Lyapunov Exponents and Phase Structure of Lifshitz and Hyperscaling Violating Black Holes

We study the phase structure of hyperscaling violating black holes usingLyapunov exponents. For describing hyperscaling violating system, we chose aparticular gravity model constructed from generalized Einstein-Maxwell-Dilatonaction which includes the Lifshitz cases in appropriate limit. We study therelationship between Lyapunov exponents and black hole phase transitionsconsidering both the timelike and null geodesics. We observe that, the blackhole phase transiton properties are reflected in Lyapunov exponent where itsmultiple branches correspond to the distinct phases of the black hole. Thediscontinuos change of the Lyapunov exponent during the phase transition serveas an order parameter with critical exponent $1/2$ near the critical point. Ournumerical study reveals that the correlation between the Lyapunov exponent andblack hole thermodynamic properties can be generalised beyond the AdSspacetime. We find that it is independent of the hyperscaling violationparameter as well as the Lifshitz exponent.