Bondi-Metzner-Sachs Group in Five Spacetime Dimensions

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.