Thermodynamics of Black Holes in Presence of String Instantons

The coupling of a Nambu-Goto string to gravity allows for Schwarzschild black holes whose entropy to area relation is $S=(A/4)(1-4\mu)$, where $\mu$ is the string tension. The departure from $A/4$ universality results from a string instanton which leads to a materialisation of the horizon at the quantum level.