Null infinity as an inverted extremal horizon: Matching an infinite set of conserved quantities for gravitational perturbations

TL;DR

This paper establishes a geometric duality linking null infinity and extremal horizons, deriving conserved gravitational charges and matching them with Newman-Penrose quantities, revealing new insights into extremal black hole perturbations.

Contribution

It introduces a conformal inversion duality between null infinity and extremal horizons, extending conserved charge results to gravitational perturbations and applying to Kerr-Newman black holes.

Findings

Derived a tower of conserved gravitational charges at extremal horizons.

Matched horizon charges with Newman-Penrose quantities for extremal Reissner-Nordström black holes.

Showed the physical relevance of spatial inversions for extremal Kerr-Newman black holes.

Abstract

Every spacetime that is asymptotically flat near null infinity can be conformally mapped via a spatial inversion onto the geometry around an extremal, non-rotating and non-expanding horizon. We set up a dictionary for this geometric duality, connecting the geometry and physics near null infinity to those near the dual horizon. We then study its physical implications for conserved quantities for extremal black holes, extending previously known results to the case of gravitational perturbations. In particular, we derive a tower of near-horizon gravitational charges that are exactly conserved and show their one-to-one matching with Newman-Penrose conserved quantities associated with gravitational perturbations of the extremal Reissner-Nordstr\"{o}m black hole geometry. We furthermore demonstrate the physical relevance of spatial inversions for extremal Kerr-Newman black holes, even if the latter are notoriously not conformally isometric under such inversions.