Ultracompact vector stars

We analytically investigate a new family of horizonless compact objects in vector-tensor theories of gravity, called ultracompact vector stars. They are sourced by a vector condensate, induced by a non-minimal coupling with gravity. They can be as compact as black holes, thanks to their internal anisotropic stress. In the spherically symmetric case their interior resembles an isothermal sphere, with a singularity that can be resolved by tuning the available integration constants. The star interior smoothly matches to an exterior Schwarzschild geometry, with no need of extra energy-momentum tensor at the star surface. We analyse the behaviour of geodesics within the star interior, where stable circular orbits are allowed, as well as trajectories crossing in both ways the star surface. We analytically study stationary deformations of the vector field and of the geometry, which break spherical symmetry, and whose features depend on the vector-tensor theory we consider. We introduce and determine the vector magnetic susceptibility as a probe of the star properties, and we analyze how the rate of rotation of the star is affected by the vector charges.