Negative Mass is an opposite sighn. If negative mass exist then it would voilate the laws of Universe: Energy, momentum and therefore, negative mass cannot exist. The reference content is available in Wikipedia.
Infact, negative and positive mass produces counterintuitive behaviours. The negative mass cannot exit because it breaks one of the essential assuption behind the brilliant brain Einstien's theory of general relativity in 1914.
We remember Albert Einstien for more than his disheveled hair, big eyes, and witty charm. He is genius and physicist who changed the way we see the world. His famous formula of E=mc2 revolutionized scientif thought and brought us into the nuclear age through his special theory of Relativity. He reasoned that since everything in the universe in motion. He also believed that the speed of light is the only constant by which we can measure space, time or physical mass.
If Negative mass exist, it would turn out that for negative mass there would be no event horizon and this will lead to naked singularity because when distance from the singularity is large, Physicists simply ignore it.
Negative mass appears to voilate the energy.