Nordtvedt effect in rotational motion

TL;DR

This paper investigates the Nordtvedt effect in the rotational motion of celestial bodies within the PPN formalism, revealing a new torque term linked to violations of the Strong Equivalence Principle.

Contribution

It introduces a local PPN reference system for extended bodies and derives rotational equations showing a Nordtvedt-like torque term due to alternative gravity theories.

Findings

Identifies a Nordtvedt-like torque in rotational motion.

Shows the torque depends on PPN parameters and energy distribution.

Highlights the violation of the Strong Equivalence Principle in rotational dynamics.

Abstract

Rotational motion of extended celestial bodies is discussed in the framework of the Parametrized Post-Newtonian (PPN) formalism with the two parameters $\gamma$ and $\beta$. A local PPN reference system of a massive extended body being a member of a system of N massive extended bodies is constructed. In the local PPN reference system the external gravitational field manifests itself only in the form of tidal potentials. Rotational equations of motion, which are then derived in the local reference system, reveal a special term in the torque analogous to the Nordtvedt effect in the translational equations of motion: it is proportional to $4\beta-\gamma-3$, to the acceleration of the body relative to the global PPN reference system and to some quantity characterizing the distribution of inertial gravitational energy within the body. This term is a direct consequence of the violation of the Strong Equivalence Principle in alternative theories of gravitation.