Super-extremal black holes in the quasitopological electromagnetic field theory

Abstract

Abstract It has recently been proved that a simple generalization of electromagnetism, referred to as quasitopological electromagnetic field theory, is characterized by the presence of dyonic black-hole solutions of the Einstein field equations that, in certain parameter regions, are characterized by four horizons. In the present compact paper we reveal the existence, in this non-linear electrodynamic field theory, of super-extremal black-hole spacetimes that are characterized by the four degenerate functional relations $$[g_{00}(r)]_{r=r_{\text {H}}}=[dg_{00}(r)/dr]_{r=r_{\text {H}}}=[d^2g_{00}(r)/dr^2]_ {r=r_{\text {H}}}=[d^3g_{00}(r)/dr^3]_{r=r_{\text {H}}}=0$$ [ g 00 ( r ) ] r = r H = [ d g 00 ( r ) / d r ] r = r H = [ d 2 g 00 ( r ) / d r 2 ] r = r H = [ d 3 g 00 ( r ) / d r 3 ] r = r H = 0 , where $$g_{00}(r)$$ g 00 ( r ) is the tt-component of the curved line element and $$r_{\text {H}}$$ r H is the black-hole horizon radius. In particular, using analytical techniques we prove that the quartically degenerate super-extremal black holes are characterized by the universal (parameter-independent) dimensionless compactness parameter $$M/r_{\text {H}}={2\over 3}(2\gamma +1)$$ M / r H = 2 3 ( 2 γ + 1 ) , where $$\gamma \equiv {_2F_1}(1/4,1;5/4;-3)$$ γ ≡ 2 F 1 ( 1 / 4 , 1 ; 5 / 4 ; - 3 ) .