The isoperimetric problem in riemannian optical geometry
Publication
, Journal Article
Roesch, HP; Werner, MC
Published in: Pure and Applied Mathematics Quarterly
January 1, 2020
In general relativity, spatial light rays of static spherically symmetric spacetimes are geodesics of surfaces in Riemannian optical geometry. In this paper, we apply results on the isoperimetric problem to show that length-minimizing curves subject to an area constraint are circles, and discuss implications for the photon spheres of Schwarzschild, Reissner-Nordström, as well as continuous mass models solving the Tolman-Oppenheimer-Volkoff equation. Moreover, we derive an isopermetric inequality for gravitational lensing in Riemannian optical geometry, using curve-shortening flow and the Gauss-Bonnet theorem.
Duke Scholars
Published In
Pure and Applied Mathematics Quarterly
DOI
EISSN
1558-8602
ISSN
1558-8599
Publication Date
January 1, 2020
Volume
16
Issue
3
Start / End Page
495 / 514
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Roesch, H. P., & Werner, M. C. (2020). The isoperimetric problem in riemannian optical geometry. Pure and Applied Mathematics Quarterly, 16(3), 495–514. https://doi.org/10.4310/PAMQ.2020.v16.n3.a6
Roesch, H. P., and M. C. Werner. “The isoperimetric problem in riemannian optical geometry.” Pure and Applied Mathematics Quarterly 16, no. 3 (January 1, 2020): 495–514. https://doi.org/10.4310/PAMQ.2020.v16.n3.a6.
Roesch HP, Werner MC. The isoperimetric problem in riemannian optical geometry. Pure and Applied Mathematics Quarterly. 2020 Jan 1;16(3):495–514.
Roesch, H. P., and M. C. Werner. “The isoperimetric problem in riemannian optical geometry.” Pure and Applied Mathematics Quarterly, vol. 16, no. 3, Jan. 2020, pp. 495–514. Scopus, doi:10.4310/PAMQ.2020.v16.n3.a6.
Roesch HP, Werner MC. The isoperimetric problem in riemannian optical geometry. Pure and Applied Mathematics Quarterly. 2020 Jan 1;16(3):495–514.
Published In
Pure and Applied Mathematics Quarterly
DOI
EISSN
1558-8602
ISSN
1558-8599
Publication Date
January 1, 2020
Volume
16
Issue
3
Start / End Page
495 / 514
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics