Pulse Propagation in Born-Infeld Theory, the World Volume Equivalence Principle and the Hagedorn-like Equation of State of the Chaplygin Gas

Abstract

A recently proposed world-volume equivalence principal involving the Boillat, as opposed to the Einstein, metric is examined in the context of some colliding wave solutions of the Born-Infeld equations for which two plane polarized pulses pass through one another without distortion. They suffer a delay with respect to the usual Einstein metric but not with respect to the Boillat metric. Both metrics are flat in this case, and the closed string and open string causal structures are interchanged by the Legendre transformation that is used for solving the associated Monge-Amp\`ere equation. In 1+1 dimensions the equations are known to be equivalent to the vorticity free motion of a Chaplygin gas. The latter is shown to be described by the scalar Born-Infeld equation in all dimensions and it is pointed out that the equation of state is Hagedorn-like: there is an upper bound to the pressure and temperature.