%0 Journal Article %1 Ching1995Wave %A Ching, E. S. C. %A Leung, P. T. %A Suen, W. M. %A Young, K. %D 1995 %J Physical Review D %K quasinormal-mode %N 4 %P 2118--2132 %R 10.1103/physrevd.52.2118 %T Wave propagation in gravitational systems: Late time behavior %U http://dx.doi.org/10.1103/physrevd.52.2118 %V 52 %X It is well-known that the dominant late time behavior of waves propagating on a Schwarzschild spacetime is a power-law tail; tails for other spacetimes have also been studied. This paper presents a systematic treatment of the tail phenomenon for a broad class of models via a Green's function formalism and establishes the following. (i) The tail is governed by a cut of the frequency Green's function \$G(ømega)\$ along the \$-\$\~Im\~\$ømega\$ axis, generalizing the Schwarzschild result. (ii) The \$ømega\$ dependence of the cut is determined by the asymptotic but not the local structure of space. In particular it is independent of the presence of a horizon, and has the same form for the case of a star as well. (iii) Depending on the spatial asymptotics, the late time decay is not necessarily a power law in time. The Schwarzschild case with a power-law tail is exceptional among the class of the potentials having a logarithmic spatial dependence. (iv) Both the amplitude and the time dependence of the tail for a broad class of models are obtained analytically. (v) The analytical results are in perfect agreement with numerical calculations.

@article{Ching1995Wave, abstract = {{It is well-known that the dominant late time behavior of waves propagating on a Schwarzschild spacetime is a power-law tail; tails for other spacetimes have also been studied. This paper presents a systematic treatment of the tail phenomenon for a broad class of models via a Green's function formalism and establishes the following. (i) The tail is governed by a cut of the frequency Green's function \$\tilde G(\omega)\$ along the \$-\$\~{}Im\~{}\$\omega\$ axis, generalizing the Schwarzschild result. (ii) The \$\omega\$ dependence of the cut is determined by the asymptotic but not the local structure of space. In particular it is independent of the presence of a horizon, and has the same form for the case of a star as well. (iii) Depending on the spatial asymptotics, the late time decay is not necessarily a power law in time. The Schwarzschild case with a power-law tail is exceptional among the class of the potentials having a logarithmic spatial dependence. (iv) Both the amplitude and the time dependence of the tail for a broad class of models are obtained analytically. (v) The analytical results are in perfect agreement with numerical calculations.}}, added-at = {2019-02-26T10:37:35.000+0100}, archiveprefix = {arXiv}, author = {Ching, E. S. C. and Leung, P. T. and Suen, W. M. and Young, K.}, biburl = {https://www.bibsonomy.org/bibtex/2fd17356d1c681156287594c8d2ac84fa/acastro}, citeulike-article-id = {11794778}, citeulike-linkout-0 = {http://arxiv.org/abs/gr-qc/9507035}, citeulike-linkout-1 = {http://arxiv.org/pdf/gr-qc/9507035}, citeulike-linkout-2 = {http://dx.doi.org/10.1103/physrevd.52.2118}, day = 15, doi = {10.1103/physrevd.52.2118}, eprint = {gr-qc/9507035}, interhash = {45488fec248e0ac1cfcdc86ffc5d470f}, intrahash = {fd17356d1c681156287594c8d2ac84fa}, issn = {0556-2821}, journal = {Physical Review D}, keywords = {quasinormal-mode}, month = aug, number = 4, pages = {2118--2132}, posted-at = {2012-11-27 16:00:19}, priority = {2}, timestamp = {2019-02-26T10:37:35.000+0100}, title = {{Wave propagation in gravitational systems: Late time behavior}}, url = {http://dx.doi.org/10.1103/physrevd.52.2118}, volume = 52, year = 1995 }