Super-extremal black holes in the quasitopological electromagnetic field theory

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 [g00(r)]r=rH=[dg00(r)/dr]r=rH=[d2g00(r)/dr2]r=rH=[d3g00(r)/dr3]r=rH=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[g_{00}(r)]_{r=r_{\ ext {H}}}=[dg_{00}(r)/dr]_{r=r_{\ ext {H}}}=[d^2g_{00}(r)/dr^2]_ {r=r_{\ ext {H}}}=[d^3g_{00}(r)/dr^3]_{r=r_{\ ext {H}}}=0$$\\end{document}, where g00(r)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g_{00}(r)$$\\end{document} is the tt-component of the curved line element and rH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_{\ ext {H}}$$\\end{document} 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)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M/r_{\ ext {H}}={2\\over 3}(2\\gamma +1)$$\\end{document}, where γ≡2F1(1/4,1;5/4;-3)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma \\equiv {_2F_1}(1/4,1;5/4;-3)$$\\end{document}.