{"title":"On the existence of conformal Killing horizons in LRS spacetimes","authors":"Abbas M. Sherif","doi":"10.1007/s10714-024-03197-w","DOIUrl":null,"url":null,"abstract":"<p>Let <i>M</i> be a locally rotationally symmetric spacetime, and <span>\\(\\xi ^a\\)</span> a conformal Killing vector for the metric on <i>M</i>, lying in the subspace spanned by the unit timelike direction and the preferred spatial direction, and with non-constant components. Under the assumption that the divergence of <span>\\(\\xi ^a\\)</span> has no critical point in <i>M</i>, we obtain the necessary and sufficient condition for <span>\\(\\xi ^a\\)</span> to generate a conformal Killing horizon. It is shown that <span>\\(\\xi ^a\\)</span> generates a conformal Killing horizon if and only if either of the components (which coincide on the horizon) is constant along its orbits. That is, a conformal Killing horizon can be realized as the set of critical points of the variation of the component(s) of the conformal Killing vector along its orbits. Using this result, a simple mechanism is provided by which to determine if an arbitrary vector in an expanding LRS spacetime is a conformal Killing vector that generates a conformal Killing horizon. In specializing the case for which <span>\\(\\xi ^a\\)</span> is a special conformal Killing vector, provided that the gradient of the divergence of <span>\\(\\xi ^a\\)</span> is non-null, it is shown that LRS spacetimes cannot admit a special conformal Killing vector field, thereby ruling out conformal Killing horizons generated by such vector fields.</p>","PeriodicalId":578,"journal":{"name":"General Relativity and Gravitation","volume":null,"pages":null},"PeriodicalIF":2.1000,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"General Relativity and Gravitation","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s10714-024-03197-w","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
Let M be a locally rotationally symmetric spacetime, and \(\xi ^a\) a conformal Killing vector for the metric on M, lying in the subspace spanned by the unit timelike direction and the preferred spatial direction, and with non-constant components. Under the assumption that the divergence of \(\xi ^a\) has no critical point in M, we obtain the necessary and sufficient condition for \(\xi ^a\) to generate a conformal Killing horizon. It is shown that \(\xi ^a\) generates a conformal Killing horizon if and only if either of the components (which coincide on the horizon) is constant along its orbits. That is, a conformal Killing horizon can be realized as the set of critical points of the variation of the component(s) of the conformal Killing vector along its orbits. Using this result, a simple mechanism is provided by which to determine if an arbitrary vector in an expanding LRS spacetime is a conformal Killing vector that generates a conformal Killing horizon. In specializing the case for which \(\xi ^a\) is a special conformal Killing vector, provided that the gradient of the divergence of \(\xi ^a\) is non-null, it is shown that LRS spacetimes cannot admit a special conformal Killing vector field, thereby ruling out conformal Killing horizons generated by such vector fields.
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.