general relativity - Negative mass of sound waves?

I have just discovered multitudes of pop science articles promoting a recent arxiv paper, "The mass of sound"[https://arxiv.org/abs/1807.08771 ], which claims that sound waves have negative gravitational mass. Is this a legitimate result? What is the essential argument?

I would normally just read the paper myself, but I am too sick to do so, and thought that an independent assessment by actual physicists might be a public service, given the press coverage.