Gauss-Bonnet Contributions to the Entropy of Extremal Black Holes in the Gauge-Gravity sector

Using the Sens mechanism we calculate the entropy for an $AdS_{2}times S^{d-2}$ extremal and static black hole in four dimensions, with higher derivative terms that comes from a three parameter non-minimal Einstein-Maxwell theory. The explicit results for Gauss-Bonnet in the gauge-gravity sector are shown.