We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Solution of Maxwell’s equations on a de Sitter background.
- Authors
Giampiero Esposito
- Abstract
Abstract The Maxwell equations for the electromagnetic potential, supplemented by the Lorenz gauge condition, are decoupled and solved exactly in de Sitter space–time studied in static spherical coordinates. There is no source besides the background. One component of the vector field is expressed, in its radial part, through the solution of a fourth-order ordinary differential equation obeying given initial conditions. The other components of the vector field are then found by acting with lower-order differential operators on the solution of the fourth-order equation (while the transverse part is decoupled and solved exactly from the beginning). The whole four-vector potential is eventually expressed through hypergeometric functions and spherical harmonics. Its radial part is plotted for given choices of initial conditions. We have thus completely succeeded in solving the homogeneous vector wave equation for Maxwell theory in the Lorenz gauge when a de Sitter space–time is considered, which is relevant both for inflationary cosmology and gravitational wave theory. The decoupling technique and analytic formulae and plots are completely original. This is an important step towards solving exactly the tensor wave equation in de Sitter space–time, which has important applications to the theory of gravitational waves about curved backgrounds.
- Subjects
NUMERICAL solutions to Maxwell equations; ELECTROMAGNETIC fields; GAUGE field theory; VECTOR fields; DIFFERENTIAL equations; DIFFERENTIAL operators; HYPERGEOMETRIC functions; GRAVITY waves; WAVE equation
- Publication
General Relativity & Gravitation, 2010, Vol 42, Issue 1, p51
- ISSN
0001-7701
- Publication type
Article