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Open AccessArticle

Flat Connection for Rotating Vacuum Spacetimes in Extended Teleparallel Gravity Theories

1
Laboratory of Theoretical Physics, Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411 Tartu, Estonia
2
Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, Yangzhou 225009, China
*
Author to whom correspondence should be addressed.
This paper is based on the talk at the Teleparallel Universes in Salamanca, Salamanca, Spain, 26–28 November 2018.
Universe 2019, 5(6), 142; https://doi.org/10.3390/universe5060142
Received: 8 May 2019 / Revised: 3 June 2019 / Accepted: 7 June 2019 / Published: 10 June 2019
(This article belongs to the Special Issue Selected Papers from Teleparallel Universes in Salamanca)
Teleparallel geometry utilizes Weitzenböck connection which has nontrivial torsion but no curvature and does not directly follow from the metric like Levi–Civita connection. In extended teleparallel theories, for instance in f ( T ) or scalar-torsion gravity, the connection must obey its antisymmetric field equations. Thus far, only a few analytic solutions were known. In this note, we solve the f ( T , ϕ ) gravity antisymmetric vacuum field equations for a generic rotating tetrad ansatz in Weyl canonical coordinates, and find the corresponding spin connection coefficients. By a coordinate transformation, we present the solution also in Boyer–Lindquist coordinates, often used to study rotating solutions in general relativity. The result hints for the existence of another branch of rotating solutions besides the Kerr family in extended teleparallel gravities. View Full-Text
Keywords: teleparallel theory of gravity; scalar-torsion gravity; rotating black holes teleparallel theory of gravity; scalar-torsion gravity; rotating black holes
MDPI and ACS Style

Järv, L.; Hohmann, M.; Krššák, M.; Pfeifer, C. Flat Connection for Rotating Vacuum Spacetimes in Extended Teleparallel Gravity Theories. Universe 2019, 5, 142.

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