Exact Solutions with w - modes

TL;DR

This paper investigates conditions for resonance scattering of axial gravitational waves in static spherically symmetric perfect fluid solutions, providing exact inhomogeneous solutions and analyzing their physical acceptability and boundary conditions.

Contribution

It introduces an explicit necessary condition for resonance scattering and presents new exact solutions demonstrating internal trapping of null geodesics.

Findings

Certain solutions exhibit trapping with tenuity between 2.8 and 2.9

Adding an envelope can increase tenuity without affecting trapping

Provides explicit conditions for resonance scattering in these spacetimes

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.