Gaussian null coordinates for rotating charged black holes and conserved charges

M. Cvetič (Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA; Center for Applied Mathematics and Theoretical Physics, University of Maribor, SI2000 Maribor, Slovenia) ; C. N. Pope (George P. & Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, College Station, Texas 77843, USA; DAMTP, Centre for Mathematical Sciences, Cambridge University, Wilberforce Road, Cambridge CB3 OWA, United Kingdom) ; A. Saha (George P. & Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, College Station, Texas 77843, USA) ; A. Satz (Sarah Lawrence College, Bronxville, New York 10708, USA)

Motivated by the study of conserved Aretakis charges for a scalar field on the horizon of an extremal black hole, we construct the metrics for certain classes of four-dimensional and five-dimensional extremal rotating black holes in Gaussian null coordinates. We obtain these as expansions in powers of the radial coordinate, up to sufficient order to be able to compute the Aretakis charges. The metrics we consider are for 4-charge black holes in four-dimensional STU supergravity (N=2 supergravity coupled to three vector multiplets) (including the Kerr-Newman black hole in the equal-charge case) and the general 3-charge black holes in five-dimensional STU supergravity. We also investigate the circumstances under which the Aretakis charges of an extremal black hole can be mapped by conformal inversion of the metric into Newman-Penrose charges at null infinity. We show that while this works for four-dimensional static black holes, a simple radial inversion fails in rotating cases because a necessary conformal symmetry of the massless scalar equation breaks down. We also discuss that a massless scalar field in dimensions higher than four does not have any conserved Newman-Penrose charge, even in a static asymptotically flat spacetime.

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      "source": "APS", 
      "value": "Motivated by the study of conserved Aretakis charges for a scalar field on the horizon of an extremal black hole, we construct the metrics for certain classes of four-dimensional and five-dimensional extremal rotating black holes in Gaussian null coordinates. We obtain these as expansions in powers of the radial coordinate, up to sufficient order to be able to compute the Aretakis charges. The metrics we consider are for 4-charge black holes in four-dimensional STU supergravity (<math><mrow><mi>N</mi><mo>=</mo><mn>2</mn></mrow></math> supergravity coupled to three vector multiplets) (including the Kerr-Newman black hole in the equal-charge case) and the general 3-charge black holes in five-dimensional STU supergravity. We also investigate the circumstances under which the Aretakis charges of an extremal black hole can be mapped by conformal inversion of the metric into Newman-Penrose charges at null infinity. We show that while this works for four-dimensional static black holes, a simple radial inversion fails in rotating cases because a necessary conformal symmetry of the massless scalar equation breaks down. We also discuss that a massless scalar field in dimensions higher than four does not have any conserved Newman-Penrose charge, even in a static asymptotically flat spacetime."
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Published on:
26 March 2020
Publisher:
APS
Published in:
Physical Review D , Volume 101 (2020)
Issue 6
DOI:
https://doi.org/10.1103/PhysRevD.101.066025
arXiv:
2001.04495
Copyrights:
Published by the American Physical Society
Licence:
CC-BY-4.0

Fulltext files: