A Note on the Dimensional Reduction of Axisymmetric Spacetimes
Nishanth Gudapati
TL;DR
This paper examines the challenges in reducing 3+1 vacuum axisymmetric Einstein equations to a 2+1 dimensional system, highlighting issues like non-asymptotic flatness and divergent energies.
Contribution
It provides an analysis of the geometric and energetic problems arising in the dimensional reduction of axisymmetric spacetimes.
Findings
The reduced system is not asymptotically flat.
The geometric mass diverges in the reduced system.
The wave map energy also diverges.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Mathematical Physics Problems · Black Holes and Theoretical Physics · Cosmology and Gravitation Theories