Extremal Hairy Black Holes

Understand

We consider a gravitating system consisting of a scalar field minimally coupled to gravity with a self-interacting potential and an U(1) electromagnetic field.

• Solving the coupled Einstein-Maxwell-scalar system we find exact hairy charged black hole solutions with the scalar field regular everywhere.
• We go to the zero temperature limit and we study the effect of the scalar field on the near horizon geometry of an extremal black hole.
• We find that except a critical value of the charge of the black hole there is also a critical value of the charge of the scalar field beyond of which the extremal black hole is destabilized.