The Gravitational Weight of Light: Teaching Radiation-sourced Spacetime Curvature through Quantitative Corrections to Lensing and Shapiro Delay

Authors: Snigdha Saha

Abstract

A common misconception in introductory General Relativity (GR) courses is that massless particles play no gravitational role. In fact, the Einstein field equations couple spacetime geometry to the full stress-energy tensor, which is non-zero for photons. A radiation field carries not only energy density but also pressure, and both contribute to the active gravitational mass with a factor-of-two enhancement over the naive E/c² estimate – a result with no Newtonian analogue. This article provides a self-contained, pedagogically motivated treatment of this effect, suitable for an advanced undergraduate or graduate GR course. Starting from the electromagnetic stress-energy tensor, we derive explicit correction formulae for two standard GR observables: (i) the gravitational lensing deflection angle and (ii) the Shapiro time delay, each modified by an ambient photon-energy background. We clearly identify the limits of validity of the linearised-GR approximation used. The treatment explicitly distinguishes photons as sources of curvature - the subject of this article - from the erroneous notion of photons as mediators of gravity, a conceptual confusion that recurs in student questions and merits clear pedagogical resolution.

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