In
general relativity, a
geodesic that is
perpendicular to itself; that is, its
inner product with itself is
zero, hence the term
null.
Obviously, null geodesics are
non-existant in
Euclidean geometry, but they do
exist in
physical four-dimensional geometries, that is, ones with
signature +/- 2.
Photons and other
null particles follow null geodesics.
Yet another bizarre and difficult-to-visualise concept in GR.