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Gaussian Null Coordinates for Rotating Charged Black Holes and Conserved Charges
High Energy Physics - Theory · Submitted 13 Jan 2020
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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 (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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | contribution 0.99 | 0.95 | 0.12 | asserted 1.00 |
| s1 | We obtain these as expansions in powers of the radial coordinate, up to sufficient order to be able to compute the Aretakis charges. | method 0.98 | 0.96 | 0.06 | asserted 1.00 |
| s2 | The metrics we consider are for 4-charge black holes in four-dimensional STU supergravity (including the Kerr-Newman black hole in the equal-charge case) and the general 3-charge black holes in five-dimensional STU supergravity. | contribution 0.97 | 0.68 | 0.05 | asserted 0.98 |
| s3 | 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. | contribution 1.00 | 0.66 | 0.08 | unclear 0.51 |
| s4 | 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. | result 0.99 | 0.93 | 0.29 | asserted 1.00 |
| s5 | 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. | result 0.98 | 0.68 | 0.09 | asserted 0.99 |
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The paper
Original abstract
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 (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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How the literature uses it
3 arXiv papers cite this in 4 sentences
Papers citing it · 1 sentence without a confident label
Cites it as background 2 papers
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The study of their properties attracted extensive efforts over years, with recent ones focusing on their enhanced symmetries, such as Aretakis and Newman-Penrose charges [ref] , and Couch-Torrence-type symmetries [ref] .
Conformal Symmetries for Extremal Black Holes with General Asymptotic Scalars in STU Supergravity · Concluding Remarks and Outlook · 0.99
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For example, there has been substantial progress in recent studies of the Aretakis charge both for extremal Reissner-Nordström black holes [ref] and extremal Kerr black holes [ref] as well as recent generalizations to extremal static 4-charge black holes [ref] and rotating ones [ref] in STU supergravity.
Generalised Couch-Torrence Symmetry for Rotating Extremal Black Holes in Maximal Supergravity · Concluding Remarks · 0.88
What it cites · 20 sentences without a confident label
Builds on 2 papers
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These generalised the mapping for extremal Reissner-Nordström that was found in [ref] .
A remark about wave equations on the extreme Reissner-Nordstr\"om black hole exterior · Introduction · 0.88
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These generalised the mapping for extremal Reissner-Nordström that was found in [ref] .
On the horizon instability of an extreme Reissner-Nordstr\"om black hole · Introduction · 0.88
Uses the method or tool of 1 paper
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A technique for constructing Gaussian null coordinates for an extremal black hole metric has been described in [ref] .
Transverse deformations of extreme horizons · General formalism · 0.93
Cites as background 7 papers
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The mapping of Aretakis charges on an extremal horizon into Newman-Penrose charges on $^+$ was investigated in a more general setting in [ref] .
Aretakis Charges and Asymptotic Null Infinity · Introduction · 0.85
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The simplest such examples arise by considering the perturbations of a scalar field [ref] .
Stability and Instability of Extreme Reissner-Nordstr\"om Black Hole Spacetimes for Linear Scalar Perturbations II · Introduction · 0.94
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The simplest such examples arise by considering the perturbations of a scalar field [ref] .
Horizon Instability of Extremal Black Holes · Introduction · 0.94
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