2014/05/21 by Alhamzawi, Ahmed, Alhamzawi, Rahim
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)
paper · doi:10.48550/arxiv.1405.5503
We show that the unification of electromagnetism and gravity into a single geometrical entity can be beautifully accomplished in a theory with non-symmetric affine connection (Γμνλ≠Γνμλ), and the unifying symmetry being projective symmetry. In addition, we show that in a purely-affine theory where there are no constrains on the symmetry of Γμνλ, the electromagnetic field can be interpreted as the field that preserves projective-invariance. The matter Lagrangian breaks the projective-invariance, generating classical relativistic gravity and quantum electromagnetism. We notice that, if we associate the electromagnetic field tensor with the second Ricci tensor and Γ[μν]ν with the vector potential, then the classical Einstein-Maxwell equation can be obtained. In addition, we explain the geometrical interpretation of projective transformations. Finally, we discuss the importance of the role of projective-invariance in f(R) gravity theories.