Vector Field Dynamics: Field Equations and Energy Tensor

Abstract

Relativistic field theory for a vector field on a curved space-time is considered assuming that the Lagrangian field density is quadratic and contains field derivatives of first order at most. By applying standard variational calculus, the general Euler-Lagrange equations for the field are derived and the existence of a conserved current is achieved. The field equations are also analyzed from an eikonal-like point of view. The Hilbert energy-momentum tensor of the field is also derived and the influence of each one of the irreducible pieces appearing in the Lagrangian is studied. Particular values of the free parameters allow to retrieve known results.

Author version of the published paper

References in corpus (17)

• The Confrontation between General Relativity and Experiment
• Generalization of the Proca Action
• A systematic approach to generalisations of General Relativity and their cosmological implications
• Cosmic Acceleration from Abelian Symmetry Breaking
• Derivative self-interactions for a massive vector field
• Dark energy as a massive vector field
• Screening Vector Field Modifications of General Relativity
• Almost-stationary motions and gauge conditions in General Relativity
• Cosmological perturbations in extended electromagnetism. General gauge invariant approach
• Cosmology in a certain vector-tensor theory of gravitation
• Almost-Killing equation: Stability, hyperbolicity, and black hole Gauss law
• More about a successful vector-tensor theory of gravitation
• On the viability of a certain vector-tensor theory of gravitation
• On the horizons in a viable vector-tensor theory of gravitation
• Spherical symmetric dust collapse in a Vector-Tensor gravity
• Proposal for the origin of the cosmological constant
• Interpreting deviations between AR-VTG and GR