For 4D R-charged black holes, the Lyapunov exponent of unstable circular orbits tracks black hole phase transitions, and its discontinuity near the critical point shows a universal critical exponent of 1/2.
Chaotic Motion around a Black Hole under Minimal Length Effects
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abstract
We use the Melnikov method to identify chaotic behavior in geodesic motion perturbed by the minimal length effects around a Schwarzschild black hole. Unlike the integrable unperturbed geodesic motion, our results show that the perturbed homoclinic orbit, which is a geodesic joining the unstable circular orbit to itself, becomes chaotic in the sense that Smale horseshoes chaotic structure is present in phase space.
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Probing Thermodynamic Phase Transitions of 4D R-Charged Black Holes via Lyapunov Exponent
For 4D R-charged black holes, the Lyapunov exponent of unstable circular orbits tracks black hole phase transitions, and its discontinuity near the critical point shows a universal critical exponent of 1/2.