Self-force on a scalar particle in a class of wormhole spacetimes

We consider the self-energy and the self-force for scalar massive and massless particles at rest in a class of wormhole spacetimes. We develop a general approach to obtain the self-force and apply it to the two specific profiles of the wormhole throat, namely, with singular and with smooth curvature. We found that the self-force changes its sign at the point where nonminimal coupling $\xi =1/8$ (for the massless case) and it tends to infinity for specific values of $\xi$. It may be attractive as well as repulsive depending on the profile of the throat. For the massless particle and minimal coupling case, the electromagnetic results are recovered.

Figure 1

The numerical simulation of the self-energy of a massive scalar field for $\xi =0$ and for different parameters $ma=0$ (thick line), $ma=0.1$ (medium line), and $ma=1$ (thin line). In the figure at right, we show the numerical simulation for $ma=1$ and for different parameters $\xi =1/10$ (thick line) up to $\xi =1/3$ (thin line). For $\xi =1/2$ it tends to infinity as should be the case.

Figure 2

The numerical simulation of the self-force on a massless scalar field for profile $r=\sqrt{{\rho }^2+a^2}$ for different parameters from $\xi =0$ (thick line) up to $\xi =\frac{3}{10}$ (thin line). For $\xi =\frac{1}{8}$ it is zero, and for $\xi =\frac{1}{2}$ it tends to infinity.