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

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.