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<p>We provide a new perspective on the general matching conditions between the future of past null infinity and the past of future null infinity, emphasizing the impact of dominant logarithmic terms in the asymptotic expansion of the fields near null infinity. We explicitly consider the cases of a massless scalar field and of electromagnetism. Key in our derivation is the identification of the physical origin of these logarithms, which are associated with advanced and retarded radiation saturating the finite energy flux condition at null infinity (in a space of functions which is made precise). The matching conditions arise then from the requirement of Coulombic (i.e., 1<i>/r</i>) behaviour at spatial infinity.</p>

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Matching conditions at null infinity in the presence of logarithms: the role of advanced and retarded radiation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月9日

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  • Matías Briceño,
  • Hernán A. González,
  • Marc Henneaux,
  • Alfredo Pérez

摘要

We provide a new perspective on the general matching conditions between the future of past null infinity and the past of future null infinity, emphasizing the impact of dominant logarithmic terms in the asymptotic expansion of the fields near null infinity. We explicitly consider the cases of a massless scalar field and of electromagnetism. Key in our derivation is the identification of the physical origin of these logarithms, which are associated with advanced and retarded radiation saturating the finite energy flux condition at null infinity (in a space of functions which is made precise). The matching conditions arise then from the requirement of Coulombic (i.e., 1/r) behaviour at spatial infinity.