A Note on the Dimensional Reduction of Axisymmetric Spacetimes

Abstract

We investigate the dimensional reduction of 3+1 vacuum axisymmetric Einstein's equations to 2+1 dimensional Einstein-wave map system and observe that the resulting system is 1) not asymptotically flat, 2) its geometric-mass diverges and 3) the energy of wave map also diverges. Subsequently, we discuss the consequences of these issues.

Cited by in corpus (2)

• Global regularity for Einstein-Klein-Gordon system with $U(1)\times \mathbb{R}$ isometry group, I
• Global regularity for Einstein-Klein-Gordon system with $U(1)\times \mathbb{R}$ isometry group, II