Slowly rotating fluid balls of Petrov type D

TL;DR

This paper numerically solves second order perturbative equations for slowly rotating perfect fluid balls of Petrov type D, characterizing their properties and matching conditions to exterior vacuum solutions, including asymptotically flat cases.

Contribution

It provides a detailed numerical analysis of Petrov type D rotating fluid balls, identifying parameter spaces for matching to exterior vacuum solutions, including asymptotically flat cases.

Findings

All such fluid balls can be matched to a stationary axisymmetric vacuum exterior.

A five-parameter family of solutions is characterized, with a four-parameter subspace matching asymptotically flat exteriors.

Physical properties like equations of state and speeds of sound are determined for various solutions.

Abstract

The second order perturbative field equations for slowly and rigidly rotating perfect fluid balls of Petrov type D are solved numerically. It is found that all the slowly and rigidly rotating perfect fluid balls up to second order, irrespective of Petrov type, may be matched to a possibly non-asymptotically flat stationary axisymmetric vacuum exterior. The Petrov type D interior solutions are characterized by five integration constants, corresponding to density and pressure of the zeroth order configuration, the magnitude of the vorticity, one more second order constant and an independent spherically symmetric second order small perturbation of the central pressure. A four-dimensional subspace of this five-dimensional parameter space is identified for which the solutions can be matched to an asymptotically flat exterior vacuum region. Hence these solutions are completely determined by the spherical configuration and the magnitude of the vorticity. The physical properties like equations of state, shapes and speeds of sound are determined for a number of solutions.