Comment on "The complete Schwarzschild interior and exterior solution in the harmonic coordinate system" [J. Math. Phys. 39, 6086 (1998)]

TL;DR

This paper critiques Liu's claim about the necessity of an integration constant in Schwarzschild solutions in harmonic coordinates, clarifying that matching conditions do not support his conclusion.

Contribution

It refutes Liu's assertion by demonstrating that the matching conditions do not imply the need for an additional integration constant in the Schwarzschild solution.

Findings

Matching conditions do not require an integration constant.

Liu's conclusion is not supported by the matching analysis.

Clarification of the Schwarzschild solution in harmonic coordinates.

Abstract

In a recent paper Liu considered the complete Schwarzschild interior and exterior solution in harmonic coordinates. There he argued about the necessity to keep an integration constant, in contrast with previous treatments. The purpose of this comment is to show that the above conclusion cannot be traced from the matching conditions between the vacuum exterior and the uniform density interior perfect fluid, as claimed.