# Metric for a single photon

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## Main Question or Discussion Point

What is a good simple metric for a single photon?

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Orodruin
Staff Emeritus
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What do you mean by "metric for a photon"? The metric is a property of spacetime, not of its contents.

Sorry, I'm prone to speaking imprecisely, and I'm still learning the correct terminology in GR. I think I'm looking for the metric perturbation caused by the existence of a single photon. Ideally I'd like christoffel symbols, or a line element, or something equivalent which describes the gravity around a photon in otherwise empty flat space.

If there's a better term for the relation between the things causing curvature and the shape of space, it would also be handy to know that.

pervect
Staff Emeritus
A photon isn't classical, and GR is a classical theory. But you might be looking for the Aichelburg-Sexl ultraboost. But I might have misunderstood your question. I think the wiki page also talks about how the AS ultraboost can be derived as the limit of the metric of a gaussian pulse.

Typically these solutions are actually for a null dust - which may not have exactly the same stress-energy tensor as a pulse of light, but has many of the same features.

A null dust has the formal definition of $T_{ab} \propto k^a k^b$ where k is a null vector. It's informally described as the stress energy tensor (or the associated space-time geometry) associated with some sort of radiation moving at the speed of light.

Interesting. I'll read up on that. Thank you.

PAllen