To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

4,5
Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
Added in 24 Hours
Languages
Recent
Show all languages
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.
.
Leo
Newton
Brights
Milds

Hawking energy

From Wikipedia, the free encyclopedia

The Hawking energy or Hawking mass is one of the possible definitions of mass in general relativity. It is a measure of the bending of ingoing and outgoing rays of light that are orthogonal to a 2-sphere surrounding the region of space whose mass is to be defined.

YouTube Encyclopedic

  • 1/3
    Views:
    172 898
    886 600
    1 530 587
  • Negative Energy - Stephen Hawking's Grand Design
  • Anti-gravity and the True Nature of Dark Energy | Space Time | PBS Digital Studios
  • What Stephen Hawking Really Said About Black Holes

Transcription

Definition

Let be a 3-dimensional sub-manifold of a relativistic spacetime, and let be a closed 2-surface. Then the Hawking mass of is defined[1] to be

where is the mean curvature of .

Properties

In the Schwarzschild metric, the Hawking mass of any sphere about the central mass is equal to the value of the central mass.

A result of Geroch[2] implies that Hawking mass satisfies an important monotonicity condition. Namely, if has nonnegative scalar curvature, then the Hawking mass of is non-decreasing as the surface flows outward at a speed equal to the inverse of the mean curvature. In particular, if is a family of connected surfaces evolving according to

where is the mean curvature of and is the unit vector opposite of the mean curvature direction, then

Said otherwise, Hawking mass is increasing for the inverse mean curvature flow.[3]

Hawking mass is not necessarily positive. However, it is asymptotic to the ADM[4] or the Bondi mass, depending on whether the surface is asymptotic to spatial infinity or null infinity.[5]

See also

References

  1. ^ Page 21 of Schoen, Richard, 2005, "Mean Curvature in Riemannian Geometry and General Relativity," in Global Theory of Minimal Surfaces: Proceedings of the Clay Mathematics Institute 2001 Summer School, David Hoffman (Ed.), pp. 113–136.
  2. ^ Geroch, Robert (1973). "Energy Extraction". Annals of the New York Academy of Sciences. 224: 108–117. Bibcode:1973NYASA.224..108G. doi:10.1111/j.1749-6632.1973.tb41445.x. S2CID 222086296.
  3. ^ Lemma 9.6 of Schoen (2005).
  4. ^ Section 4 of Yuguang Shi, Guofang Wang and Jie Wu (2008), "On the behavior of quasi-local mass at the infinity along nearly round surfaces".
  5. ^ Section 2 of Finster, Felix; Smoller, Joel; Yau, Shing-Tung (2000). "Some recent progress in classical general relativity". Journal of Mathematical Physics. 41 (6): 3943–3963. arXiv:gr-qc/0001064. Bibcode:2000JMP....41.3943F. doi:10.1063/1.533332. S2CID 18904339.

Further reading

This page was last edited on 28 October 2023, at 14:34
Basis of this page is in Wikipedia. Text is available under the CC BY-SA 3.0 Unported License. Non-text media are available under their specified licenses. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. WIKI 2 is an independent company and has no affiliation with Wikimedia Foundation.