Two-dimensional Lifshitz-like AdS black holes in F(R) gravity

Two-dimensional (2D) Lifshitz-like black holes in special F(R) gravity cases are extracted. We indicate an essential singularity at r = 0, covered by an event horizon. Then, conserved and thermodynamic quantities, such as temperature, mass, entropy, and the heat capacity of 2D Lifshitz-like black holes in F(R) gravity, are evaluated. Our analysis shows that 2D Lifshitz-like black hole solutions can be physical solutions, provided that the cosmological constant is negative (Λ < 0). Indeed, there is a phase transition between stable and unstable cases by increasing the radius of AdS black holes. In other words, the 2D Lifshitz-like AdS black holes with large radii are physical and enjoy thermal stability. The obtained 2D Lifshitz-like AdS-black holes in F(R) gravity turn into the well-known 2D Schwarzschild AdS-black holes when the Lifshitz-like parameter is zero (s = 0). Moreover, correspondence between these black hole solutions and the 2D rotating black hole solutions is found by adjusting the Lifshitz-like parameter.