Speaker
Giampiero Esposito
Description
We prove that the equation for the amplitude function for the parametrix of the scalar wave equation can be obtained by covariant differentiation of a first-order non-linear equation.
The construction of such a first-order non-linear equation relies upon a pair of auxiliary 1-forms "psi,rho".
The 1-form "psi" satisfies the divergenceless condition div(psi)=0, whereas the 1-form "rho" fulfills the non-linear equation div(rho)+<rho,rho>=0.
The auxiliary 1-forms "psi,rho" are evaluated explicitly in Kasner space-time, hence, amplitude and phase function in the parametrix are eventually obtained.
Thus, our novel method can be used with profit in physical applications.
