Relativistic glider

We present a purely relativistic effect according to which asymmetric oscillations of a quasirigid body slow down or accelerate its fall in a gravitational background.

Figure 1

(a) Family of constraint functions $l_{\alpha }(t)$ [6]. (b) Net displacement $\delta r=r_1(T)-r_p(T)$ of the dumbbell, relative to the falling point mass, after one period. The initial conditions are set by ${\dot{r}}_p(0)={\dot{r}}_1(0)=0$, $r_p(0)=r_1(0)=120$ and $\delta l=5\times {10}^{-3}$ (in units of $GM/c^2$). The relativistic (Newtonian) case is represented by solid (dashed) lines. The plot shows that the Newtonian $\delta r$ is always negative and that it is negligible for $\omega \gtrsim 0.03c^3/GM$, irrespective of $\alpha$. In contrast, we see that the relativistic $\delta r$ crucially depends on the asymmetry parameter $\alpha$, and does attain positive values (for positive $\alpha$). Causality problems (due to large velocities) only start to appear at much higher frequencies, not shown above.

Figure 2

Adimensional scale factor ${\Gamma }_{\alpha }$ as a function of the asymmetry parameter $\alpha$.