2006/06/21 by Brent Preston, Eric Poisson · 13 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Classical mechanics #Coordinate system #Coordinate time #Cosmology and Gravitation Theories #General relativity #Geodesic #Geodesics in general relativity #Geometry #Light cone #Mathematical physics #Mathematics #Physics #Proper time #Quantum mechanics #Relativity and Gravitational Theory #Spacetime #World line #gr-qc
paper · pdf · doi:10.1103/physrevd.74.064009
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 74(6) (American Physical Society) · 11 pages, 1 figure
arxiv created 2006/06/21 · openalex publication_date 2006/09/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Continuing work initiated in an earlier publication [Phys. Rev. D 69, 084007 (2004)], we construct a system of light-cone coordinates based at a geodesic world line of an arbitrary curved spacetime. The construction involves (i) an advanced-time or a retarded-time coordinate that labels past or future light cones centered on the world line, (ii) a radial coordinate that is an affine parameter on the null generators of these light cones, and (iii) angular coordinates that are constant on each generator. The spacetime metric is calculated in the light-cone coordinates, and it is expressed as an expansion in powers of the radial coordinate in terms of the irreducible components of the Riemann tensor evaluated on the world line. The formalism is illustrated in two simple applications, the first involving a comoving world line of a spatially flat cosmology, the other featuring an observer placed on the axis of symmetry of Melvin's magnetic universe.