Charged rotating BTZ black hole and thermodynamic behavior of field equations at its horizon

In this Letter, we study different cases of the charged rotating BTZ black hole with reference to their horizons. For the existence of these cases conditions on mass, charge and angular momentum of the black hole are obtained. It is also shown that the Einstein field equations for the charged rotating BTZ black hole at the horizon can be expressed as first law of thermodynamics, dE=TdS+ΩdJ+Φdq+PrdA.