Gravitational and Electromagnetic Fields near a de Sitter–Like Infinity

We present a characterization of general gravitational and electromagnetic fields near de Sitter–like conformal infinity which supplements the standard peeling behavior. This is based on an explicit evaluation of the dependence of the radiative component of the fields on the null direction from which infinity is approached. It is shown that the directional pattern of radiation has a universal character that is determined by the algebraic (Petrov) type of the spacetime. Specifically, the radiation field vanishes along directions opposite to principal null directions.

Figure 1

Specific directional patterns of radiation for spacetimes of Petrov types N, III, D, II, and I. Directions in the diagrams represent all spatial directions tangent to ${\mathcal{I}}^{+}$. For each type, the radiative component $|{\Psi }_4^i|$ along a null geodesic is depicted in the corresponding spatial direction ${\mathbf{k}}^{\perp }$ parametrized by spherical angles $\theta ,\varphi$. [Degenerate] principal null directions (PNDs) are indicated by [multiple] bold arrows. Thick lines represent spatial directions (opposite to PNDs) along which the radiation vanishes.