Mathematical analysis of some couplings for the Eddington-inspired-Born-Infeld theory of bi-gravity in Bondi coordinates. (27th October 2021) - Tadmon, Calvin; Djiodjo-Seugmo, Guichard
Abstract: In the Eddington-inspired-Born-Infeld theory, we consider a metric tensor g, an auxiliary tensor q, a scalar field and an electromagnetic field in Bondi coordinates. Using 'the null tetrad' associated with each metric, we derive a system of nonlinear partial differential equations and, after some reduction process, we obtain a second order ordinary differential equation coupled to a first order partial differential equations with strong nonlinearities. Using both the solution-tube concept and the nonlinear analysis tools such as the fixed point theorem, we prove an existence and uniqueness result for the nonlinear system obtained.