Skip to main content

P. D. E. 'S which imply the penrose conjecture

Publication ,  Journal Article
Bray, HL; Khuri, MA
Published in: Asian Journal of Mathematics
January 1, 2011

In this paper, we show how to reduce the Penrose conjecture to the known Riemannian Penrose inequality case whenever certain geometrically motivated systems of equations can be solved. Whether or not these special systems of equations have general existence theories is therefore an important open problem. The key tool in our method is the derivation of a new identity which we call the generalized Schoen-Yau identity, which is of independent interest. Using a generalized Jang equation, we use this identity to propose canonical embeddings of Cauchy data into corresponding static spacetimes. In addition, we discuss the Carrasco-Mars counterexample to the Penrose conjecture for generalized apparent horizons (added since the first version of this paper was posted on the arXiv) and instead conjecture the Penrose inequality for time-independent apparent horizons, which we define. © 2011 International Press.

Duke Scholars

Published In

Asian Journal of Mathematics

DOI

EISSN

1945-0036

ISSN

1093-6106

Publication Date

January 1, 2011

Volume

15

Issue

4

Start / End Page

557 / 610

Related Subject Headings

  • General Mathematics
  • 0101 Pure Mathematics
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Bray, H. L., & Khuri, M. A. (2011). P. D. E. 'S which imply the penrose conjecture. Asian Journal of Mathematics, 15(4), 557–610. https://doi.org/10.4310/AJM.2011.v15.n4.a5
Bray, H. L., and M. A. Khuri. “P. D. E. 'S which imply the penrose conjecture.” Asian Journal of Mathematics 15, no. 4 (January 1, 2011): 557–610. https://doi.org/10.4310/AJM.2011.v15.n4.a5.
Bray HL, Khuri MA. P. D. E. 'S which imply the penrose conjecture. Asian Journal of Mathematics. 2011 Jan 1;15(4):557–610.
Bray, H. L., and M. A. Khuri. “P. D. E. 'S which imply the penrose conjecture.” Asian Journal of Mathematics, vol. 15, no. 4, Jan. 2011, pp. 557–610. Scopus, doi:10.4310/AJM.2011.v15.n4.a5.
Bray HL, Khuri MA. P. D. E. 'S which imply the penrose conjecture. Asian Journal of Mathematics. 2011 Jan 1;15(4):557–610.

Published In

Asian Journal of Mathematics

DOI

EISSN

1945-0036

ISSN

1093-6106

Publication Date

January 1, 2011

Volume

15

Issue

4

Start / End Page

557 / 610

Related Subject Headings

  • General Mathematics
  • 0101 Pure Mathematics