Numerical Solutions to GR: Exploring the Computational Physics Field

In summary, the conversation discusses the use of "Numerical Solution" to General Relativity and whether it falls under the field of "Computational Physics". It involves using triangles as finite-coordinates to represent the hyper-surface and the challenges of defining quantities such as the metric, Riemann Tensor, and Energy-momentum tensor in this discrete space-time. The concept of "Regge Calculus" is mentioned as a potential solution, but the person is having trouble understanding its explanation and how it relates to recovering the Riemann Tensor.
  • #1
lokofer
106
0
Hello could someone give some info about the "Numerical solution" to GR...is this a field of "Computational Physics"?..

- What i know is that you take the Hyper-surface, and you " split " it into triangles..and use the ¿angles? of every triangle as finite-coordinates..then you get a problem with finite degrees of freedom...but What happens with the metric, Riemann Tensor Energy-momentum tensor in this discrete space-time?..could you use discrete espace but continuous time so the usual Einstein Lagrangian becomes a finite one in the form:

[tex] L(q_i ,\dot q_i ,t) [/tex] so it's easier to "Quantize" than the continuous one?..

- Main questions: how do you define [tex] g_{ab} [/tex] [tex] R_{ab} [/tex] and other quantities into a finite "triangularized" surface..thanks :rolleyes: :rolleyes:
 
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  • #2
Look up "Regge Calculus".
 
  • #3
robphy said:
Look up "Regge Calculus".

I was afraid of this answer... :cry: :cry: i have looked it up in "Wikipedia" and "Arxiv.org" but i don't see or can't understand the explanation...or how you recover the Riemann Tensor in the end...
 

1. What is numerical solution in the context of General Relativity (GR)?

Numerical solution in GR refers to using computational methods to solve the equations of General Relativity, which describe the behavior of gravity in the universe. These methods involve breaking down the equations into discrete steps and using mathematical algorithms to approximate the solutions.

2. Why is numerical solution important in GR?

Numerical solutions are important in GR because the equations of General Relativity are highly complex and cannot always be solved analytically. By using numerical methods, scientists and researchers can gain insight into the behavior of gravity in situations that are not easily described by analytical solutions. This allows for a deeper understanding of the universe and its properties.

3. What are some common numerical techniques used in GR?

Some common numerical techniques used in GR include finite difference methods, finite element methods, and spectral methods. These methods involve breaking down the equations into smaller, more manageable parts and using numerical algorithms to approximate the solutions. Other techniques such as Monte Carlo simulations and adaptive mesh refinement are also used in GR.

4. What are the challenges in using numerical solutions in GR?

One of the main challenges in using numerical solutions in GR is the high computational cost and complexity of the equations. This often requires powerful computers and sophisticated algorithms to accurately solve the equations. Additionally, numerical solutions may be limited in their applicability to certain situations and may not always capture the full complexity of the physical system being studied.

5. What are some current research areas in numerical solutions to GR?

Some current research areas in numerical solutions to GR include black hole simulations, gravitational wave detection and analysis, and cosmological simulations. Other areas of interest include studying the behavior of matter and energy in extreme gravitational environments and using numerical methods to explore the early universe. Ongoing advancements in computing technology are also enabling researchers to tackle more complex and challenging problems in GR using numerical solutions.

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