Some asymptotically Euclidean tangent bundles and their ADM masses

Document Type : Research Paper

Author

Department of Mathematical Sciences, Isfahan University of Technology, 8415683111, Isfahan, Iran

Abstract

Geometric relativity is mostly referred to the study of spatial manifolds in space-time manifolds as main objects in general relativity. Our goal in this paper, is to study spatial models of the universe that are themselves tangent bundles. In Arnowitt, Deser and Misner's formulation of general relativity as a Hamiltonian system, the main quantities that are studied are total energy and mass of a system and in this paper, we will look at the ADM mass for some asymptotically Euclidean tangent bundles. First, we will completely characterize asymptotically Euclidean interpolation metrics on tangent bundles of simple manifolds. We will then consider a family of interpolation metrics that we will call admissible metrics. We will define the notion of lower ADM mass (that is weaker than ADM mass) and estimate the lower ADM mass of admissible metrics. From the said estimate, we show that a stronger version of Schoen and Yau's positive mass and rigidity of positive mass holds for admissible metrics.

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References

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Mathematics and Society
Volume 10, Issue 4 - Serial Number 4
December 2025
Pages 85-104

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History

  • Receive Date: 03 December 2024
  • Revise Date: 14 January 2025
  • Accept Date: 15 January 2025
  • Publish Date: 03 September 2025

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