Gravity without mass: energy - momentum as the source of spacetime curvature

Gravity Without Mass: Energy-Momentum as the Source of Space-Time Curvature A Discussion Paper C. J. Tully, Independent Researcher, Engineer, Australia [email protected] Prepared for academic discussion November 2026 Abstract Newtonian gravity identifies rest mass as the source of the gravitational field. General relativity replaces this with the stress-energy tensor, which incorporates energy density, momentum flux, pressure, and stress. Consequently, systems possessing zero rest mass—most notably electromagnetic radiation and gravitational waves—can and do curve spacetime. This paper examines the gravitational field of photons and laser beams, reviews exact and approximate solutions showing that light generates curvature, and discusses the energy carried by gravitational waves as confirmed by binary pulsar observations and direct detection. The non-localisability of gravitational energy is addressed as a conceptual subtlety rather than a barrier to the conclusion that gravity does not require rest mass. The discussion remains within the framework of classical general relativity while noting open questions at the interface with quantum gravity. Keywords: general relativity; stress-energy tensor; gravitational field of light; gravitational waves; massless fields; energy-momentum 1. Introduction The intuitive association of gravity with mass is deeply rooted in Newtonian physics, where the force between two bodies is proportional to the product of their masses. Einstein’s general relativity fundamentally revises this picture. The Einstein field equations relate the Einstein tensor, describing spacetime curvature, to the stress-energy tensor: Gμν = (8πG/c⁴) Tμν Here Tμν encodes the density and flux of energy and momentum. Rest-mass density contributes to T00 in the rest frame, but it is neither necessary nor sufficient for a non-vanishing stress-energy tensor. Electromagnetic fields, for example, possess a non-zero stress-energy tensor even when composed entirely of massless photons. Gravitational waves, solutions of the vacuum equations, carry energy and momentum that can be extracted and measured. This paper develops the thesis that gravity can exist without rest mass. Section 2 reviews the stress-energy tensor of the electromagnetic field. Section 3 surveys calculations of the gravitational field produced by light, from the classic work of Tolman, Ehrenfest and Podolsky to modern treatments of laser beams. Section 4 examines the energy content of gravitational waves and its observational confirmation. Section 5 addresses conceptual issues surrounding the definition of mass and gravitational energy. The conclusion summarises the implications for the understanding of gravity.