General relation between Aretakis charge and Newman-Penrose charge

Abstract

We reexamine the relation between the Aretakis charge of an extremal black hole spacetime and the Newman-Penrose charge of a weakly asymptotically flat spacetime obtained from the original one through radial inversion and conformal mapping. Building on recent work by Godazgar, Godazgar and Pope, we present an explicit general relation between these quantities showing how the charge densities are mapped. As a non-trivial example we provide the computation of both quantities and their explicit relation for the extremal Kerr spacetime.

11 pages. A reference added and minor corrections

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Cited by in corpus (8)

• A non-degenerate scattering theory for the wave equation on extremal Reissner-Nordstrom
• Generalised Couch-Torrence Symmetry for Rotating Extremal Black Holes in Maximal Supergravity
• Horizon Hair from Inversion Symmetry
• The Aretakis constants and instability in general spherically symmetric extremal black hole spacetimes: higher multipole modes, late-time tails, and geometrical meanings
• Gaussian null coordinates, near-horizon geometry and conserved charges on the horizon of extremal non-dilatonic black $p$-branes
• Revisiting the Aretakis constants and instability in two-dimensional Anti-de Sitter spacetimes
• Gaussian Null Coordinates for Rotating Charged Black Holes and Conserved Charges
• Gravitation and General Relativity at King's College London