Stringy Generalization of the First Law of Thermodynamics for Rotating BTZ Black Hole with a Cosmological Constant as State Parameter

In this paper we will show that using the cosmological constant as a new thermodynamical state variable, the differential and integral mass formulas of the first law of thermodynamics for asymptotic flat spacetimes can be extended to be used at the two horizons of the (2+1) dimensional BTZ black hole. We also extend this equations to the stringy description of the BTZ black hole, in which two new systems that resemble the right and left modes of effective string theory, are defined in terms of the inner and outer horizons.