Two extremal black holes with secondary scalar hair are identified in a two-U(1) Einstein-Maxwell-scalar theory using scalarization and entropy function methods, implying primary hair is difficult to obtain.
Stationary black holes and attractor mechanism
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abstract
We investigate the symmetries of the near horizon geometry of extremal stationary black holes in four dimensional Einstein gravity coupled to abelian gauge fields and neutral scalars. Careful consideration of the equations of motion and the boundary conditions at the horizon imply that the near horizon geometry has $SO(2,1)\times U(1)$ isometry. This complements the rotating attractors proposal of hep-th/0606244 that had assumed the presence of this isometry. The extremal solutions are classified into two families differentiated by the presence or absence of an ergo-region. We also comment on the attractor mechanism of both branches.
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gr-qc 1years
2026 1verdicts
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Scalarized extremal black holes in the Einstein-Maxwell-scalar theory with two U(1) fields
Two extremal black holes with secondary scalar hair are identified in a two-U(1) Einstein-Maxwell-scalar theory using scalarization and entropy function methods, implying primary hair is difficult to obtain.