Impulsive waves in ghost-free infinite derivative gravity in anti–de Sitter spacetime

We study exact impulsive gravitational waves propagating in anti–de Sitter spacetime in the context of the ghost-free infinite derivative gravity. We show that the source-free theory does not admit any anti–de Sitter wave solutions other than that of Einstein’s general relativity. The situation is significantly different in the presence of sources. We construct impulsive-wave solutions of the infinite derivative gravity generated by massless particles and linear sources in four and three dimensions. The singularities corresponding to distributional curvature at the locations of the sources get smeared by the nonlocalities. The obtained solutions are regular everywhere. They reduce to the corresponding solutions of general relativity in the infrared regime and in the local limit.

Figure 1

The function $H(y,z)$ for $z_0=1$, $G=1$, $E=1$, $\ell =1$, and $M_s=4$. The meshed red surface represents the solution of IDG, and the gray surface depicts the corresponding solution of GR.

Figure 2

The trajectory of the source at $z=z_0$ represented in Poincaré spherical model of the Lobachevsky space. The solid lines correspond to the location of the source at a given time $t$. They extend from $y=0$ (at the dashed line) toward $y=\pm \infty$ (at the conformal infinity).

Figure 3

The function $H(z)$ for $z_0=1$, $G=1$, $E=1$, $\ell =1$, and $M_s=4$. The dashed red curve denotes the solution of IDG, and the solid black curve represents the corresponding solution of GR.

Figure 4

The function $H(z)$ for $z_0=1$, $G_3=1$, $E=1$, $\ell =1$, and $M_s=4$. The dashed red curve represents the solution of IDG, and the solid black curve depicts the corresponding solution of GR.

Figure 5

Surfaces of constant $x$, $y$, and $z$ coordinates of the Lobachevsky space depicted in the Poincaré spherical model.