped through spatial inversions onto the geometry near an extremal, non-expanding and non-rotating horizon located at a finite distance. This mapping is conformal, ensuring the dissimilar physics on each type of null surface, but also emphasizing their similarities. Typically, the conformally related asymptotic geometries do not reside in the same spacetime. When they do, however, the finite-distance horizon is a true black hole event horizon, and the corresponding spatial inversions become conformal isometries of the spacetime that exchange the two null surfaces. The prototypical example of this situation is the four-dimensional extremal Reissner-Nordström black hole, equipped with the characteristic Couch-Torrence inversion conformal isometry. This correspondence then enforces matching conditions between near-horizon and near–null-infinity data, leading, in particular, to the identification between infinite towers of conserved quantities: the near-horizon Aretakis constants and the near–null-infinity Newman-Penrose constants. I will also present hints of a broader relationship between disconnected null hypersurfaces under less restrictive boundary conditions, extending beyond extremal, static horizons to include rotating or even non-extremal cases.

general relativity and quantum cosmologyHEP - experimentHEP - latticeHEP - phenomenologyHEP - theory

Audience: researchers in the topic

( slides )

NKUA HEP Seminars

Series comments: Please email tomeasb(at)gmail(dot)com to obtain the meeting link and password. Unless explicitly requested otherwise, your email address will be included in our seminar mailing list.