Abstract
We show that (n + 1)-dimensional Myers–Perry metrics, n ≥ 4, have a conformal completion at space-like infinity of Cn−3,1 differentiability class and that the result is optimal in even spacetime dimensions. The associated asymptotic symmetries are presented.
Highlights
One of the classical questions in general relativity is that of the behavior of the gravitational field when receding to infinity in spacelike directions
As is well known, Minkowski spacetime has a conformal completion that includes a point at spacelike infinity, called i0, such that the conformally extended metric is smooth near this point
It is well known that the usual extension of the Minkowskian construction to four-dimensional Schwarzschild spacetime leads to a conformal completion with a metric, which is continuous,2,5,9 but no such extension which is C1 is known
Summary
One of the classical questions in general relativity is that of the behavior of the gravitational field when receding to infinity in spacelike directions This has been studied in detail in many works in spacetime dimension four; see, e.g., Refs. That the Riemannian metric obtained from quotienting the spacetime metric of stationary, odd-dimensional, electrovacuum metrics by the stationary isometries admits a conformal completion at a point at infinity, which is real-analytic.4 This result does not translate in any obvious way to the associated spacetime metric. Recall that the usual results of causality theory, except perhaps the ones explicitly involving geodesics, apply for metrics that are Lipschitz continuous, and in dimensions n ≥ 4 for metrics with the Myers–Perry asymptotics by our results here.
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