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arXiv · 1406.2350

Proper time and length in Schwarzschild geometry

O. Brauer·H. A. Camargo·M. Socolovsky
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Abstract

We study proper time ($τ$) intervals for observers at rest in the universe ($U$) and anti-universe ($\bar{U}$) sectors of the Kruskal-Schwarzschild eternal spacetime of mass $M$, and proper lengths ($ρ$) in the black hole (BH) and white hole (WH) sectors. The fact that in asymptotically flat regions, coordinate time $t$ at infinity is proper time, leads to a past directed Kruskal time $T$ in $\bar{U}$. In the BH and WH sectors maximal proper lengths coincide with maximal proper time intervals, $πM$, in these regions, i.e. with the proper time of radial free falling (ejection) to (from) the singularity starting (ending) from (at) rest at the horizon.

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O. Brauer, H. A. Camargo, M. Socolovsky. 2014-06-05. Proper time and length in Schwarzschild geometry. https://arxiv.org/abs/1406.2350

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