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Flatly foliated relativity

Publication ,  Journal Article
Bray, H; Hamm, B; Hirsch, S; Wheeler, J; Zhang, Y
Published in: Pure and Applied Mathematics Quarterly
January 1, 2019

Flatly Foliated Relativity (FFR) is a new theory which conceptually lies between Special Relativity (SR) and General Relativity (GR), in which spacetime is foliated by flat Euclidean spaces. While GR is based on the idea that “matter curves spacetime”, FFR is based on the idea that “matter curves spacetime, but not space”. This idea, inspired by the observed spatial flatness of our local universe, is realized by considering the same action as used in GR, but restricting it only to metrics which are foliated by flat spatial slices. FFR can be thought of as describing gravity without gravitational waves. In FFR, a positive cosmological constant implies several interesting properties which do not follow in GR: the metric equations are elliptic on each euclidean slice, there exists a unique vacuum solution among those spherically symmetric at infinity, and there exists a geometric way to define the arrow of time. Furthermore, as gravitational waves do not exist in FFR, there are simple analogs to the positive mass theorem and Penrose-type inequalities. Importantly, given that gravitational waves have a negligible effect on the curvature of spacetime, and that the universe appears to be locally flat, FFR may be a good approximation of GR. Moreover, FFR still admits many notable features of GR including the big bang, an accelerating expansion of the universe, and the Schwarzschild spacetime. Lastly, FFR is already known to have an existence theory for some simplified cases, which provokes an interesting discussion regarding the possibility of a more general existence theory, which may be relevant to understanding existence of solutions to GR.

Duke Scholars

Published In

Pure and Applied Mathematics Quarterly

DOI

EISSN

1558-8602

ISSN

1558-8599

Publication Date

January 1, 2019

Volume

15

Issue

2

Start / End Page

707 / 747

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

Citation

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Bray, H., Hamm, B., Hirsch, S., Wheeler, J., & Zhang, Y. (2019). Flatly foliated relativity. Pure and Applied Mathematics Quarterly, 15(2), 707–747. https://doi.org/10.4310/PAMQ.2019.v15.n2.a4
Bray, H., B. Hamm, S. Hirsch, J. Wheeler, and Y. Zhang. “Flatly foliated relativity.” Pure and Applied Mathematics Quarterly 15, no. 2 (January 1, 2019): 707–47. https://doi.org/10.4310/PAMQ.2019.v15.n2.a4.
Bray H, Hamm B, Hirsch S, Wheeler J, Zhang Y. Flatly foliated relativity. Pure and Applied Mathematics Quarterly. 2019 Jan 1;15(2):707–47.
Bray, H., et al. “Flatly foliated relativity.” Pure and Applied Mathematics Quarterly, vol. 15, no. 2, Jan. 2019, pp. 707–47. Scopus, doi:10.4310/PAMQ.2019.v15.n2.a4.
Bray H, Hamm B, Hirsch S, Wheeler J, Zhang Y. Flatly foliated relativity. Pure and Applied Mathematics Quarterly. 2019 Jan 1;15(2):707–747.

Published In

Pure and Applied Mathematics Quarterly

DOI

EISSN

1558-8602

ISSN

1558-8599

Publication Date

January 1, 2019

Volume

15

Issue

2

Start / End Page

707 / 747

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics