Gaussian curvature at the light ring inherits the swallowtail multivaluedness of free energy in first-order black hole phase transitions, following directly from K = -λ².
Phase transition and Quasinormal modes for Charged black holes in 4D Einstein-Gauss-Bonnet gravity
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In this paper, we study the quasinormal modes(QNMs) of massless scalar perturbations to probe the Van der Waals like small and large black holes(SBH/LBH) phase transition of (charged) AdS black holes in the 4-dimensional Einstein Gauss-Bonnet gravity. We find that the signature of this SBH/LBH phase transition in the isobaric process can be detected since the slopes of the QNMs frequencies change drastically different in small and large black holes near the critical point. The obtained results further support that the QNMs can be a dynamic probe of the thermodynamic properties in black holes.
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Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions
Gaussian curvature at the light ring inherits the swallowtail multivaluedness of free energy in first-order black hole phase transitions, following directly from K = -λ².