Galactic dynamo seeds and black hole singularities driven by Einstein–Cartan QCD walls

Abstract

Torsion spin polarised wall solution of Einstein–Cartan equations as torsion defects (Garcia de Andrade, Ann Phys 432 (2021)) where spin is distributed orthogonally to the wall has recently been obtained. Moreover, torsional inflating defect [Class and Quantum Gravity, 16 (1999) 2097] in the form of a dilatonic domain wall has also been found. Our goal in this paper is to obtain thin torsion wall solutions as teleparallel and Riemann–Cartan (RC) spacetime walls, with Einstein–Cartan stress–energy tensor, similar to Kalb–Ramond torsion fields. In thin teleparallel wall, we show that torsion is proportional to a time Dirac delta function which possesses a time singularity at the wall like Big Bang and black hole GR ones. This magnetic field has a torsional contribution of BQCD∼1017G in RC walls, which is suitable for dynamo amplification from a seed field of Bseed∼1012G as Big Bang Nucleosynthesis (BBN). From QCD cosmic time scale of tQCD∼10−6s torsion of the order of J0∼10−11cm−1 is obtained. From a 1 MeV torsion and seed field of Bseed∼10−32G, found by Barrow et al [PRD] in the framework of general relativity (GR) which is suitable to seed galactic dynamo field. In this case a domain wall magnetic field of BDW∼10−28G which is stronger, and more suitable as a galactic dynamo seed, is obtained. Magnetic field seed of 10−14G, quite close to orders of magnitude of O(10−15−10−18G) obtained by Atrayed et al. (EPJC (2018) 78: 1027) on a torsionless GR domain wall, generates a wall (DW) magnetic field of order of BDW∼1018G obtained at 1 kpc scales. These similarities between GR results and teleparallel one were expected due to the fact that the teleparallel theory of gravity considered in this paper is the teleparallel equivalent to GR or (TEGR). Chiral dynamos in dilatonic conformally flat metric are also discussed.