Reverse stealth construction and its thermodynamic imprints

We study a class of solutions within the context of modified gravity theories, characterized by a non-trivial field that does not generate any back-reaction on the metric. These stealth configurations are effectively defined by the stealth conditions, which correspond to a vanishing stress-energy tensor. In this work, we introduce a novel approach to constructing this class of solutions. In contrast to the standard procedure, the starting point requires satisfying the stealth conditions for a given ansatz independently of the gravitational dynamics. This approach simultaneously determines the non-trivial field and the geometries capable of supporting it as a stealth configuration. Consequently, a gravity model can accommodate a stealth field only if its vacuum solution falls within the geometries permissible under stealth conditions. By applying this reverse procedure in the non-minimal Rϕ ² coupling, we recover all previously known stealth configurations and present new solutions. Although it seems intuitive to assume that this “gravitationally undetectable” scalar field leaves no physical traces, it remarkably reveals thermodynamic imprints, as its presence screens the black hole mass and modifies the entropy according to the first law.