{"title":"Quadratic perturbations of the Schwarzschild black hole: the algebraically special sector","authors":"Jibril Ben Achour and Hugo Roussille","doi":"10.1088/1475-7516/2024/07/085","DOIUrl":null,"url":null,"abstract":"We investigate quadratic algebraically special perturbations (ASPs) of the Schwarzschild black hole. Their dynamics are derived from the expansion up to second order in perturbation of the most general algebraically special twisting vacuum solution of general relativity. Following this strategy, we present analytical expressions for the axial-axial, polar-polar and polar-axial source terms entering in the dynamical equations. We show that these complicated inhomogeneous equations can be solved analytically and we present explicit expressions for the profiles of the quadratic ASPs. As expected, they exhibit exponential growth both at the past and future horizons even in the non-linear regime. We further use this result to analyze the quadratic zero modes and their interpretation in terms of quadratic corrections to mass and spin of the Schwarzschild black hole. The present work provides a direct extension beyond the linear regime of the original work by Couch and Newman.","PeriodicalId":15445,"journal":{"name":"Journal of Cosmology and Astroparticle Physics","volume":null,"pages":null},"PeriodicalIF":5.3000,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Cosmology and Astroparticle Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1475-7516/2024/07/085","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
引用次数: 0
Abstract
We investigate quadratic algebraically special perturbations (ASPs) of the Schwarzschild black hole. Their dynamics are derived from the expansion up to second order in perturbation of the most general algebraically special twisting vacuum solution of general relativity. Following this strategy, we present analytical expressions for the axial-axial, polar-polar and polar-axial source terms entering in the dynamical equations. We show that these complicated inhomogeneous equations can be solved analytically and we present explicit expressions for the profiles of the quadratic ASPs. As expected, they exhibit exponential growth both at the past and future horizons even in the non-linear regime. We further use this result to analyze the quadratic zero modes and their interpretation in terms of quadratic corrections to mass and spin of the Schwarzschild black hole. The present work provides a direct extension beyond the linear regime of the original work by Couch and Newman.
我们研究了施瓦兹柴尔德黑洞的二次代数特殊扰动(ASPs)。它们的动力学是从广义相对论最一般的代数特殊扭转真空解的扰动扩展到二阶推导出来的。根据这一策略,我们提出了进入动力学方程的轴-轴、极-极和极-轴源项的分析表达式。我们证明了这些复杂的非均质方程可以通过分析求解,并给出了四元 ASP 曲线的明确表达式。不出所料,即使在非线性状态下,它们在过去和未来的水平面上都呈现指数增长。我们进一步利用这一结果分析了二次零模及其对施瓦兹柴尔德黑洞质量和自旋二次修正的解释。目前的工作直接扩展了库奇和纽曼最初工作的线性范围。
期刊介绍:
Journal of Cosmology and Astroparticle Physics (JCAP) encompasses theoretical, observational and experimental areas as well as computation and simulation. The journal covers the latest developments in the theory of all fundamental interactions and their cosmological implications (e.g. M-theory and cosmology, brane cosmology). JCAP''s coverage also includes topics such as formation, dynamics and clustering of galaxies, pre-galactic star formation, x-ray astronomy, radio astronomy, gravitational lensing, active galactic nuclei, intergalactic and interstellar matter.