Phase Transitions and Chaos Bound in Horava Lifshitz Black Holes using Lyapunov Exponents

We probe the thermodynamic phase structure of four dimensional Horava Lifshitz black holes by Lyapunov exponent analysis. For both massless and massive test particles, the Lyapunov exponent exhibits a multivalued dependence on temperature in regimes with a first-order phase transition, with distinct branches corresponding to small, intermediate, and large black hole phases, and this behaviour disappears at the critical point. The discontinuity in the Lyapunov exponent acts as an effective order parameter with critical exponent $\delta =1\mathrm{/}2$, consistent with mean-field universality. We also find that the chaos bound is generically violated below a threshold horizon radius, with the violation occurring within the thermodynamically stable phase and persisting even in the absence of a phase transition. These results establish the robustness and universality of Lyapunov exponents as probes of black hole thermodynamics in alternative theories of gravity.