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Multiparticle Solutions to Einstein's Equations.

Humberto Gomez1,2, Renann Lipinski Jusinskas3

  • 1Department of Mathematical Sciences, Durham University, Stockton Road, DH1 3LE Durham, United Kingdom.

Physical Review Letters
|November 12, 2021
PubMed
Summary

This study introduces the first multiparticle solutions to Einstein's field equations with matter, utilizing the perturbiner method for complex gravitational calculations. This advance simplifies computing field theory amplitudes with multiple gravitons and matter fields.

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Area of Science:

  • Theoretical Physics
  • Gravitational Physics
  • Quantum Field Theory

Background:

  • Einstein's field equations describe gravity but lack general multiparticle solutions in the presence of matter.
  • Calculating interactions involving multiple gravitons and matter fields is computationally challenging.

Purpose of the Study:

  • To present the first multiparticle solutions to Einstein's field equations that include matter.
  • To develop a method that simplifies the computation of complex gravitational interactions.

Main Methods:

  • Iterative application of the perturbiner method.
  • Definition of a multiparticle expansion for the inverse spacetime metric.
  • Construction of tree-level field theory amplitudes.

Main Results:

  • Successfully derived multiparticle solutions to Einstein's field equations with matter.
  • The perturbiner method circumvents the issue of infinite vertices in gravity.
  • A simplified framework for computing amplitudes with any number of gravitons and matter fields.

Conclusions:

  • The developed method offers a significant advancement in solving Einstein's field equations for multiparticle systems.
  • This work provides a foundational tool for studying quantum gravity and field theories with matter.
  • The solutions are applicable in D spacetime dimensions and accommodate supersymmetry.