The Schwarzschild metric is a solution of the vacuum Einstein equations for any value of the mass, which can be positive or negative. The negative mass solution has a naked singularity, there is no event horizon. It was shown [1–3] how to fill in a “negative mass star” so that the singularity is smoothed out, and the energy-momentum satisfies the dominant energy condition and can even gives rise to a dynamically stable configuration. However, some puzzles persist. Firstly, the exchange of a spin two graviton normally provides an attractive force between sources, while a simple calculation of the geodesic motion in the presence of a negative mass star shows repulsion. Secondly, how does a gas of negative mass particles behave thermally? If the energy is negative, the partition function makes no sense, it certainly does not converge. Should the temperature also be taken negative? The solution of these puzzles is still at large.