The authors have extended here the isolated horizon framework to include non-minimally coupled scalar fields. It is found from the analysis, which is based on the Killing horizon, that entropy is no longer given just by (a quarter of) the horizon area but it also depends directly upon the scalar field itself.
Specifically, a scalar field \(\varphi\) coupled to gravity through an action \(S[g_{ab},\varphi]\) involving the scalar curvature of metric \(g_{ab}\) and the potential \(V\) for the field, is dealt with. The standard entropy is recovered. Non-minimally coupled fields in the first-order formalism, boundary conditions and action principle, phase space and the first law and the discussions form the section headings. Various related theories are also referred to for useful comparisons.