Evolution equations for the perturbations of slowly rotating relativistic stars

• Main Authors: Ruoff, Johannes, Stavridis, Adamantios, Kokkotas, Kostas D
• Format: Journal Article
• Language: English
• Published: 19-09-2001
• Subjects: Physics - Astrophysics of Galaxies; Physics - Cosmology and Nongalactic Astrophysics; Physics - Earth and Planetary Astrophysics; Physics - General Relativity and Quantum Cosmology; Physics - High Energy Astrophysical Phenomena; Physics - Instrumentation and Methods for Astrophysics; Physics - Solar and Stellar Astrophysics
• DOI: 10.48550/arxiv.gr-qc/0109065

Mon.Not.Roy.Astron.Soc. 332 (2002) 676 We present a new derivation of the equations governing the oscillations of
slowly rotating relativistic stars. Previous investigations have been mostly
carried out in the Regge-Wheeler gauge. However, in this gauge the process of
linearizing the Einstein field equations leads to perturbation equations which
as such cannot be used to perform numerical time evolutions. It is only through
the tedious process of combining and rearranging the perturbation variables in
a clever way that the system can be cast into a set of hyperbolic first order
equations, which is then well suited for the numerical integration. The
equations remain quite lengthy, and we therefore rederive the perturbation
equations in a different gauge, which has been first proposed by Battiston et
al. (1970). Using the ADM formalism, one is immediately lead to a first order
hyperbolic evolution system, which is remarkably simple and can be numerically
integrated without many further manipulations. Moreover, the symmetry between
the polar and the axial equations becomes directly apparent.