Slowly rotating fluid balls with linear equation of state

TL;DR

This paper investigates slowly rotating perfect fluid balls with linear equations of state, demonstrating that the Petrov type D condition cannot be satisfied under these assumptions, thus constraining possible models.

Contribution

It provides a detailed analysis of the Petrov D condition for rotating fluid balls and shows its incompatibility with linear equations of state.

Findings

Petrov D condition is incompatible with linear equations of state in this context

Second-order rotation effects are analyzed for regular fluid balls

Constraints on fluid models for rotating stars are identified

Abstract

Slowly rotating perfect fluid balls with regular center and asymptotically flat exterior are considered to second order in the rotation parameter. The necessary condition for being Petrov type D is given for general perfect fluid matter. As a special case, fluids with a linear equation of state are considered. Using a power series expansion at the regular center, it is shown that the Petrov D condition is inconsistent with the linear equation of state assumption.