Greybody factor and sparsity of Hawking radiation from a charged spherical black hole with scalar hair

Abstract

The ‘no-hair’ conjecture claims that for a spherically symmetric black hole, only the information regarding the mass and charge of the black hole is available to an external observer. However, there are numerous counterexamples to the ‘no-hair’ conjecture. In this work, we consider a particular counter-example to the ‘no-hair’ conjecture in (3+1) dimensions, namely, a static spherically symmetric charged black hole with a scalar hair. We provide semi-analytic bounds on the greybody factors and study the sparsity of Hawking radiation of mass-less uncharged scalar fields. Our results show that the scalar and electric charges contribute oppositely to the greybody factor and the sparsity of the Hawking radiation cascade. Also, the greybody factor decreases and the Hawking emission spectra become more sparse with the reduction in the black hole (ADM) mass.