# Writing the EFE in a different form

• Matterwave
In summary, the conversation discusses the search for the EFE's written in terms of the metric tensor and stress-energy tensor. The possibility of using software like Maxima and ctensor or cadabra is mentioned, but the speaker is not familiar with it. They recall using it for a previous presentation but cannot find the complete expression. The conversation ends with the suggestion to reconstruct it manually from a Wikipedia article, but due to time constraints, the speaker cannot do it at the moment.
Matterwave
Gold Member
Anyone know where I can, possiblely, find the EFE's written only in terms of the metric tensor and the stress-energy tensor? I know that the Ricci Curvature tensor and the Ricci scalar are derived (eventually) from the metric tensor (after a roundabout way through Christoffel symbols). The expression, I would think would be immensely long, but is there a place that has it?

You could probably generate it using software like Maxima and ctensor, or cadabra.

I.C. I'm not familiar with such software...do you think any website may have it?

It's not that important, I'd just like to see the thing so it becomes a little more concrete in my mind.

I did that for a presentation a couple of years ago, but I can't seem to find the latex file with the complete expression. As I remember, there were around 50 terms on the LHS, with all sorts of permutations of up to 4 factors of g per term, the whole thing looked remarkably messy and lacked any visible patterns.

You can reconstruct it by hand in less than an hour, starting here

http://en.wikipedia.org/wiki/Einstein_tensor

Ok, I may do that sometime...I just don't have the time right now hehe, essay for school due tomorrow, and I haven't started yet! D=

## 1. What is the EFE?

The EFE, or Einstein field equations, are a set of equations that describe the relationship between matter, energy, and the curvature of spacetime in Einstein's theory of general relativity.

## 2. Why would someone want to write the EFE in a different form?

Writing the EFE in a different form can provide a more elegant or simplified representation of the equations, making them easier to solve or interpret. It can also reveal new insights or connections between different physical phenomena.

## 3. How can the EFE be rewritten?

The EFE can be rewritten in various forms, such as using different mathematical notations or rearranging the equations in a different order. It can also be expressed in different coordinate systems or with different variables representing physical quantities.

## 4. Are there any limitations to rewriting the EFE in a different form?

While rewriting the EFE can offer advantages, there are limitations to consider. The rewritten form must still accurately represent the physical phenomena described by the original equations, and it should not introduce any new assumptions or constraints.

## 5. What are some examples of rewritten forms of the EFE?

Some examples of rewritten forms of the EFE include the Hamiltonian formulation, which expresses the equations in terms of canonical variables, and the vacuum field equations, which describe the behavior of empty space without matter or energy. Other examples include the Newman-Penrose formalism and the conformal gravity formulation.

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