Spin-2 particles in gravitational fields

Abstract

We give a solution of the wave equation for massless, or massive spin-2 particles propagating in a gravitational background. The solution is covariant, gauge-invariant and exact to first order in the background gravitational field. The background contribution is confined to a phase factor from which geometrical and physical optics can be derived. The phase also describes Mashhoon's spin-rotation coupling and, in general, the spin-gravity interaction.

Perspectives on Gravity-Induced Radiative Processes in Astrophysics

“…The examples given involve spin-1 2 and spin-1 particles, but the procedure can be extended to any spin. An essential point here is that the dispersion relations are altered by the external gravitational field and can be calculated if the corresponding wave equations can be solved to O(γ µν ) or higher [20,[34][35][36][37]. It follows, in particular, that kinematically-forbidden processes similar to that of Figure 1 become physical, and their transition probabilities can be determined.…”

“…This should be expected, because in metric theories of gravitation [30], general relativity in particular, the space parameter of Berry's theory coincides with space-time. It has been shown that the wave equations for fermions and bosons can be solved exactly to first order in the metric deviation γ µν = g µν − η µν for any metric g µν and that the phases so calculated [20,[31][32][33][34] give reliable results in interferometry, gyroscopy [28] and optics [35,36], give the correct Einstein deflection, can be used in the study of neutrino helicity and flavour oscillations [37] and of spin-gravity coupling in general [31,34]. They also reproduce a variety of known effects, as discussed in [32,33,38].…”

Maximal acceleration and radiative processes

“…of (10) is required by the condition that both sides of the equation agree when the MA contribution vanishes. Similar solutions can also be found for all covariant wave equations [81][82][83][84]. We choose Ψ 0 (x) ∝ e −ipαx α and drop carets in what follows.…”

Radiative processes in external gravitational fields

“…The example given refers to fermions, but the procedure can be extended to particles of different spins. An essential point is here that the dispersion relations are altered by the external gravitational field and can be calculated if the corresponding wave equations can be solved to O(γ µν ), or higher [1,[5][6][7][8]. The treatment of particle lines in Feynman diagrams therefore necessitates care when external gravitational fields are present.…”

“…This can be done exactly to first order in the metric deviation γ µν = g µν − η µν , where η µν is the Minkowski metric [1][2][3][4][5][6][7][8]. The solutions contain the gravitational field in a phase operator that alters in effect a particle four-momentum by acting on the wave function of the field-free equations.…”