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The isoperimetric problem in riemannian optical geometry

Publication ,  Journal Article
Roesch, HP; Werner, MC
Published in: Pure and Applied Mathematics Quarterly
January 1, 2020
Published version (DOI)

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

Marcus Christian Werner
Author Marcus Christian Werner DKU Faculty

Published In

Pure and Applied Mathematics Quarterly

DOI

10.4310/PAMQ.2020.v16.n3.a6

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

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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

10.4310/PAMQ.2020.v16.n3.a6

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