xPert: Computer algebra for metric perturbation theory. We present the tensor computer algebra package xPert for fast construction and manipulation of the equations of metric perturbation theory, around arbitrary backgrounds. It is based on the combination of explicit combinatorial formulas for the nth order perturbation of curvature tensors and their gauge changes, and the use of highly efficient techniques of index canonicalization, provided by the underlying tensor system xAct, for Mathematica. We give examples of use and show the efficiency of the system with timings plots: it is possible to handle orders n=4 or n=5 within seconds, or reach n=10 with timings below 1 h.

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  1. de Giorgi, A.; Vogl, S.: Unitarity in KK-graviton production, a case study in warped extra-dimensions (2021)
  2. Draper, Tom; Knorr, Benjamin; Ripken, Chris; Saueressig, Frank: Graviton-mediated scattering amplitudes from the quantum effective action (2020)
  3. Herrero-Valea, Mario; Santos-Garcia, Raquel: Non-minimal tinges of unimodular gravity (2020)
  4. Markus B. Fröb: FieldsX - An extension package for the xAct tensor computer algebra suite to include fermions, gauge fields and BRST cohomology (2020) arXiv
  5. Jafari, Ghadir; Soltanpanahi, Hesam: Instability of BTZ black holes in parity-even massive gravity (2019)
  6. Knorr, Benjamin: Lorentz symmetry is relevant (2019)
  7. Castro, Alejandra; Godet, Victor; Larsen, Finn; Zeng, Yangwenxiao: Logarithmic corrections to black hole entropy: the non-BPS branch (2018)
  8. Knorr, Benjamin: Infinite order quantum-gravitational correlations (2018)
  9. Saffer, Alexander; Yunes, Nicolás; Yagi, Kent: The gravitational wave stress-energy (pseudo)-tensor in modified gravity (2018)
  10. Nutma, Teake: \textitxTras: a field-theory inspired \textitxActpackage for Mathematica (2014)
  11. Pitrou, Cyril; Roy, Xavier; Umeh, Obinna: (\textxPand): an algorithm for perturbing homogeneous cosmologies (2013)
  12. Gómez-Lobo, Alfonso García-Parrado; Martín-García, José M.: \textitSpinors: a Mathematica package for doing spinor calculus in general relativity (2012)
  13. Virmani, Amitabh: Supertranslations and holographic stress tensor (2012)
  14. Brizuela, David; Martín-García, José M.; Mena Marugán, Guillermo A.: (xPert): Computer algebra for metric perturbation theory (2009)