Stars creating a gravitational repulsion

TL;DR

This paper explores theoretical models of stars with negative mass density that generate gravitational repulsion, balancing forces through unconventional pressure and density distributions within the framework of General Relativity.

Contribution

It introduces novel star models with negative mass density creating gravitational repulsion, a concept not previously modeled in standard astrophysics.

Findings

Stars with negative mass density can produce gravitational repulsion.

Equilibrium is maintained by a balance between negative mass gravity and pressure gradients.

Multiple models with different equations of state are constructed.

Abstract

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.