Reeb–Wolf improved Landauer principle for hairy black holes via gravitational decoupling

Abstract

We investigated the thermodynamic and quantum-information cost of irreversible information erasure at the event horizon of hairy black holes generated through gravitational decoupling via extended geometric deformation. Starting from the Schwarzschild black-hole seed solution, we considered two families of hairy geometries satisfying the strong and dominant energy conditions. Landauer’s principle was used to relate the minimum energy required to erase one bit of information to the Hawking temperature of the deformed horizon. We derived the corresponding horizon radii, Hawking temperature, Bekenstein–Hawking entropy, and Landauer cost as functions of the gravitational decoupling parameter, the hair length scale, and the effective charge associated with the additional gravitational sector. For the parameter ranges analysed, our results show that gravitational hair tends to reduce the Hawking temperature and the minimum Landauer erasure cost, while simultaneously increasing the horizon area and the Bekenstein–Hawking entropy. The Reeb–Wolf finite-size correction provides an additional positive contribution to the erasure cost, but remains subdominant due to the large effective dimension of the horizon reservoir. We further separated the Reeb–Wolf correction into mutual-information and relative entropy contributions, showing that the former is governed by the area-spacing parameter, whereas the latter is controlled by the actual energy gap between neighbouring horizon levels. Furthermore, the Landauer spectrum obtained by quantising the area decreases as the quantum number associated with the horizon increases, although this variation does not occur in the same way in the SEC and DEC branches.