Chirality in gravitational and electromagnetic interactions with matter

Abstract

It has been suggested that single and double jets observed emanating from certain astrophysical objects may have a purely gravitational origin. We discuss new classes of pulsed gravitational wave solutions to the equation for perturbations of Ricci-flat spacetimes around Minkowski metrics, as models for the genesis of such phenomena. We discuss how these solutions are motivated by the analytic structure of spatially compact finite energy pulse solutions of the source-free Maxwell equations generated from complex chiral eigenmodes of a chirality operator. Complex gravitational pulse solutions to the linearised source-free Einstein equations are classified in terms of their chirality and generate a family of non-stationary real spacetime metrics. Particular members of these families are used as backgrounds in analysing time-like solutions to the geodesic equation for test particles. They are found numerically to exhibit both single and double jet-like features with dimensionless aspect ratios suggesting that it may be profitable to include such backgrounds in simulations of astrophysical jet dynamics from rotating accretion discs involving electromagnetic fields.

Scalar Pre-potentials for Spinor and Tensor Fields on Spacetime

“…for any complex 0-form α ∈ ΓΛ 0 M. A direct computation now verifies that if α is the complex pulse solution (19) satisfying…”

“…It has been suggested that gravitation may also play a role in initiating such processes [18]. We have suggested in [19,17] that an analysis of the timelike geodesics associated with a propagating, gravitational chiral pulse may provide some insight into the relevance of gravitational chirality in initiating the magnetohydrodynamic mechanism. As we shall show, chiral pulses can be shown to account for both uni-directional and bi-directional jet structures.…”

“…where 0 , a, b are real constants. When a, b are strictly positive constants, (19) defines a nonsingular solution to α = 0. This scalar field is a non-separable solution to (18) with the relative sizes of a and b determining both the direction of propagation along the z-axis of the dominant peak of the real or imaginary part of the scalar field and the number of oscillations in its peak.…”

“…This should be compared with(19) 5. Since ∇ (η) is a flat connection, if K is an η-Killing vector then the operator ∇ (η) LK = LK ∇ (η) on all tensors.…”

Twisted gravitational waves of Petrov type D

“…With respect to the set of fiducial observers that are all at rest in space, timelike geodesics in such spacetimes generally line up at late times in the direction of wave propagation with Lorentz factors that asymptotically tend to infinity. This cosmic jet feature of plane gravitational waves has been the subject of previous investigations [10][11][12][13].…”