Asymptotic behaviour of the Weyl tensor in higher dimensions

Abstract

We determine the leading order fall-off behaviour of the Weyl tensor in higher dimensional Einstein spacetimes (with and without a cosmological constant) as one approaches infinity along a congruence of null geodesics. The null congruence is assumed to "expand" in all directions near infinity (but it is otherwise generic), which includes in particular asymptotically flat spacetimes. In contrast to the well-known four-dimensional peeling property, the fall-off rate of various Weyl components depends substantially on the chosen boundary conditions, and is also influenced by the presence of a cosmological constant. The leading component is always algebraically special, but in various cases it can be of type N, III or II.

32 pages. v2: added refs., corrected ref. [2] and a few typos (but equations unchanged), added 2 summarizing tables, minor changes to match the published version

References in corpus (10)

• Algebraic classification of higher dimensional spacetimes based on null alignment
• Robinson-Trautman spacetimes in higher dimensions
• Generalization of the Geroch-Held-Penrose formalism to higher dimensions
• Type D Einstein spacetimes in higher dimensions
• Higher dimensional Kerr-Schild spacetimes
• Global solutions of the Einstein-Maxwell equations in higher dimensions
• Kerr-Schild spacetimes with (A)dS background
• Peeling of the Weyl tensor and gravitational radiation in higher dimensions
• Newman-Penrose formalism in higher dimensions: vacuum spacetimes with a non-twisting geodetic multiple Weyl aligned null direction
• Higher Dimensional Bondi Energy with a Globally Specified Background Structure

Cited by in corpus (8)

• Asymptotic behaviour of Maxwell fields in higher dimensions
• On the uniqueness of the Myers-Perry spacetime as a type II(D) solution in six dimensions
• On higher dimensional Einstein spacetimes with a non-degenerate double Weyl aligned null direction
• Peeling property and asymptotic symmetries with a cosmological constant
• On the uniqueness of the Kerr-(A)dS metric as a type II(D) solution in six dimensions
• Free data at spacelike $\mathcal{I}$ and characterization of Kerr-de Sitter in all dimensions
• A peeling theorem for the Weyl tensor in higher dimensions
• Asymptotic properties of gravitational and electromagnetic fields in higher dimensions