发表机构
Universidad de La Frontera; Universidad de Antofagasta（拉弗龙特拉大学; 安托法加斯塔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究标量-高斯-博内引力中耦合项在Bondi--Sachs层级中的进入位置，发现其首次出现在角度量$O(r^{-3})$系数的演化方程中，且不产生对数项，对质量损失和角动量演化无影响。
AI 中文摘要
我们整合了具有任意耦合函数 $f(\Phi)$ 和辐射无质量标量的标量-高斯-博内引力的Bondi--Sachs层级，并确定了耦合 $\lambda$ 在每个场方程中首次出现的 $1/r$ 阶数。我们获得了有效高斯-博内应力张量的渐近衰减及其在球面上的协变形式中的前导系数：每个分量都比与光滑零无穷大相容的最慢衰减快一到三个 $1/r$ 幂次衰减。因此，(i) Bondi质量损失公式和角动量方面的演化方程与最小耦合的爱因斯坦-标量系统相同，这一陈述在光滑展开假设下对 $\lambda$ 是精确的；(ii) 耦合在所考虑的阶数内不产生对数项，尽管该理论的Horndeski表示涉及对数泛函；(iii) 耦合首次进入动力学方程是在角度量 $O(r^{-3})$ 系数的演化中，通过渐近标量电荷方面与新闻时间导数之间的交叉项 $-2\lambda f'(\vp_0)\\,\vp_1\\,\partial_u N_{AB}$。在Newman--Penrose形式中，$\Psi_0$ 前导系数的演化方程获得源项 $-12\lambda f'(\vp_0)\\,\vp_1\bar\Psi_4^0$，而 $\Psi_1$ 和 $\Psi_2$ 的演化方程不变。高斯-博内不变量按 $r^{-6}$ 衰减，并且仅从 $r^{-5}$ 系数的演化开始影响标量层级。对于真空黑洞时空，其中标量由耦合本身提供源，所有这些效应都是 $\lambda^2$ 阶的；如果 $f'(\vp_0)=0$，它们被推迟到 $1/r$ 的更高一阶。
英文摘要
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 $-2λf'(\vp_0)\,\vp_1\,\partial_u N_{AB}$ 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 $-12λf'(\vp_0)\,\vp_1\barΨ_4^0$, 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 $1/r$.
Comments9 pages
