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The space–time line element for static ellipsoidal objects
R. Brahma,
Published in Springer
2023
Volume: 55
   
Issue: 2
Abstract
In this paper, we solved the Einstein’s field equation and obtained a line element for static, ellipsoidal objects characterized by the linear eccentricity (η) instead of quadrupole parameter (q). This line element recovers the Schwarzschild line element when η is zero. In addition to that it also reduces to the Schwarzschild line element, if we neglect terms of the order of r- 2 or higher which are present within the expressions for metric elements for large distances. Furthermore, as the ellipsoidal character of the derived line element is maintained by the linear eccentricity (η), which is an easily measurable parameter, this line element could be more suitable for various analytical as well as observational studies. © 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
About the journal
JournalGeneral Relativity and Gravitation
PublisherSpringer
ISSN00017701