Maybe that's precisely why objects with negative mass do not exist on the Earth? But what stops them to exist in the void of space, between regular matter? And

Maybe that's precisely why objects with negative mass do not exist on the Earth? But what stops them to exist in the void of space, between regular matter? And it doesn't need to be actual "objects", but isolated particles or a particle gas. In relativistic physics mass is dependent on the body's energy, so negative mass implies negative energy.