[Paper Review] Gravitational Poynting Vector and Gravitational Larmor Theorem in Rotating Bodies with Angular Acceleration

Clovis Jacinto de Matos, Martin Tajmar|ArXiv.org|Jul 4, 2001

Relativity and Gravitational Theory9 references3 citations

TL;DR

This paper introduces a gravitational Poynting vector and extends the gravitational Larmor theorem to explain how rotating bodies with angular acceleration acquire rotational kinetic energy via gravitational energy transfer from external mechanical forces. The authors derive a formalism showing that gravitational energy flux, analogous to electromagnetic Poynting flux, accounts for energy input during rotational acceleration, offering a novel mechanism for rotational energy gain in massive bodies under non-inertial conditions.

ABSTRACT

The gravitational Poynting vector provides a mechanism for the transfer of gravitational energy to a system of falling objects. In the following we will show that the gravitational poynting vector together with the gravitational Larmor theorem also provides a mechanism to explain how massive bodies acquire rotational kinetic energy when external mechanical forces are applied on them.

Motivation & Objective

• To develop a gravitational analog of the electromagnetic Poynting vector for energy flux in gravitational systems.
• To extend the Larmor theorem to rotating bodies experiencing angular acceleration, linking mechanical work to rotational energy gain.
• To explain how external forces can transfer gravitational energy to induce rotational kinetic energy in massive bodies.
• To provide a theoretical framework for energy transfer in rotating systems beyond standard Newtonian mechanics.
• To explore the implications of gravitational energy flux in non-inertial reference frames with rotational dynamics.

Proposed method

• Formalism is developed using general relativity to define a gravitational Poynting vector analogous to the electromagnetic Poynting vector.
• The gravitational Poynting vector is derived from the energy-momentum pseudotensor in linearized gravity, representing gravitational energy flux.
• The gravitational Larmor theorem is extended to include angular acceleration, linking mechanical work to rotational energy gain.
• The authors analyze energy transfer in rotating bodies under external torque, using the gravitational Poynting vector to quantify energy inflow.
• The formalism is applied to systems with non-zero angular acceleration, showing consistent energy conservation via gravitational flux.
• Theoretical derivations are based on the Einstein-Infeld-Hoffmann method and linearized gravity approximations.

Experimental results

Research questions

• RQ1 How can gravitational energy flux be defined analogously to the electromagnetic Poynting vector in rotating systems?
• RQ2 What is the role of the gravitational Poynting vector in transferring energy to rotating bodies under angular acceleration?
• RQ3 How does the extended gravitational Larmor theorem account for rotational kinetic energy gain in massive bodies?
• RQ4 Can mechanical work applied to a rotating body be fully accounted for by gravitational energy flux in general relativity?
• RQ5 What is the nature of energy transfer in rotating systems when angular acceleration is present?

Key findings

• The gravitational Poynting vector provides a mechanism for energy transfer to rotating bodies, analogous to electromagnetic energy flux.
• The extended gravitational Larmor theorem explains how rotational kinetic energy increases during angular acceleration via gravitational energy input.
• Energy transfer occurs through the gravitational Poynting vector, which quantifies the flux of gravitational energy in rotating systems.
• The formalism demonstrates consistency with energy conservation in rotating systems under external mechanical forces.
• The results suggest that rotational energy gain in massive bodies can be attributed to gravitational energy flux rather than purely mechanical work.
• The framework applies to systems with non-zero angular acceleration, offering a new perspective on energy transfer in rotating massive bodies.