Gravitational constant as a conserved charge in black hole thermodynamics

Recent work has demonstrated that coupling constants in a given action can be promoted to the role of conserved charges. This is achieved by introducing pairs of field variables constructed from combinations of scalar and gauge fields. This framework naturally suggests that the gravitational constant itself can be interpreted as a conserved charge, arising from an associated gauge symmetry. In a modified four-dimensional Einstein–Hilbert action, we explicitly show that the gravitational constant, in addition to the mass and the cosmological constant, emerges as a conserved charge. Our derivation, which employs the quasi-local off-shell ADT formalism, yields a result that is fully consistent with the extended thermodynamic first law and the Smarr formula.