{"title":"Gravitational self-force with hyperboloidal slicing and spectral methods","authors":"Benjamin Leather","doi":"10.1007/s10714-025-03443-9","DOIUrl":null,"url":null,"abstract":"<div><p>We present a novel approach for calculating the gravitational self-force (GSF) in the Lorenz gauge, employing hyperboloidal slicing and spectral methods. Our method builds on the previous work that applied hyperboloidal surfaces and spectral approaches to a scalar-field toy model [Phys. Rev. D 105, 104033 (2022)], extending them to handle gravitational perturbations. Focusing on first-order metric perturbations, we address the construction of the hyperboloidal foliation, detailing the minimal gauge choice. The Lorenz gauge is adopted to facilitate well-understood regularisation procedures, which are essential for obtaining physically meaningful GSF results. We calculate the Lorenz gauge metric perturbation for a secondary on a quasicircular orbit in a Schwarzschild background via a (known) gauge transformation from the Regge-Wheeler gauge. Our approach yields a robust framework for obtaining the metric perturbation components needed to calculate key physical quantities, such as radiative fluxes, the Detweiler redshift, and self-force corrections. Furthermore, the compactified hyperboloidal approach allows us to efficiently calculate the metric perturbation throughout the entire spacetime. This work thus establishes a foundational methodology for future second-order GSF calculations within this gauge, offering computational efficiencies through spectral methods.</p></div>","PeriodicalId":578,"journal":{"name":"General Relativity and Gravitation","volume":"57 7","pages":""},"PeriodicalIF":2.8000,"publicationDate":"2025-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10714-025-03443-9.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"General Relativity and Gravitation","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s10714-025-03443-9","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
引用次数: 0
Abstract
We present a novel approach for calculating the gravitational self-force (GSF) in the Lorenz gauge, employing hyperboloidal slicing and spectral methods. Our method builds on the previous work that applied hyperboloidal surfaces and spectral approaches to a scalar-field toy model [Phys. Rev. D 105, 104033 (2022)], extending them to handle gravitational perturbations. Focusing on first-order metric perturbations, we address the construction of the hyperboloidal foliation, detailing the minimal gauge choice. The Lorenz gauge is adopted to facilitate well-understood regularisation procedures, which are essential for obtaining physically meaningful GSF results. We calculate the Lorenz gauge metric perturbation for a secondary on a quasicircular orbit in a Schwarzschild background via a (known) gauge transformation from the Regge-Wheeler gauge. Our approach yields a robust framework for obtaining the metric perturbation components needed to calculate key physical quantities, such as radiative fluxes, the Detweiler redshift, and self-force corrections. Furthermore, the compactified hyperboloidal approach allows us to efficiently calculate the metric perturbation throughout the entire spacetime. This work thus establishes a foundational methodology for future second-order GSF calculations within this gauge, offering computational efficiencies through spectral methods.
我们提出了一种计算洛伦兹规范中引力自力(GSF)的新方法,采用双曲面切片和谱方法。我们的方法建立在先前的工作基础上,该工作将双曲面和光谱方法应用于标量场玩具模型[物理学]。Rev. D 105, 104033(2022)],将它们扩展到处理引力扰动。聚焦于一阶度量摄动,我们讨论了双曲叶理的构造,详细说明了最小规范的选择。采用洛伦兹规范是为了方便易于理解的正则化程序,这对于获得物理上有意义的GSF结果是必不可少的。我们通过Regge-Wheeler规范的(已知的)规范变换,计算了在史瓦西背景下准圆轨道上次级粒子的洛伦兹规范度量摄动。我们的方法产生了一个强大的框架,用于获得计算关键物理量所需的度量摄动分量,如辐射通量、德维勒红移和自力校正。此外,紧化双曲方法使我们能够有效地计算整个时空的度规摄动。因此,这项工作建立了一个基础的方法,为未来的二阶GSF计算在这个量规内,通过谱方法提供计算效率。
期刊介绍:
General Relativity and Gravitation is a journal devoted to all aspects of modern gravitational science, and published under the auspices of the International Society on General Relativity and Gravitation.
It welcomes in particular original articles on the following topics of current research:
Analytical general relativity, including its interface with geometrical analysis
Numerical relativity
Theoretical and observational cosmology
Relativistic astrophysics
Gravitational waves: data analysis, astrophysical sources and detector science
Extensions of general relativity
Supergravity
Gravitational aspects of string theory and its extensions
Quantum gravity: canonical approaches, in particular loop quantum gravity, and path integral approaches, in particular spin foams, Regge calculus and dynamical triangulations
Quantum field theory in curved spacetime
Non-commutative geometry and gravitation
Experimental gravity, in particular tests of general relativity
The journal publishes articles on all theoretical and experimental aspects of modern general relativity and gravitation, as well as book reviews and historical articles of special interest.