The monodromy matrix method of solving an exterior boundary value problem for a given stationary axisymmetric perfect fluid solution

TL;DR

This paper presents a method to match a stationary axisymmetric perfect fluid solution with an exterior vacuum solution by deriving the Ernst potential from data on the zero pressure surface, enabling full metric construction.

Contribution

It introduces the monodromy matrix method for solving exterior boundary value problems for stationary axisymmetric perfect fluids.

Findings

Provides a procedure to determine the Ernst potential from boundary data.

Enables construction of the full exterior metric from the Ernst potential.

Facilitates matching interior fluid solutions to exterior vacuum spacetimes.

Abstract

A procedure is described for matching a given stationary axisymmetric perfect fluid solution to a not necessarily asymptotically flat vacuum exterior. Using data on the zero pressure surface, the procedure yields the Ernst potential of the matching vacuum metric on the symmetry axis. From this the full metric can be constructed using a variety of well established procedures.