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We reveal a novel nonlinear deformation of asymptotic symmetries in five-dimensional spacetimes. This nonlinear algebra, including nontrivial central charges, is essential for understanding spatial infinity in gravity theories.

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Area of Science:

  • Theoretical Physics
  • General Relativity
  • Mathematical Physics

Background:

  • Asymptotically flat spacetimes are crucial for understanding gravity.
  • Hamiltonian methods provide a powerful framework for studying spacetime symmetries.
  • Previous analyses often linearized conditions at spatial infinity.

Purpose of the Study:

  • To investigate asymptotic symmetries in five-dimensional spacetimes using Hamiltonian methods.
  • To precisely define boundary conditions for a consistent variational principle at spatial infinity.
  • To uncover and characterize the algebra of these asymptotic symmetries, including nonlinear aspects.

Main Methods:

  • Application of Hamiltonian methods to asymptotically flat spacetimes.
  • Focus on boundary conditions at spatial infinity.
  • Analysis of transformation laws and charge generators, retaining nonlinearities.

Main Results:

  • Precise boundary conditions for a consistent variational principle were established.
  • A previously undiscovered algebra of asymptotic symmetries was revealed.
  • This algebra is a nonlinear deformation of the Lorentz algebra, involving arbitrary functions and nontrivial central charges.

Conclusions:

  • The study highlights the importance of nonlinearities at spatial infinity, which are missed in linearized approaches.
  • The discovered nonlinear symmetry algebra offers new insights into the structure of gravity in higher dimensions.
  • This work provides a foundation for further exploration of asymptotic structures in theoretical physics.