Abstract
In this paper, we study gauged solutions associated to a massive vector field representing a spin-one condensate, namely the Proca field. We focus on regular spherically-symmetric solutions which we construct either using a self-interaction potential or general relativity in order to glue the solutions together. We start generating non-gravitating solutions, so-called, Proca Q-balls and charged Proca Q-balls. Then, we turn-on backreaction on the metric, allowing gravity to hold together the Proca condensate, to study the so-called Proca stars, charged Proca stars, Proca Q-stars and charged Proca Q-stars.
Highlights
Boson stars are gravitationally bounded macroscopic states made up of bosons
For our solutions we find ηmax = 0.30 (PS), 0.32 (IPS), 0.24 (CPS), 0.23 (CIPS) which are less than the Schwarzschild black hole value η = 1
We have studied a broad class of spherically symmetric regular solutions involving a complex massive vector
Summary
Boson stars are gravitationally bounded macroscopic states made up of bosons. Firstly introduced in [7, 8] as spherically symmetric solutions of the Einstein-Klein-Gordon equations, they remain being objects of study until present. An important family of classical objects was introduced in [1], where regular solutions for the non-gravitating Klein-Gordon equation of motion were found, known as Q-balls These objects rely on the existence of a conserved charge and can be obtained through the minimization of their corresponding free energy. New models of boson stars and Q-balls where presented in [6, 21] In these works, a vector field representing a spin-one condensate is studied, namely the Proca field. The paper organizes as follows: in Section II we present our general model, in Section III we study non-gravitating solutions, i.e. Proca Q-balls and charged Proca Q-balls and, in Section IV, we turn-on backreaction on the metric, allowing gravity to glue together the Proca condensate, giving rise to solutions named: Proca stars, charged Proca stars, Proca Q-stars and charged Proca Q-stars.
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