arXiv 2610.185212026-10-14gr-qchep-th

黑洞形变的线性响应

Linear Response to Black Hole Deformations

IP2I（粒子物理与核物理研究所）

Stefan Hohenegger

备注：: 40 pages, 16 figures

阅读 PDF

arXiv 页面 ↗HTML 原文 ↗

AI总结：

本研究受线性响应理论启发，提出一种可计算黑洞视界外可观测量主导阶修正的形式体系，通过该体系可将可观测量与有效物理模型关联，还能利用可观测量约束相关本征值以探究黑洞附近有效物理。

摘要：

超越真空广义相对论的引力修正对黑洞周围的物理过程存在微妙影响，然而，要在不同可观测量中描述这些效应，先验上具有很强的模型依赖性。尽管几何的有效描述能有效捕捉与基准预测的偏差，但它们有时缺乏通向（有效）新物理的清晰途径。受线性响应理论启发，本研究提出一种形式体系，可计算时空中任意位置（视界外）相对于史瓦西黑洞的可观测量的主导阶修正：修正阶数由爱因斯坦张量的本征值$\boldsymbol{\textit{E}}$确定，该本征值与产生几何形变的外部能量动量张量相关联，由此$\boldsymbol{\textit{E}}$可与有效物理模型建立联系。聚焦于球对称且静态的黑洞，本研究通过视界附近的一系列可观测量说明该方法，例如黑洞周围运动粒子的特征量（如黑洞阴影或最内稳定圆轨道半径），或标量准正则模的谱。反过来，本研究认为，对这类可观测量的认知能为$\boldsymbol{\textit{E}}$提供非平凡约束，进而让人们深入了解黑洞附近的有效物理。

英文摘要：

Modifications of gravity beyond (vacuum) General Relativity have a subtle impact on the physics around black holes. Describing these effects across different observables is, however, a priori strongly model dependent. While effective descriptions of the geometry allow to efficiently capture deviations from benchmark predictions, they sometimes lack a clear passage towards (effective) new physics. Inspired by linear response theory, in this work I therefore propose a formalism that allows to calculate leading corrections of observables relative to the Schwarzschild black hole anywhere in space-time (outside of the horizon): the order of corrections is fixed through an eigenvalue $\mathcal{E}$ of the Einstein tensor, which is identified with an external energy momentum tensor that generates the deformation of the geometry. In this ways, $\mathcal{E}$ can be linked to effective physics models. Focusing on spherically symmetric and static black holes, I illustrate the approach at the hand of a number of observables in the vicinity of the horizon, such as characteristic quantities of particles moving around the black hole (e.g. the black hole shadow or the radius of the innermost stable circular orbit) or the spectrum of scalar quasi-normal modes. Reversing the logic, I argue that the knowledge of such observables provides non-trivial constraints on $\mathcal{E}$, which in turn grant insights into the effective physics in the vicinity of the black hole.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

AI总结：

摘要：

英文摘要：

相关论文