Super-extremal black holes in the quasitopological electromagnetic field theory

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 [g₀₀(r)]_r=rH=[dg₀₀(r)/dr]_r=rH=[d²g₀₀(r)/dr²]_ r=rH=[d³g₀₀(r)/dr³]_r=rH=0, where g₀₀(r) is the $tt$-component of the curved line element and rH 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/rH=23(2γ+1), where γ≡₂F₁(1/4,1;5/4;-3).