Spin-2 particles in gravitational fields

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.

Figure 1

Geometry of a two-image gravitational lens or, equivalently, of a double slit interference experiment. The solid lines represent the particle paths between the particle source at $S$ and the observer at $O$. $M$ is the spherically symmetric gravitational lens. $S$, $M$, $O$ and the particle paths lie in the same plane. The physical variables are $r_S$, $r_0$, $b^{\pm }$, $s$, while the lensing variables are indicated by $D_{dS}$, $D_{dO}$, $D_S$, ${\theta }^{\pm }$, $\beta$. ${\alpha }^{\pm }$ are the deflection angles.