Gravitational waves from pulsating stars: Evolving the perturbation equations for a relativistic star

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 58, Issue 12, 1998, Pages

  Allen, Gabrielle ^a,b   Andersson, Nils ^c,d   Kokkotas, Kostas D ^a,e   Schutz, Bernard F ^a,b  

^a ALBERT EINSTEIN INSTITUT   (Germany)

^b CARDIFF UNIVERSITY   (United Kingdom)

^c WASHINGTON UNIVERSITY   (United States)

^d UNIVERSITY OF TÜBINGEN   (Germany)

^e ARISTOTLE UNIVERSITY OF THESSALONIKI   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000235420     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.58.124012     Document Type: Article

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31. If the angular dependence of the perturbed quantities were to be accounted for, we should use (Formula presented) etc., where (Formula presented) are the standard spherical harmonics. The fluid variables (Formula presented) (Formula presented) and δρ are, of course, also expanded in spherical harmonics. For a more detailed description of the appropriate angular functions, see 1424. Our shorthand notation should not lead to any confusion, since we focus on the perturbation functions and never actually reconstruct the perturbed metric. Furthermore, it should be noted that we only consider the quadrupole case (Formula presented) in our numerical examples, and since the background geometry is spherically symmetric, it is sufficient to consider (Formula presented)
32. The wave equation for (Formula presented) comes from the (Formula presented) component of the perturbed Einstein equations, the equation for (Formula presented) follows when one combines the (Formula presented) and the (Formula presented) components of the perturbed Einstein equations, and the wave equation for the variable (Formula presented) follows from the time-derivative of the (Formula presented)-component of the equations of motion for the fluid. The Hamiltonian constraint corresponds to the (Formula presented)-component of the perturbed Einstein equations. For more details of the origin of all these equations, we refer to 2425.
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