
A nearly conserved quantity associated with the scalar field in Horndeski gravity.In Horndeski gravity, the most general scalar-tensor theory with second-order field equations, the scalar charge is a quantity that measures how strongly a body couples to the scalar field. Unlike electric charge, which is exactly conserved, the scalar charge is only approximately conserved — it can change slowly over time or in strong gravitational fields. This near-conservation is crucial because it determines how objects move and radiate in modified gravity theories.
The concept emerged from studies of scalar-tensor theories in the 1970s, particularly through the work of Damour and Esposito-Farèse on tensor-multi-scalar theories, and was later extended to Horndeski gravity.
The scalar charge arises from the coupling between matter and the scalar field in the action. In the weak-field limit, it acts like a 'fifth force' charge, dictating the strength of the scalar-mediated interaction between masses. Because the scalar field can vary in space and time, the charge is not strictly constant; its evolution is governed by the field equations and the body's internal structure.
It is used to test general relativity with gravitational-wave observations, as the presence of scalar charge would cause binary systems to emit scalar radiation and lose orbital energy faster than predicted.
In some Horndeski models, the scalar charge can be 'screened' in dense environments, making the fifth force invisible in the Solar System but potentially strong in low-density cosmic voids.








