Radiation transport equations in non-Riemannian space-times

Abstract

The transport equations for polarized radiation transfer in non-Riemannian, Weyl-Cartan type space-times are derived, with the effects of both torsion and non-metricity included. To obtain the basic propagation equations we use the tangent bundle approach. The equations describing the time evolution of the Stokes parameters, of the photon distribution function and of the total polarization degree can be formulated as a system of coupled first order partial differential equations. As an application of our results we consider the propagation of the cosmological gamma ray bursts in spatially homogeneous and isotropic spaces with torsion and non-metricity. For this case the exact general solution of the equation for the polarization degree is obtained, with the effects of the torsion and non-metricity included. The presence of a non-Riemannian geometrical background in which the electromagnetic fields couple to torsion and/or non-metricity affect the polarization of photon beams. Consequently, we suggest that the observed polarization of prompt cosmological gamma ray bursts and of their optical afterglows may have a propagation effect component, due to a torsion/non-metricity induced birefringence of the vacuum. A cosmological redshift and frequency dependence of the polarization degree of gamma ray bursts also follows from the model, thus providing a clear observational signature of the torsional/non-metric effects. On the other hand, observations of the polarization of the gamma ray bursts can impose strong constraints on the torsion and non-metricity and discriminate between different theoretical models.Comment: 12 pages, 3 figures, accepted for publication in PR

Standard Model in Weyl conformal geometry

“…35 TeV. Note that if there is no term (1/η) C2 μνρσ in the original gravity action, then γ = 1 and then χ = χ. Alternatively, using the current lower bound on the nonmetricity scale (represented by m ω ) which is of the order of the TeV scale [39,40], then tan χ ≤ 0.16 (56) This is consistent with the non-metricity constraint. These bounds are significant and affect other phenomenological studies.…”

“…to this problem; other implications can be for example in the birefringence of the vacuum induced by ω μ . This can impact on the propagation of the observed polarization of the gamma-ray bursts [56] 11 or of the CMB [57].…”

Standard Model in Weyl conformal geometry

“…One can also use these constraints when studying the role of ω µ for phenomenology in other examples, such as the dark matter problem [38] or the birefringence of the vacuum induced by ω µ . This can impact on the propagation of the observed polarization of the gamma-ray bursts [39] 9 or of the CMB [40].…”

B →f 0 (980)(π,η(′)) decays in the PQCD approach

“…Very recently, some B → SP decays have been studied, for example, by employing the QCD factorization (QCDF) approach or the perturbative QCD (pQCD) approach [1][2][3] . In the B factory, the first scalar meson f 0 (980) was observed in the decay mode B → f 0 (980)K by Belle [4] , and later confirmed by BaBar [5] , then many B → SP channels have been measured [6,7] .…”

“…where f n 0 and f s 0 represent the quark flavor states of f 0 (980). Using the QCD sum rules method, one can find that the scale-dependent scalar decay constants f n f 0 and f s f 0 are very close [1,11] . So one usually assumes f n f 0 = f s f 0 and denotes them as ff 0 in the following.…”