Thermodynamics, phase transitions and Ruppeiner geometry for Einstein-dilaton Lifshitz black holes in the presence of Maxwell and Born-Infeld electrodynamics

Understand

In this paper, we first obtain the ($n+1$)-dimensional dilaton-Lifshitz black hole (BH) solutions in the presence of Born-Infeld (BI) electrodynamics.

• We find that there are two different solutions for $z=n+1$ and $z\neq n+1$ cases ($z$ is dynamical critical exponent).
• We show that the thermodynamics first law is satisfied for both cases.
• Then, we turn to study different phase transitions (PTs) for our BHs.