Writing the Euler-Lagrange equation for an action functional parameterized with respect to proper time, then multiplying by the inverse metric tensor, produces an equation named for these entities.
A phenomenon named for these entities occurs under conditions given by the Ehlers-Geroch (AY-lerz geh-ROKE) theorem in the limit of small size and mass. The divergence of a congruence of these entities becomes in nite at a  nite value of the a  ne parameter under appropriate energy conditions, according to the focusing theorem. Cotangent bundles are split into level sets of constant energy by the namesake  low of these entities. The Penrose-Hawking theorems state that spacelike and timelike singularities possess their namesake incompleteness. Writing the Euler-Lagrange equation for an action functional parameterized with respect to proper time, then multiplying by the inverse metric tensor, produces an equation named for these entities. For 10 points, name these paths that are traced out by a particle in free fall in general relativity and generalize the concept of a straight line to curved space.
A phenomenon named for these entities occurs under conditions given by the Ehlers-Geroch (AY-lerz geh-ROKE) theorem in the limit of small size and mass.
geodesics [or geodesic motion; or geodesic congruence; or geodesic  low; or geodesic incompleteness; or geodesic equation; prompt on paths or trajectories or world lines; anti-prompt on light rays]