Scholarlink

In this work we examine the causal boundary of a spacetime by means of a foliation of future-incomplete timelike curves, representing a preferred class of observers. We find conditions that ensure that the future causal boundary is purely spacelike, inherits the topology of the foliation space, and can be viewed, when regarded as a subset of the future completion, as the boundary of a manifold-with-boundary. The intended model spacetime for this class is given by interior Schwarzschild. By further assuming that the drift form vanishes, we provide integral conditions on its sectional curvature that allow for a \(C^0\) -extension of the metric to the boundary. The main improvement we present in this contribution consists of refining the framework by replacing a condition that failed for interior Schwarzschild—considered in the previous preliminary report—by one which does hold in that space.

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Spacelike Causal Boundary at Finite Distance and Continuous Extension of the Metric: Second Preliminary Report

  • 会议论文

  • 发表日期：

    2025年

查看全文
  • Stacey G. Harris

摘要

In this work we examine the causal boundary of a spacetime by means of a foliation of future-incomplete timelike curves, representing a preferred class of observers. We find conditions that ensure that the future causal boundary is purely spacelike, inherits the topology of the foliation space, and can be viewed, when regarded as a subset of the future completion, as the boundary of a manifold-with-boundary. The intended model spacetime for this class is given by interior Schwarzschild. By further assuming that the drift form vanishes, we provide integral conditions on its sectional curvature that allow for a \(C^0\) -extension of the metric to the boundary. The main improvement we present in this contribution consists of refining the framework by replacing a condition that failed for interior Schwarzschild—considered in the previous preliminary report—by one which does hold in that space.