2021/05/31 by Alexey Golovnev · 41 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Connection (principal bundle) #Cosmology and Gravitation Theories #General relativity #Geometry #Gravitation #Invariant (physics) #Lorentz covariance #Lorentz transformation #Mathematical physics #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Spacetime #Spin connection #Symmetry (geometry) #Tetrad #Theoretical physics #gr-qc #hep-th
paper · pdf · doi:10.1088/1361-6382/ac2136
published in Classical and Quantum Gravity 38(19), 197001 (IOP Publishing) · 13 pages; some more explanations added
arxiv created 2021/07/14 · openalex publication_date 2021/08/25 · arxiv updated 2021/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract The f ( T ) gravity is nowadays being widely used for cosmological model building, as well as for constructing spherically symmetric solutions. In its classical pure tetrad formulation it violates the local Lorentz symmetry in the space of tetrads. By using an appropriate spin connection it can be brought to a formally Lorentz invariant shape. However, despite some mathematical elegance obtained and new options of looking for non-standard couplings to matter probably made possible, it is fully equivalent in itself to the initial formulation. It seems that this fact, that the covariantisation does not in principle change anything, is not understood well by the community. Therefore we give a pedagogical introduction to these topics. And, on top of that, we show that obtaining the explicit equations for spherically symmetric solutions in f ( T ) gravity is not very difficult computationally and can be easily done even without any computer at hand.