Energy momentum, wave velocities and characteristic shocks in Euler’s variational equations with application to the Born–Infeld theory

Abstract

We consider the Euler’s variational equations deriving from a general Lagrangian ${\mathrm{L(\partial }}_{\alpha }{q}^r{\mathrm{,q}}^s)$ . Under the assumption of convexity of energy, we write down some inequalities for the energy-momentum tensor including Hawking–Ellis energy conditions. We show that there exists the same number of positive and negative wave velocities and no velocity can change sign. Finally, we study the structure of the characteristic shocks with particular attention to the generalized Born–Infeld Lagrangian describing the electron with spin.