Quasi-Normal Mode Expansion for Linearized Waves in Gravitational Systems

Details Quasi-Normal Mode Expansion for Linearized Waves in Gravitational Systems Quasi-Normal Mode Expansion for Linearized Waves in Gravitational Systems

1994-08-31

arxiv.org/abs/gr-qc/9408043v1

Phys.Rev.Lett. 74 (1995) 4588-4591

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, WUGRAV-94-9

Scientific paper

10.1103/PhysRevLett.74.4588

The quasinormal modes (QNM's) of gravitational systems modeled by the Klein-Gordon equation with effective potentials are studied in analogy to the QNM's of optical cavities. Conditions are given for the QNM's to form a complete set, i.e., for the Green's function to be expressible as a sum over QNM's, answering a conjecture by Price and Husain [Phys. Rev. Lett. {\bf 68}, 1973 (1992)]. In the cases where the QNM sum is divergent, procedures for regularization are given. The crucial condition for completeness is the existence of spatial discontinuities in the system, e.g., the discontinuity at the stellar surface in the model of Price and Husain.

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