Where the Gauss--Bonnet coupling enters the Bondi--Sachs hierarchy

@misc{munozpalma2026where,
  title = {{Where the Gauss--Bonnet coupling enters the Bondi--Sachs hierarchy}},
  author = {Maickol Muñoz-Palma and Alvaro Restuccia and Francisco Tello-Ortiz},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.07200},
  eprint = {2610.07200},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.07200},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Where the Gauss--Bonnet coupling enters the Bondi--Sachs hierarchy
AU  - Maickol Muñoz-Palma
AU  - Alvaro Restuccia
AU  - Francisco Tello-Ortiz
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.07200
UR  - https://arxiv.org/abs/2610.07200
AB  - We integrate the Bondi--Sachs hierarchy of scalar--Gauss--Bonnet gravity with an arbitrary coupling function f(Φ) and a radiating massless scalar, and determine the first order in 1/r at which the coupling λ becomes visible in each field equation. We obtain the asymptotic falloff of the effective Gauss--Bonnet stress tensor together with its leading coefficients in covariant form on the sphere: every component decays between one and three powers of 1/r faster than the slowest falloff compatible with a smooth null infinity. As a consequence, (i) the Bondi mass-loss formula and the evolution equation of the angular-momentum aspect are those of the minimally coupled Einstein--scalar system, a statement that is exact in λ under the assumption of a smooth expansion; (ii) the coupling generates no logarithmic terms through the orders considered, even though the Horndeski representation of the theory involves logarithmic functionals; and (iii) the coupling first enters a dynamical equation in the evolution of the O(r^−3) coefficient of the angular metric, through the cross term −2λf'(vp_0) vp_1 ∂_u N_AB between the asymptotic scalar charge aspect and the time derivative of the news. In Newman--Penrose form, the evolution equation of the leading coefficient of Ψ_0 acquires the source −12λf'(vp_0) vp_1Ψ̅_4^0, while those of Ψ_1 and Ψ_2 are unchanged. The Gauss--Bonnet invariant decays as r^−6 and affects the scalar hierarchy only from the evolution of the r^−5 coefficient onward. For vacuum black-hole spacetimes, where the scalar is sourced by the coupling itself, all these effects are of order λ^2; if f'(vp_0)=0 they are pushed one further order in 1/r.
ER  -