Speaker
Description
The Israel-Carter theorem (famously known as ``no-hair theorem'') puts a restriction on the existence of parameters other than mass, electric charge, and angular momentum of a black hole. On the other hand, Bekenstein showed the possibility of existence of scalar hair by considering a massless conformal scalar field non-minimally coupled to gravity. The Einstein-Maxwell-scalar solution for a static spherically symmetric metric was found to be unbounded at the horizon. Bekenstein's study established scalar charges, like other parameters allowed by the no-hair theorem, to be also admissible in black hole solutions. There also exists a new family of Einstein-Maxwell-scalar field models where the scalar field is non-minimally coupled with the Maxwell field.
In the present work, we consider a novel Einstein-Maxwell-scalar model where an electrically charged scalar field is gauge-coupled with the Maxwell field, generating interaction of the charge $e$ with the electromagnetic field, described by the action
$$ S=\int d^{4}x\sqrt{-g}\left[\frac{R}{16\pi G}-\left(D_{\mu}\phi\right)^{*}D^{\mu}\phi-\mu^{2}\phi^{*}\phi-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}\right] $$ where $D_{\mu}=\partial_{\mu}+ieA_{\mu}$ is the covariant derivative, $\mu$ is the mass of the scalar field, and $F_{\mu\nu}=\partial_\mu A_\nu-\partial_\nu A_\mu$, with $A_\mu$ the vector potential.
Detailed solution of this Einstein-Maxwell-scalar model in the background of a static spherically symmetric Reissner-Nordstr\"om spacetime yields a charged hairy black hole solution. A stability analysis shows that this charged hair is stable against time-dependent perturbations.
| shafeeque.mhd@gmail.com | |
| Affiliation | Department of Physics, Indian Institute of Technology Guwahati, Guwahati 781 039, India |
