The Maximally Rotating Black Hole as a Critical Point in Astronomy

Abstract

This work represents a novel application of an old tool---conformal symmetry---to a new arena: black hole astrophysics. Emergent conformal symmetries near critical points play a profound role in modern condensed matter and particle physics. A maximally rotating black hole (one that saturates the Kerr bound |angular momentum| <= mass^2) can be viewed as a critical point in astronomy. In this extremal regime, the black hole throat---the region of spacetime near the event horizon---grows to infinite size and develops an enhanced isometry group. General relativity predicts that this geometrically-realized global conformal symmetry extends to an even larger emergent infinite-dimensional local conformal symmetry. This observation suggests that physics near extremal black holes should be constrained by conformal symmetry in much the same way as many near-critical condensed matter systems are governed by conformal field theories. Proceeding from these insights, this thesis exploits the conformal symmetry of rapidly spinning black holes to determine universal properties of near-horizon fields and geodesics. Analytic expressions are derived for the limiting form of the electromagnetic field and plasma magnetosphere, and potential signatures of conformal symmetry in the sky are investigated. These results bear direct relevance to the characterization of electromagnetic emissions from the vicinity of an extremal black hole, an outstanding problem that now arises at the experimental frontier of observational astronomy.