Nonexistence of Solutions to the Coupled Generalized Jang Equation/Zero Divergence System

Abstract

In [5], Bray and Khuri proposed coupling the generalized Jang equation to several different auxiliary equations. The solutions to these coupled systems would then imply the Penrose inequality. One of these involves coupling the generalized Jang equation to $\overline{div}(\varphi q)=0$, as this would guarantee the non-negativity of the scalar curvature in the Jang surface. This coupled system of equations has not received much attention, and we investigate it's solvability. We prove that there exists a spherically symmetric initial data set for the Einstein equations for which there do not exist smooth radial solutions to the system having the appropriate asymptotics for application to the Penrose inequality.

References in corpus (4)

• The area of horizons and the trapped region
• Extensions of the Charged Riemannian Penrose Inequality
• The Penrose inequality and positive mass theorem with charge for manifolds with asymptotically cylindrical ends
• Spherically symmetric counter examples to the Penrose inequality and the positive mass theorem under the assumption of the weak energy condition

Cited by in corpus (1)

• Conformal deformations of initial data sets to the strict dominant energy condition using a spacetime Poisson equation