New formulation of the first law of black hole thermodynamics: a stringy analogy

We consider the first laws of thermodynamics for a pair of systems made up of the two horizons of a Kerr-Newman black hole. These two systems are constructed in such a way that we only demand their “horizon areas” to be the sum and difference of that of the outer and inner horizons of their prototype. Remarkably, these two copies bear a striking resemblance to the right- and left-movers in string theory and D-brane physics. Our reformulation of the first law of black hole thermodynamics can be thought of as an analogy of thermodynamics of effective string or D-brane models.