SciPost Submission Page
Null infinity as an inverted extremal horizon: Matching an infinite set of conserved quantities for gravitational perturbations
by Shreyansh Agrawal, Panagiotis Charalambous, Laura Donnay
Submission summary
| Authors (as registered SciPost users): | Panagiotis Charalambous |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202507_00065v1 (pdf) |
| Date submitted: | July 23, 2025, 8:05 p.m. |
| Submitted by: | Panagiotis Charalambous |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
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-Nordström 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.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
In refereeing
Reports on this Submission
Report #1 by Simone Speziale (Referee 1) on 2025-9-11 (Invited Report)
Report
Dear editor,
first of all my apologies to the authors for the delay of my report.
The paper studies the relation between future null infinity and certain physical horizons. It extends previous results in a non trivial way, and I am very happy to recommend it for publication. It does a nice job of reviewing the existing literature and results, including comparing notations, and of explaining in which new directions they are extending them, and their motivations. Among the results, I find particularly remarkable the matching of charges for higher spins described at the end of section 3, and in section 4 the extension of the already surprising result of Couch and Torrence in mapping scalar perturbation, to higher spins.
I have some small suggestions for optional amendments:
p1. It may be useful to stress in the introduction that the dictionary set up in this paper is based on divergence-free conformal frames, namely on describing null infinity as surface with vanishing expansion
Footnote 1: i find the term "dynamical event horizons” confusing, usually these two adjectives are opposite of one another: an event horizon is global, teleological and completely stationary, hence non dynamical. Maybe the authors could explain better what they mean?
p3: I think it would be useful to include the references 117-120 with 44-52 at the end of the paragraph; and also to say explicitly that the key difference between the full NU group (which the authors use) and the smaller group considered in [117-120] (which is the analogue of the BMSW group at null infinity) is due to adding the inaffinity of the arbitrary null normal to the universal structure, a possibility already pointed out in [45]. I would also suggest adding the reference https://inspirehep.net/literature/2641560 to that list of relevant works for the phase space on null hypersurfaces.
In the fourth paragraph of that page, the authors talk about Aretakis conserved quantities, but their existence has not been mentioned yet, so the sentence is a bit out of context.
p.10 : I would add in the first sentence of 2.3 the specification “…whose boundary is scri **in a divergence-free completion**, is diffeomorphic…”
Below 2.21, \alpha (an arbitrary real function at this stage I suppose? can it be time dependent? or a constant only?) is not defined
Page 12, Footnote 15: Among the references given, [36] seems to contain a similar idea of mapping between null infinity and horizons, and investigating sub-leading charges. If the authors know the differences/similarities in scopes and results, it would be useful to the reader to comment on them.
p13: in reference to my comment earlier, and given the attention the authors are giving to comparing the literature, it may be useful to add below 2.31 that the case considered in 117 corresponds to n=2 (this characterization is only valid at k=0, but this is anyways the context of the present paper)
p.27: is the lack of self-mapping in the extremal KN case ultimately due to the fact that the Hajicek 1-form vanishes in one case but not the other? if yes, it may be useful to add this comment
first of all my apologies to the authors for the delay of my report.
The paper studies the relation between future null infinity and certain physical horizons. It extends previous results in a non trivial way, and I am very happy to recommend it for publication. It does a nice job of reviewing the existing literature and results, including comparing notations, and of explaining in which new directions they are extending them, and their motivations. Among the results, I find particularly remarkable the matching of charges for higher spins described at the end of section 3, and in section 4 the extension of the already surprising result of Couch and Torrence in mapping scalar perturbation, to higher spins.
I have some small suggestions for optional amendments:
p1. It may be useful to stress in the introduction that the dictionary set up in this paper is based on divergence-free conformal frames, namely on describing null infinity as surface with vanishing expansion
Footnote 1: i find the term "dynamical event horizons” confusing, usually these two adjectives are opposite of one another: an event horizon is global, teleological and completely stationary, hence non dynamical. Maybe the authors could explain better what they mean?
p3: I think it would be useful to include the references 117-120 with 44-52 at the end of the paragraph; and also to say explicitly that the key difference between the full NU group (which the authors use) and the smaller group considered in [117-120] (which is the analogue of the BMSW group at null infinity) is due to adding the inaffinity of the arbitrary null normal to the universal structure, a possibility already pointed out in [45]. I would also suggest adding the reference https://inspirehep.net/literature/2641560 to that list of relevant works for the phase space on null hypersurfaces.
In the fourth paragraph of that page, the authors talk about Aretakis conserved quantities, but their existence has not been mentioned yet, so the sentence is a bit out of context.
p.10 : I would add in the first sentence of 2.3 the specification “…whose boundary is scri **in a divergence-free completion**, is diffeomorphic…”
Below 2.21, \alpha (an arbitrary real function at this stage I suppose? can it be time dependent? or a constant only?) is not defined
Page 12, Footnote 15: Among the references given, [36] seems to contain a similar idea of mapping between null infinity and horizons, and investigating sub-leading charges. If the authors know the differences/similarities in scopes and results, it would be useful to the reader to comment on them.
p13: in reference to my comment earlier, and given the attention the authors are giving to comparing the literature, it may be useful to add below 2.31 that the case considered in 117 corresponds to n=2 (this characterization is only valid at k=0, but this is anyways the context of the present paper)
p.27: is the lack of self-mapping in the extremal KN case ultimately due to the fact that the Hajicek 1-form vanishes in one case but not the other? if yes, it may be useful to add this comment
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)