On gravitational Lagrangians in flat spacetime.
Abstract
Consideration is given to the set of all gravitational theories based on a unique variational principle with a generic Lagrangian that leads to a flat spacetime such that the theory is free of internal inconsistencies. Motion and field equations are derived from a variational principle on the model of electromagnetic action in flat spacetime, assuming that the only symmetry of the Lagrangian is that it is not an explicit function of the arc length. It is shown that the necessary and sufficient condition for the spacetime to be flat is that the particle plus interaction Lagrangians be equal to the sum of a homogeneous function of degree 1 of the absolute velocity and an arbitrary function of the constant metric tensor of flat spacetime and the particle velocity, which is not equal to the sum of a constant product of the parameters and a constant.
 Publication:

Nuovo Cimento Lettere
 Pub Date:
 August 1980
 Bibcode:
 1980NCimL..28..471C
 Keywords:

 EulerLagrange Equation;
 Gravitation Theory;
 Particle Motion;
 SpaceTime Functions;
 Variational Principles;
 Differential Equations;
 Equations Of Motion;
 Tensors;
 Physics (General);
 Gravitation Theory:SpaceTime