Gravitational Decoupling algorithm modifies the value of the conserved charges and thermodynamics properties in Lovelock Unique Vacuum theory

Abstract: We provide an extension of the Gravitational Decoupling (algorithm) for the Lovelock theory with Unique Vacuum (LUV), which represents a simple way to solve the equations of motion. Due to the application of this algorithm, the energy of the system splits in the {\it energy of the seed solution} and the {\it energy of each quasi-LUV sector}. Under certain assumptions imposed, the total energy varies due to the contribution of energy of each quasi-LUV sector. It is provided a new solution, whose energy differs from the energy of the seed solution in a quantity that depends on the number of extra sources. The new solution has two inner horizons, which is a proper characteristic of itself. Furthermore, its thermodynamics differs from the seed solution, since our solution is always stable and does not have phase transitions. Since the first law of thermodynamics is modified by the presence of the matter fields, we provide a new version of the first law for LUV, where a local definition of the variation of energy is defined, and, where the entropy and temperature are consistent for LUV theory.