Repulsive gravity in tension stars

In stars, pressure opposes the attractive force of gravity. In general relativity, if the pressure is negative (a tension) and $$P \lt -\frac{1}{3}\rho c^2$$ then the resulting gravity is repulsive. Such material is invoked in cosmology to give the inflation of the Universe. In tension stars this repulsive gravity is balanced by the tension. The simplest tension stars only exist in esoteric situations beyond the neck of an Einstein–Rosen bridge in Schwarzs-child space. Here we confine tension material within a massive shell of normal matter. The resulting object, while still repulsive inside, has an attractive exterior gravity and can, in principle, exist without horizons.