Neutrino Asymmetry Around Black Holes: Neutrinos Interact With Gravity

Abstract

Propagation of a fermion in curved space-time generates a gravitational interaction due to coupling of its spin with the space-time curvature connection. This gravitational interaction, which is an axialfour-vector multiplied by a four gravitational vector potential, appears as a CPT violating term in the Lagrangian which generates an opposite sign and thus asymmetry between the left-handed and the right handed partners under the CPT transformation. In the case of neutrinos, this property can generate a neutrino asymmetry in the Universe. If the background metric is of the rotating black hole, i.e. the Kerr geometry, this interaction for the neutrino is non-zero. Therefore, the dispersion energy relations for the neutrino and its anti-neutrino are different which give rise to the difference in their number densities and the neutrino asymmetry in the Universe in addition to the known relic asymmetry.

Neutrino Spin Oscillations in Gravitational Fields

“…the function u a (r, t), which is involved in the spin evolution equations) of massless particles differs from that of massive particles. However in the case of massless particles the helicity and chirality are the same and one can apply the methods used in the recent work [26].…”

Spacetime Curvature Coupling of Spinors in Early Universe: Neutrino Asymmetry and a Possible Source of Baryogenesis

“…The various aspects of this feature have been studied in past (e.g., [4][5][6][7][8][9][10][11][12]). It has also been shown that this interaction may be responsible for an additional neutrino asymmetry even in the present era of universe [13][14][15]. However, it is very difficult to visualize as the strength of the above mentioned interaction is negligible in our earth which is practically flat.…”

“…However, it is very difficult to visualize as the strength of the above mentioned interaction is negligible in our earth which is practically flat. In a similar fashion, the space-time around a black hole can generate neutrino asymmetry locally [13,15], but as we do not have overall information about number of black holes and their * ujjal@iucaa.ernet.in † bmukhopa@cfa.harvard.edu ‡ nkd@iucaa.ernet.in 1 corresponding spin orientation, it is very difficult to predict whether it produces a significant asymmetry over the relic value or not. A similar mechanism to produce asymmetry was noted earlier [16].…”

“…Therefore, if neutrinos are considered to be propagating in the non-flat early universe era, then due to presence of lepton number violating GUT processes a net asymmetry may arise between neutrinos and anti-neutrinos at the thermodynamic equilibrium. With time, as temperature goes down, this neutrino asymmetry also goes down and gets frozen-in when the lepton number violating GUT processes decouple at the era when temperature, T < ∼ 10 15 GeV. Note that according to the Linde's chaotic inflation model [22], inflation would start at the Planck time and end at the era when temperature, T ∼ 10 14 −10 15 GeV.…”

Gravity-induced neutrino–antineutrino oscillation: CPT and lepton number non-conservation under gravity

“…Hence, one can obtain the oscillation phase δ from eqn. (8). If we consider a special case when S(t) = arbitrary constant = k, then B 0 , B 2 → 0 at t → ∞ 3 , which verifies that the curvature coupling is insignificant in the present universe to exhibit any such oscillation.…”