Figure 1

Six analytically known mirror trajectories. In the left panel, the mirror trajectories are plotted in $t$ and $x$ coordinates. The right panel depicts the same trajectories in a Penrose diagram. The Carlitz-Willey trajectory, with $\kappa =1$, and the modified Carlitz-Willey trajectory, with $\kappa =1$ and $\sigma =1/3$, are shown as solid curves. The Carlitz-Willey trajectory gives rise to a horizon at $v=0$, while the modified Carlitz-Willey trajectory ends at future timelike infinity ($i^{+}$). The short-dashed curve indicates the Arctx mirror with $\mu =1$, which is static in the distant past and future. The long-dashed curve is the Darcx trajectory with $\nu =1$ and asymptotic future velocity $\xi =-1/2$. The Walker-Davies trajectory for $A=2$, $B=1$ is shown as the dotted-dashed curve. The Proex trajectory with $\rho =1$ is denoted by the dotted curve. We consider only the region of spacetime to the right of a mirror. Thus, past null infinity on the left (not labeled) plays no role in our analysis. Similarly, there is an abbreviated portion of future null infinity on the left (${\mathcal{I}}_L^{+}$), but only in the case of the Carlitz-Willey trajectory. All of the other mirror trajectories begin and end at $i^{-}$ and $i^{+}$, respectively.Reuse & Permissions

Figure 2

The energy flux $⟨T_{uu}⟩$ vs time is plotted for the various mirror trajectories. The parameters $\kappa$, $\mu$, $\nu$, and $\rho$ have all been set equal to 1. For the Darcx trajectory, the value $\xi =1/2$ was chosen, and for the modified Carlitz-Willey trajectory, $\sigma =1/3$ was chosen. For the Walker-Davies trajectory, $A=2$ and $B=1$ were chosen. The energy flux in the Carlitz-Willey case is the constant solid line. The energy flux associated with the modified Carlitz-Willey trajectory is the solid curve, which coincides with the Carlitz-Willey value at early times but then diverges, briefly resulting in a burst of negative energy before decaying to zero. The flux associated with the Arctx trajectory is shown as the short-dashed curve, and that of the Darcx trajectory is indicated by the long-dashed curve. The flux from the Proex trajectory is depicted by the dotted curve and that of the Walker-Davies case by the dotted-dashed curve.Reuse & Permissions

Figure 3

The particle number as measured by wave packets, $⟨N_{jn}⟩$, is plotted as a function of the packet time parameter $n$ for the Carlitz-Willey (filled circles) and modified Carlitz-Willey (open circles) trajectories. In both cases the packet frequency width parameter $ϵ$ has been set to $\sqrt{2}\pi$, and the first nondivergent frequency bin, $j=1$, is shown. The parameter $\kappa$ has been set to one, and for the modified Carlitz-Willey trajectory, we have taken $\sigma =1/3$.Reuse & Permissions

Figure 4

The particle number as measured by wave packets, $⟨N_{jn}⟩$, is plotted as a function of the packet time parameter $n$. In each case the packet frequency width parameter $ϵ$ has been set to $\sqrt{2}\pi$, and the lowest frequency bin $j=0$ is shown. The parameters $\mu$, $\nu$, and $\rho$ have all been set to one. For the Darcx trajectory, the value $\xi =1/2$ was chosen, and for the Walker-Davies case, $A=2$ and $B=1$ were chosen. The value of $N_{0n}$ is denoted by the open circles for the Arctx trajectory, the triangles for the Darcx trajectory, the filled circles for the Proex trajectory, and the pluses for the Walker-Davies trajectory.Reuse & Permissions

Figure 5

The particle number as measured by wave packets, $⟨N_{jn}⟩$, is plotted as a function of the packet frequency parameter $j$, with $n=0$ and $ϵ=0.01$ for the Arctx trajectory.Reuse & Permissions