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A New Class of Obstructions to the Smoothness of Null Infinity

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Abstract

Expansions of the gravitational field arising from the development of asymptotically Euclidean, time symmetric, conformally flat initial data are calculated in a neighbourhood of spatial and null infinities up to order 6. To this end a certain representation of spatial infinity as a cylinder is used. This setup is based on the properties of conformal geodesics. It is found that these expansions suggest that null infinity has to be non-smooth unless the Newman-Penrose constants of the spacetime, and some other higher order quantities of the spacetime vanish. As a consequence of these results it is conjectured that similar conditions occur if one were to take the expansions to even higher orders. Furthermore, the smoothness conditions obtained suggest that if time symmetric initial data which are conformally flat in a neighbourhood of spatial infinity yield a smooth null infinity, then the initial data must in fact be Schwarzschildean around spatial infinity.

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Authors and Affiliations

  1. Max Planck Institut für Gravitationphysik, Albert Einstein Institut, Am Mühlenberg 1, 14476, Golm, Germany

    Juan Antonio Valiente Kroon

  2. Institut für Theoretische Physik der Universität Wien, Boltzmanngasse 5, 1180 Wien, Austria

    Juan Antonio Valiente Kroon

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  1. Juan Antonio Valiente Kroon
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Correspondence to Juan Antonio Valiente Kroon.

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Communicated by H. Nicolai

It will be assumed that the reader is familiar with the ideas of the so-called conformal framework to describe the properties of isolated bodies and the concept of asymptotic flatness. For a recent review, the reader is remitted to [18]

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Valiente Kroon, J. A New Class of Obstructions to the Smoothness of Null Infinity. Commun. Math. Phys. 244, 133–156 (2004). https://doi.org/10.1007/s00220-003-0967-5

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  • DOI: https://doi.org/10.1007/s00220-003-0967-5

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