Exact Solutions with w - modes

Abstract

An explicit necessary condition for the occurrence of resonance scattering of axial gravitational waves, along with the internal trapping of null geodesics, is proposed for static spherically symmetric perfect fluid solutions to Einstein's equations. Some exact inhomogeneous solutions which exhibit this trapping are given with special attention to boundary conditions and the physical acceptability of the space times. In terms of the tenuity ($\alpha =R/M$ at the boundary) all the examples given lie in the narrow range $2.8<\alpha <2.9$. The tenuity can be raised to more interesting values by the addition of an envelope without altering the trapping.

Final form to appear in Phys. Rev. D. Further information on the web at http://grtensor.phy.queensu.ca/trap/

References in corpus (3)

• The geometry of photon surfaces
• Trapped and excited w modes of stars with a phase transition and R>=5M
• Constructing stellar objects with multiple necks

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