Bardeen-Dirac stars in Anti-de Sitter spacetime

In this paper, we construct a static spherical symmetric Bardeen-Dirac stars (BDSs) in the four-dimensional Anti-de Sitter (AdS) spacetime, which consists of the electromagnetic field and Dirac field coupled to gravity. We investigate the ADM mass, No ether charge and light rings of BDSs in AdS spacetime. In asymptotically Minkowski spacetime, the maximum frequency of BDSs is one. However, we observe that the maximum frequency of BDSs increases as the cosmological constant decreases in AdS spacetime. Additionally, BDSs can exhibit extreme behavior at low frequencies, refer to as Frozen Bardeen-Dirac stars (FBDSs) in AdS spacetime. FBDSs have a critical event horizon, where the metric function g tt is very close to zero. The matter is entirely encapsulated by this critical horizon, highly concentrated within it. When the magnetic charge is fixed, the FBDSs gradually disappear as the cosmological constant decreases.