論文

2011年8月17日

A trapped surface in the higher-dimensional self-similar Vaidya spacetime

  • Masahiro Shimano
  • ,
  • Tomohiro Harada
  • ,
  • Naoki Tsukamoto

DOI
10.1088/1742-6596/314/1/012068

We investigate a trapped surface and naked singularity in a $D$-dimensional<br />
Vaidya spacetime with a self-similar mass function. A trapped surface is<br />
defined as a closed spacelike $(D-2)$-surface which has negative both null<br />
expansions. There is no trapped surface in the Minkowski spacetime. However, in<br />
a four-dimensional self-similar Vaidya spacetime, Bengtsson and Senovilla<br />
considered non-spherical trapped surfaces and showed that a trapped surface can<br />
penetrate into a flat region, if and only if the mass function rises fast<br />
enough [I. Bengtsson and J. M. M. Senovilla, Phys. Rev. D \textbf{79}, 024027<br />
(2009).]. We apply this result to a $D$-dimensional spacetime motivated by the<br />
context of large extra dimensions or TeV-scale gravity. In this paper,<br />
similarly to Bengtsson and Senovilla&#039;s study, we match four types of<br />
$(D-2)$-surfaces and show that a trapped surface extended into the flat region<br />
can be constructed in the $D$-dimensional Vaidya spacetime, if the increasing<br />
rate of the mass function is greater than 0.4628. Moreover, we show that the<br />
maximum radius of the trapped surface constructed here approaches the<br />
Schwarzschild-Tangherlini radius in the large $D$ limit. Also, we show that<br />
there is no naked singularity, if the spacetime has the trapped surface<br />
constructed here.

リンク情報
DOI
https://doi.org/10.1088/1742-6596/314/1/012068
arXiv
http://arxiv.org/abs/arXiv:1108.3471
Arxiv Url
http://arxiv.org/abs/1108.3471v1
Arxiv Url
http://arxiv.org/pdf/1108.3471v1 本文へのリンクあり
ID情報
  • DOI : 10.1088/1742-6596/314/1/012068
  • arXiv ID : arXiv:1108.3471

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