Initial Data for General Relativity: EFE

In summary, the conversation revolved around the topic of initial data in general relativity and how it is used to determine the metric at all later times. The speaker suggested reading a chapter on the Cauchy problem from a GR text and provided links to further readings on the subject.
  • #1
HomogenousCow
737
213
I'm getting pretty lost with how initial data works in general relativity.
Assuming the energy momentum tensor is known (coupled with the metric somehow), what is initial data required to determine the metric at all later times?
 
Physics news on Phys.org
  • #2
The initial value problem is an extremely standard topic in most (all?) advanced GR texts. You would benefit much more from a thorough reading of a chapter on the Cauchy problem from a GR text and subsequently asking more specific questions here. See for example chapter 10 of Wald. You can also find a lot of readings online on the Cauchy problem e.g.

http://www.icm2006.org/proceedings/Vol_III/contents/ICM_Vol_3_22.pdf

http://arxiv.org/pdf/gr-qc/0002074v1.pdf

http://projecteuclid.org/download/pdf_1/euclid.cmp/1103841822

See also chapter 27 of Geroch's GR notes: http://home.uchicago.edu/~geroch/Links_to_Notes.html
 
Last edited by a moderator:

Related to Initial Data for General Relativity: EFE

What is initial data for General Relativity?

Initial data for General Relativity refers to the initial conditions or parameters that are used to solve Einstein's field equations (EFE). These initial conditions consist of the spacetime geometry and matter distribution at a specific instant in time, which are used to predict the evolution of the universe over time.

What are Einstein's field equations (EFE)?

Einstein's field equations are a set of equations formulated by Albert Einstein in his theory of General Relativity. These equations describe the relationship between the curvature of spacetime and the distribution of matter and energy within it. They are used to model the gravitational interactions between objects in the universe.

What is the role of initial data in solving EFE?

The initial data provides the starting point for solving the EFE. By plugging in the initial conditions for the spacetime geometry and matter distribution, the EFE can be solved to determine the evolution of the universe over time. Without proper initial data, the EFE cannot be accurately solved.

What are some examples of initial data used in solving EFE?

Examples of initial data include the mass and energy distribution of matter in the universe, the initial velocities and positions of objects, and the initial conditions of the spacetime geometry (such as the initial curvature and metric tensor).

How is initial data for General Relativity obtained?

Initial data for General Relativity can be obtained through various methods, including observations of the universe, simulations, and theoretical models. The data is then used to create a mathematical representation of the initial conditions, which can be plugged into the EFE for solving.

Similar threads

  • Special and General Relativity
Replies
4
Views
555
  • Special and General Relativity
Replies
3
Views
1K
  • Special and General Relativity
6
Replies
186
Views
7K
  • Special and General Relativity
Replies
2
Views
1K
  • Special and General Relativity
Replies
19
Views
1K
  • Special and General Relativity
Replies
17
Views
1K
  • Special and General Relativity
Replies
7
Views
2K
  • Special and General Relativity
3
Replies
95
Views
4K
  • Special and General Relativity
Replies
10
Views
268
  • Special and General Relativity
Replies
7
Views
1K
Back
Top