Stars creating a gravitational repulsion

In the framework of the theory of general relativity, models of stars with an unusual equation of state $\ensuremath{\rho}{c}^{2}<0$, $P>0$, where $\ensuremath{\rho}$ is the mass density and $P$ is the pressure, are constructed. These objects create outside themselves the forces of gravitational repulsion. The equilibrium of such stars is ensured by a nonstandard balance of forces. Negative mass density, acting gravitationally on itself, creates an acceleration of the negative mass, directed from the center. Therefore, in the absence of pressure, such an object tends to expand. At the same time, the positive pressure, which falls just like in ordinary stars from the center to the surface, creates a force directed from the center. This force acts on the negative mass density, which causes acceleration directed opposite of the acting force, that is, to the center of the star. This acceleration balances the gravitational repulsion produced by the negative mass. Thus, in our models, gravity and pressure change roles: the negative mass tends to create a gravitational repulsion, while the gradient of the pressure acting on the negative mass tends to compress the star. In this paper, we construct several models of such a star with various equations of state.