Pith Number

pith:CJUJY5UU

pith:2026:CJUJY5UUZ3WF2BRKRTKEAN5G4K

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Analytical Fluxes from Generic Schwarzschild Geodesics

Chris Kavanagh, Majed Khalaf, Ofri Telem

A Chebyshev expansion of radiation coefficients yields analytic gravitational-wave fluxes for eccentric Schwarzschild geodesics.

arxiv:2605.13847 v1 · 2026-05-13 · gr-qc · hep-th

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Claims

C1strongest claim

we implement the method using a 15PN-expanded input and find that it reproduces the total flux for the case (p,e)=(12.5,0.5) to relative accuracy 10^{-5}, while for the stronger-field case (p,e)=(10,0.8) it yields weighted mode-by-mode errors below 10^{-6} for the selected dominant modes analyzed.

C2weakest assumption

The Chebyshev expansion of the radiation Fourier coefficients converges rapidly enough for generic bound geodesics when the input is a 15PN series; this is assumed rather than proven for all eccentricities and field strengths.

C3one line summary

A Chebyshev-basis expansion reduces gravitational-wave fluxes from arbitrary-eccentricity bound Schwarzschild geodesics to sums of previously derived Keplerian Fourier coefficients, achieving 10^{-5} relative accuracy on total flux for tested orbits.

References

38 extracted · 38 resolved · 13 Pith anchors

[1] The latter are crucial to ensure convergence over the entire intervalr p ≤r≤ ra

[2] we showed how relativistic Keplerian Fourier ele- ments, computed using (13), can be analytically contin- ued to the unbound regime and benchmarked against post-Minkowski/post-Newtonian computations.

[3] Observation of Gravitational Waves from a Binary Black Hole Merger 2016 · arXiv:1602.03837

[4] GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral 2017 · arXiv:1710.05832

[5] GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run 2021 · arXiv:2010.14527

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:09.331183Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12689c7694ceec5d062a8cd44037a6e2a65c62370d21399c9d5b9266bd238fe8

Aliases

arxiv: 2605.13847 · arxiv_version: 2605.13847v1 · doi: 10.48550/arxiv.2605.13847 · pith_short_12: CJUJY5UUZ3WF · pith_short_16: CJUJY5UUZ3WF2BRK · pith_short_8: CJUJY5UU

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CJUJY5UUZ3WF2BRKRTKEAN5G4K \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 12689c7694ceec5d062a8cd44037a6e2a65c62370d21399c9d5b9266bd238fe8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "78d82347c3c079f4acd7498d437f70faf98cdc401b2caf94c32bc85a0f970530",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-05-13T17:59:59Z",
    "title_canon_sha256": "82e8989f4ea3716faf377fb001f4d262c7aab0be731d5d4a2602cd57e060714a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13847",
    "kind": "arxiv",
    "version": 1
  }
}