Stability and the inverse isoperimetric inequality impose 2Λr_+^2/((d-1)(d-2)) < g^2 < -2Λr_+^2/((d-1)(d-2)) on gravity's rainbow functions, and super-entropic black holes occur exactly when f>1.
Smolin, Nucl
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Super-entropic black holes in gravity's rainbow and determining constraints on rainbow functions
Stability and the inverse isoperimetric inequality impose 2Λr_+^2/((d-1)(d-2)) < g^2 < -2Λr_+^2/((d-1)(d-2)) on gravity's rainbow functions, and super-entropic black holes occur exactly when f>1.