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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): | Shreyansh Agrawal · Panagiotis Charalambous · Laura Donnay |
| Submission information | |
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| Preprint Link: | scipost_202507_00065v2 (pdf) |
| Date submitted: | Jan. 26, 2026, 12:38 p.m. |
| Submitted by: | Panagiotis Charalambous |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| 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.
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List of changes
- Corrected Footnote 1 (removed "dynamical").
- Added Footnote 5.
- Included Refs. [117, 119,120] with Refs. [44-52] and added Ref. https://arxiv.org/abs/2303.07262 at the end of the first paragraph on Page 3 (now displayed as Refs. [44-56] there).
- Rephrased the sentence in the third paragraph on Page 3 about the Aretakis conserved quantities to make it clearer.
- In the first sentence of Section 2.3, clarified that scri is as defined previously (with a choice of divergence-free conformal frames).
- Added definition for $\alpha$ after Eq. (2.21).
- Added the definition of $\Sigma$ in Sec. 2.4 on Page 13.
- Added $T$ next to the word supertranslation under Eq. (2.27).
- Pointed out that Refs. [45,52] correspond to the case n=2 below Eq. (2.31).
- Added Footnote 21 in Page 17 to emphasize the geodesic point of view of the CT inversions.
- Added Footnote 28 on Page 27 about the comparison with Ref. [36].
- At beginning of Section 4 (Page 27), specified that the absence for a self-dual map for EKN is due to a non-vanishing twist.
- Fixed the formatting of line 901.
- Corrected the text at the top of Page 38 and added Footnote 31 for clarifications.
- Fixed the appearance of "References" in the table of contents.