Non-extremal, ${\alpha }^{\mathrm{\prime }}$-corrected black holes in 5-dimensional Heterotic Superstring Theory

We compute the first-order ${\alpha }^{\mathrm{\prime }}$ corrections of the non-extremal Strominger-Vafa black hole and its non-supersymmetric counterparts in the framework of the Bergshoeff-de Roo formulation of the heterotic superstring effective action. The solution passes several tests: its extremal limit is the one found in an earlier publication and the effect of a T duality transformation on it is another solution of the same form with T dual charges. We compute the Hawking temperature and Wald entropy showing that they are related by the first law and Smarr formula. On the other hand, these two contain additional terms in which the dimensionful parameter ${\alpha }^{\mathrm{\prime }}$ plays the role of thermodynamical variable.