  In the framework of the Theory of General Relativity, models of stars with an
unusual equation of state $\rho c^2<0$, $P>0$ where $\rho$ 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 non-standard 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 the 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.
