$C^3$ matching conditions for anisotropic fluids

TL;DR

This paper introduces the $C^3$ invariant formalism for matching anisotropic fluid spacetimes with vacuum solutions, including discontinuities, and applies it to neutron star models matched to Schwarzschild spacetime.

Contribution

It develops the $C^3$ matching conditions for anisotropic fluids and demonstrates their application to realistic neutron star models.

Findings

Successfully matches neutron star solutions to Schwarzschild spacetime.

Handles discontinuities on the matching surface.

Provides a new invariant formalism for spacetime matching.

Abstract

The $C^3$ approach is an invariant formalism that utilizes the eigenvalues of the Riemann curvature tensor to match spacetimes across a specific matching surface. We apply this approach to match an anisotropic fluid with an exterior vacuum solution, including the case in which discontinuities appear on the matching surface. As a particular example, a class of analytic solutions, which describe the gravitational field of realistic neutron stars, is matched to the exterior Schwarzschild spacetime.