General Relativity & Quantum Cosmology

We reconsider a gauge theory of gravity in which the gauge group is the conformal group SO(4,2), and the action is of the Yang-Mills form, quadratic in the curvature. The vacuum sector of the resulting gravitational theory exhibits local conformal symmetry. We allow for conventional matter coupled to the spacetime metric as well as matter coupled to the field that gauges special conformal transformations.  When the theory is linearized about flat space, we find there is a long range gravitational force in addition to Newton’s inverse square law.  Furthermore, the cosmological sector of the theory exhibits late time acceleration, an early time bounce, and a post-bounce quasi-de Sitter ``inflationary'' phase of arbitrary duration (without an inflaton).

Aretakis' discovery of a horizon instability of extremal black holes came as something of a surprise given earlier proofs that individual frequency modes are bounded. Is this kind of instability invisible to frequency-domain analysis? The answer is no: We show that the horizon instability can be recovered in a mode analysis as a branch point at the horizon frequency.  We use the approach to generalize to nonaxisymmetric gravitational perturbations and reveal that certain Weyl scalars are unbounded in time on the horizon.  We will also discuss new results showing how the instability manifests for *nearly* extremal black holes: long-lived quasinormal modes collectively give rise to a transient period of growth near the horizon.  This period lasts arbitrarily long in the extremal limit, reproducing the Aretakis instability precisely on the horizon.   We interpret these results in terms of near-horizon geometry and discuss potential astrophysical implications.