The Wahlquist metric cannot describe an isolated rotating body

TL;DR

The paper proves that the Wahlquist metric, representing a rotating perfect fluid, cannot be matched to an exterior asymptotically flat vacuum, implying it cannot model an isolated rotating body.

Contribution

It demonstrates, through a second-order angular velocity expansion, that the Wahlquist metric cannot describe an isolated rotating astrophysical object.

Findings

Matching conditions are mutually contradictory.

Wahlquist metric is a special case of rotating Whittaker space-time.

Cannot smoothly join Wahlquist interior to exterior vacuum.

Abstract

It is proven that the Wahlquist perfect fluid space-time cannot be smoothly joined to an exterior asymptotically flat vacuum region. The proof uses a power series expansion in the angular velocity, to a precision of the second order. In this approximation, the Wahlquist metric is a special case of the rotating Whittaker space-time. The exterior vacuum domain is treated in a like manner. We compute the conditions of matching at the possible boundary surface in both the interior and the vacuum domain. The conditions for matching the induced metrics and the extrinsic curvatures are mutually contradictory.