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Area of Science:

  • Theoretical physics
  • String theory
  • General relativity

Background:

  • General relativity describes spacetime using Riemannian geometry.
  • Singularities in general relativity pose theoretical challenges.
  • Double field theory offers a broader framework for spacetime.

Purpose of the Study:

  • To investigate the nature of singular spacetimes within double field theory.
  • To re-interpret singularities in general relativity as regular geometries.
  • To analyze the behavior of particles and strings near these identified geometries.

Main Methods:

  • Utilizing the framework of double field theory.
  • Analyzing generalized metrics and coordinate transformations.
  • Computing geodesic completeness and string frame behavior.

Main Results:

  • Singular spacetimes of general relativity correspond to regular non-Riemannian geometries in double field theory.
  • Divergences are identified as coordinate singularities of the generalized metric.
  • An impenetrable non-Riemannian sphere is found, outside which geodesics are complete.

Conclusions:

  • The concept of spacetime singularities in general relativity can be resolved within double field theory.
  • Non-Riemannian geometries provide a more complete description of spacetime.
  • Physical phenomena near these points include particle freezing and chiral string behavior.