Phys. Rev. Lett. 74, 4588–4591 (1995)Quasinormal Mode Expansion for Linearized Waves in Gravitational SystemsReceived 30 August 1994; published in the issue dated 5 June 1995 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 R. H. Price and V. Husain [Phys. Rev. Lett. 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. © 1995 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.74.4588
DOI:
10.1103/PhysRevLett.74.4588
PACS:
04.30.-w, 95.30.Sf
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