Symmetry Reduction in Twisted Noncommutative Gravity with Applications to Cosmology and Black Holes

TL;DR

This paper investigates symmetry reductions in twisted noncommutative gravity, classifies admissible deformations, and constructs examples compatible with cosmological and black hole symmetries, advancing the mathematical foundation for noncommutative gravitational physics.

Contribution

It provides a classification of twists compatible with symmetric spacetimes and explicitly constructs examples for cosmology and black holes, enabling consistent noncommutative gravity models.

Findings

Classified admissible twists for symmetry reductions

Constructed compatible twists for FRW cosmologies

Constructed compatible twists for Schwarzschild black holes

Abstract

As a preparation for a mathematically consistent study of the physics of symmetric spacetimes in a noncommutative setting, we study symmetry reductions in deformed gravity. We focus on deformations that are given by a twist of a Lie algebra acting on the spacetime manifold. We derive conditions on those twists that allow a given symmetry reduction. A complete classification of admissible deformations is possible in a class of twists generated by commuting vector fields. As examples, we explicitly construct the families of vector fields that generate twists which are compatible with Friedmann-Robertson-Walker cosmologies and Schwarzschild black holes, respectively. We find nontrivial isotropic twists of FRW cosmologies and nontrivial twists that are compatible with all classical symmetries of black hole solutions.