SciPost Submission Page
A toolbox for black hole scattering
by Nava Gaddam, Nico Groenenboom
Submission summary
| Authors (as registered SciPost users): | Nava Gaddam |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2207.11277v2 (pdf) |
| Date submitted: | Dec. 23, 2025, 10:31 a.m. |
| Submitted by: | Nava Gaddam |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Hawking's free field theory is expected to break down after Page time. In previous work, we have shown that a primary dynamical reason for this breakdown is the dominance of graviton fluctuations of the horizon that mediate scattering processes. In this article, we present a toolbox for such `black hole scattering' computations. The toolbox comprises of explicit expressions for the graviton propagator near the horizon in an angular momentum basis for all angular momentum modes of either parity, the leading interaction rules, and most importantly a rewriting of the theory in terms of a scalar theory with an interesting four-vertex. We demonstrate how this rewriting drastically reduces the number of diagrams to be calculated in the original formulation. Finally and perhaps most remarkably, we observe that the black hole entropy appears to emerge from the multiplicity of external legs of the dominant $2\rightarrow2N$ amplitudes in this theory.
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
Author comments upon resubmission
List of changes
We have addressed all the issues raised by the two referees. Here, we list the changes made: 1) We have added a clarifying note at the top of page 11 comparing the dynamical mode we have with that in the literature. Limitations to Schwarzschild added in Sec 7. 2) There is no first principle derivation or argument that we are able to propose for why the scattering energy. However, as we explain in Sec 6, since the scattering process conserves momentum, adding a scattering energy of the black hole mass results in an entropy associated with the the typical entropy for decay of a state with energy E = M_BH into a large number of particles, analogous to black hole evaporation. We have added this clarifying comment in the discussion below eq (6.3) to make the importance of the scattering energy E = M_BH clearer. 3) We have included a reference to lectures with a pedagogical overview of the time scales associated with he black hole in the introduction. 4) We added a reference (in the first bullet point in the Shortcomings paragraph in the Introduction) where the problem of asymptotic states in black hole backgrounds is indirectly addressed by resorting to lower-dimensional AdS/CFT. 5) The metric in standard Kruskal-Szekeres coordinates has unwarranted numerical factors on the horizon. The variant we use ensures that the metric on the horizon is such that A(r=R)=1. We have added this comment below (A.2). 6) We reversed the order of appendices. There was a typo in (2.7) which has been fixed, and we referenced the equation in the appendix it originates from, in the text below eqn 2.8. 7) We made a note on the possible ambiguity in choice of conventions at the top of pg. 11. 8) We have added a clarifying sentence below Eq (4.23) about the usefulness of the simplified vertex in some elastic amplitudes (despite its uselessness for most observables). 9) We clarified the distinction we would like to point out between 't Hooft's quantum mechanics approach vs the second quantised approach being taken in the present article in footnote 8.