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O.W. Day (Department of Physics, East Carolina University), D.W. Pravica (Department of Mathematics, East Carolina University, Greenville, NC USA)
Lowest-frequency standing-wave solutions for graviton and photon waves are obtained from the linearized general relativistic equations [Teukolsky, 1973. ApJ. 185, 635] which determine the gravitational and electromagnetic fields in the region immediately surrounding a compact object. The wave functions, obtained via the complex scaling method for various angles of rotation in the complex plane (as described by [W. Hunziker, 1986. Ann. Inst. H. Poincare' Phys. Theor. 45, 339] and [D. W. Pravica, 1999. Proc. R. Soc. Lond. A 455, 3003]), are subsequently rotated back to the real axis to determine the radial distribution of energy in each respective oscillation. These waves are resonances, where the electromagnetic oscillations are driven by oscillations in the metric, which are, in turn, caused by the source of the gravitational waves. They have finite lifetimes in the time domain, and are also localized in the spatial domain, extending from the surface of the compact object out to a few times 3M in the radial direction. Their maxima occur at a radial distance slightly larger than 3M in the case of gravitons but at a distance of 3M in the case of photons, which in fact causes slightly lower frequencies for the gravitational than the electromagnetic standing waves. Similarities and differences are discussed between compact-object resonance states (obtained from the Zerilli or Regge-Wheeler potentials in Schrodinger-type equations), and bound, low-energy hydrogenic wavefunctions (obtained from the Schrodinger equation for a single electron). Results obtained for some compact objects of small specific angular momentum compare well with corresponding experimentally measured asymptotic QPO frequencies.
Bulletin of the American Astronomical Society,
© 2003. The American Astronomical Soceity.