Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

General Relativity and Quantum Cosmology

arXiv:1401.6976 (gr-qc)
[Submitted on 27 Jan 2014 (v1), last revised 16 Oct 2014 (this version, v2)]

Title:Blowup solutions of Jang's equation near a spacetime singularity

Authors:Amir Babak Aazami, Graham Cox
View PDF
Abstract:We study Jang's equation on a one-parameter family of asymptotically flat, spherically symmetric Cauchy hypersurfaces in the maximally extended Schwarzschild spacetime. The hypersurfaces contain apparent horizons and are parametrized by their proximity to the singularity at $r = 0$. We show that on those hypersurfaces sufficiently close to the singularity, every radial solution to Jang's equation blows up. The proof depends only on the geometry in an arbitrarily small neighborhood of the singularity, suggesting that Jang's equation is in fact detecting the singularity. We comment on possible applications to the weak cosmic censorship conjecture.
Comments: 18 pages, 1 figure; second version has expanded Introduction, and new description of blowup solutions in Section 4
Subjects: General Relativity and Quantum Cosmology (gr-qc); Differential Geometry (math.DG)
Cite as: arXiv:1401.6976 [gr-qc]
  (or arXiv:1401.6976v2 [gr-qc] for this version)
  https://doi.org/10.48550/arXiv.1401.6976
Journal reference: Class. Quantum Grav. 31 (2014)
Related DOI: https://doi.org/10.1088/0264-9381/31/11/115007

Submission history

From: Graham Cox [view email]
[v1] Mon, 27 Jan 2014 19:33:01 UTC (129 KB)
[v2] Thu, 16 Oct 2014 18:55:03 UTC (124 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
gr-qc
< prev   |   next >
new | recent | 2014-01
Change to browse by:
math
math.DG

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)
IArxiv Recommender (What is IArxiv?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)