Static Isotropic Spacetimes with Radially Imperfect Fluids

TL;DR

This paper explores static, isotropic spacetimes with a combined perfect and radial imperfect fluid stress-energy tensor, deriving exact solutions and examining implications for dark matter phenomenology.

Contribution

It introduces the most general form of stress-energy tensor for such spacetimes and derives exact solutions, highlighting potential observational effects of the imperfect fluid component.

Findings

Deviations from Schwarzschild solutions can be small.

Imperfect fluid causes a shift in angular momentum scaling.

Potential to model dark matter effects with imperfect fluids.

Abstract

When solving the equations of General Relativity in a symmetric sector, it is natural to consider the same symmetry for the geometry and stress-energy. This implies that for static and isotropic spacetimes, the most general natural stress-energy tensor is a sum of a perfect fluid and a radial imperfect fluid component. In the special situations where the perfect fluid component vanishes or is a spacetime constant, the solutions to Einstein's equations can be thought of as modified Schwarzschild and Schwarzschild-de Sitter spaces. Exact solutions of this type are derived and it is shown that whereas deviations from the unmodified solutions can be made small, among the manifestations of the imperfect fluid component is a shift in angular momentum scaling for orbiting test-bodies at large radius. Based on this effect, the question of whether the imperfect fluid component can feasibly describe dark matter phenomenology is addressed.