Gödel-type universes in Lorentz-violating Kalb-Ramond gravity with Ricci- and Riemann-tensor nonminimal couplings
Abstract
This paper studies homogeneous \Godel-type geometries in a gravitational model where local Lorentz symmetry is spontaneously broken by the vacuum expectation value of an antisymmetric Kalb-Ramond two-form. We consider the Einstein-Hilbert action supplemented by two independent nonminimal curvature couplings: a Ricci-tensor coupling of the form BacBbcRab and a Riemann-tensor coupling of the form BabBcdRabcd. In the homogeneous vacuum sector, where the Kalb-Ramond field strength and the first derivatives of the symmetry-breaking potential vanish, the field equations reduce to a closed algebraic system in the tetrad frame of the \Godel-type metric. We derive the curvature tensors, the reduced metric equations, and the Kalb-Ramond consistency equations for several inequivalent orientations of the vacuum two-form. Particular attention is given to the pseudo-magnetic background B12=b, because it preserves the symmetry of the rotation plane and yields a transparent deformation of the usual bumblebee result. For this sector the Kalb-Ramond equation fixes m2/ω2=(2(ξ1+3ξ2))/(ξ1+2ξ2), where ξ1 and ξ2 are the Ricci and Riemann couplings. The Ricci coupling alone reproduces the noncausal \Godel value m2=2ω2, while the Riemann coupling shifts the chronology bound and allows the critical causal value m2=4ω2 for ξ2=−ξ1. We also show that the Riemann coupling can move the critical radius for closed timelike curves, but ordinary positive-energy matter severely restricts completely causal solutions. Finally, we discuss perfect fluid, scalar field, and electromagnetic sources.
Related
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BibTeX
@misc{belchior2026gödeltype,
title = {{Gödel-type universes in Lorentz-violating Kalb-Ramond gravity with Ricci- and Riemann-tensor nonminimal couplings}},
author = {Fernando M. Belchior},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.26472},
eprint = {2608.26472},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.26472},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gödel-type universes in Lorentz-violating Kalb-Ramond gravity with Ricci- and Riemann-tensor nonminimal couplings
AU - Fernando M. Belchior
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.26472
UR - https://arxiv.org/abs/2608.26472
AB - This paper studies homogeneous \Godel-type geometries in a gravitational model where local Lorentz symmetry is spontaneously broken by the vacuum expectation value of an antisymmetric Kalb-Ramond two-form. We consider the Einstein-Hilbert action supplemented by two independent nonminimal curvature couplings: a Ricci-tensor coupling of the form B_a^cB_bcR^ab and a Riemann-tensor coupling of the form B^abB^cdR_abcd. In the homogeneous vacuum sector, where the Kalb-Ramond field strength and the first derivatives of the symmetry-breaking potential vanish, the field equations reduce to a closed algebraic system in the tetrad frame of the \Godel-type metric. We derive the curvature tensors, the reduced metric equations, and the Kalb-Ramond consistency equations for several inequivalent orientations of the vacuum two-form. Particular attention is given to the pseudo-magnetic background B_12=b, because it preserves the symmetry of the rotation plane and yields a transparent deformation of the usual bumblebee result. For this sector the Kalb-Ramond equation fixes m^2/ω^2=(2(ξ_1+3ξ_2))/(ξ_1+2ξ_2), where ξ_1 and ξ_2 are the Ricci and Riemann couplings. The Ricci coupling alone reproduces the noncausal \Godel value m^2=2ω^2, while the Riemann coupling shifts the chronology bound and allows the critical causal value m^2=4ω^2 for ξ_2=−ξ_1. We also show that the Riemann coupling can move the critical radius for closed timelike curves, but ordinary positive-energy matter severely restricts completely causal solutions. Finally, we discuss perfect fluid, scalar field, and electromagnetic sources.
ER -