# Talk:Einstein field equations

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## Whether the geodesic equation is dependent on EFE?

To Michael C Price (talk · contribs): You said "GE is independent of EFE." and provided a reference. Although many people say that they are independent, none-the-less they are not. See Post-Newtonian expansion which has an external link to "ON THE MOTION OF PARTICLES IN GENERAL RELATIVITY THEORY" by Albert Einstein and Leopold Infeld. Basically, each elementary particle is viewed as a (possibly charged) (possibly rotating) black-hole — a gravitational monopole. The ability to match these local solutions to the surrounding metric field, without introducing gravitational dipoles and thus negative energy, uniquely determines the motion of the particles. JRSpriggs (talk) 21:02, 27 September 2011 (UTC)

That shows that disturbances in the metric are determined by the EFEs, as we would expect, but says nothing about actual particles. I think most physicists would concede that particles are more than just metric distortions, despite Einstein's love of the idea. -- cheers, Michael C. Price talk 21:47, 27 September 2011 (UTC)

Is inacurate, as the gridding should converge towards the core of the depicted Mass.. — Preceding unsigned comment added by 120.148.18.177 (talk) 00:28, 17 July 2012 (UTC)

## Invariant formulation

Meanwhile there is an invariant (basis free) formulation of curvature structures (by Singer and Thorpe) and hence an invariant formulation of the field equations. In this formulation the Lorentzgroup easily is chased around the structures. The index notation here is disgusting and not very powerful! — Preceding unsigned comment added by 130.133.134.44 (talk) 18:12, 29 June 2012 (UTC)

## EFE in spinor formalism

I think, it's useful to have a section about EFE in spinor formalism. Anyone has a comment?Earthandmoon (talk) 08:26, 22 December 2013 (UTC)

I would be interested in that, if you know enough about it to write a section on it. JRSpriggs (talk) 06:41, 23 December 2013 (UTC)
Oh, i'm not familiar with spinor. :( Earthandmoon (talk) 15:53, 23 December 2013 (UTC)

## Should the equations be named after Einstein, Hilbert, or both?

IP user 12.72.186.xx has twice changed the name of the equations from "Einstein field equations (EFE)" to "Einstein-Hilbert field equations (EHFE)". His edit summaries explain this by saying "Einstein field equations should correctly read Einstein-Hilbert field equations with Hilbert having them before Einstein in the form of Hamilton's principle" and "Hilbert had the same equations before Einstein in the form of Hamilton's principle with the Ricci curvature scalar as the Lagrange density". As I said when I reverted him the first time, "whether or not Hilbert deserves credit, it is called EFE, not HFE or EHFE".

To aid the users' understanding and searches for terms, we are required to use the most common names for things (in reliable sources) regardless of the origin or technical accuracy of the name. See WP:AT for the application of this to article names. It is not appropriate to re-argue here the issues discussed at Relativity priority dispute#General relativity and History of general relativity#Einstein and Hilbert.

If you wish to change the name, please provide evidence that most reliable sources refer to the equations by a different name than that which has historically been used in this article (i.e. EFE). JRSpriggs (talk) 01:17, 31 March 2014 (UTC)

## Proper definition of trace

It should be clarified that the trace is the trace defined according to the metric not the banal (Euclidean) trace of a matrix.TonyMath (talk) 14:22, 14 April 2015 (UTC)

Calling it a trace at all is a misnomer, IMO, the result of a degree of sloppiness in terminology. A trace is really only defined on a tensor over a pair of indices of opposite variance, and the term "trace with respect to the metric" is probably an attempt to find a brief description that sort of works. I agree with the sentiment, and have made the suggested change, but would like to see a more precise description, perhaps a term involving "contraction" rather than "trace". —Quondum 20:33, 14 April 2015 (UTC)
Agreed but I am nonetheless happier with this result. At least the hyperlink is going to the right place.TonyMath (talk) 04:52, 18 April 2015 (UTC)

## 10 equations?

The introduction says there are 10 equations, but nowhere in the article does it identify which are the 10 equations. — Preceding unsigned comment added by 23.242.49.114 (talk) 00:31, 24 March 2016 (UTC)

The ten equations are:
${\displaystyle R_{00}-{\tfrac {1}{2}}R\,g_{00}+\Lambda g_{00}={\frac {8\pi G}{c^{4}}}T_{00}}$
${\displaystyle R_{01}-{\tfrac {1}{2}}R\,g_{01}+\Lambda g_{01}={\frac {8\pi G}{c^{4}}}T_{01}}$
${\displaystyle R_{02}-{\tfrac {1}{2}}R\,g_{02}+\Lambda g_{02}={\frac {8\pi G}{c^{4}}}T_{02}}$
${\displaystyle R_{03}-{\tfrac {1}{2}}R\,g_{03}+\Lambda g_{03}={\frac {8\pi G}{c^{4}}}T_{03}}$
${\displaystyle R_{11}-{\tfrac {1}{2}}R\,g_{11}+\Lambda g_{11}={\frac {8\pi G}{c^{4}}}T_{11}}$
${\displaystyle R_{12}-{\tfrac {1}{2}}R\,g_{12}+\Lambda g_{12}={\frac {8\pi G}{c^{4}}}T_{12}}$
${\displaystyle R_{13}-{\tfrac {1}{2}}R\,g_{13}+\Lambda g_{13}={\frac {8\pi G}{c^{4}}}T_{13}}$
${\displaystyle R_{22}-{\tfrac {1}{2}}R\,g_{22}+\Lambda g_{22}={\frac {8\pi G}{c^{4}}}T_{22}}$
${\displaystyle R_{23}-{\tfrac {1}{2}}R\,g_{23}+\Lambda g_{23}={\frac {8\pi G}{c^{4}}}T_{23}}$
${\displaystyle R_{33}-{\tfrac {1}{2}}R\,g_{33}+\Lambda g_{33}={\frac {8\pi G}{c^{4}}}T_{33}}$
Since all these tensors are symmetric, the six equations where the first index is larger than the second are redundant, and thus not counted. JRSpriggs (talk) 16:48, 24 March 2016 (UTC)

## Einstein field equations

The typical reasoning about space-time curvature is since light travels in a curve around massive objects, space time must be curved.  In fact, the effective refractive index of space time around the massive object is increased because spacetime is compressed around these objects.  The only curving involved is when light moves into a medium of different refractive index. Len loker (talk) 06:30, 26 March 2016 (UTC)

Is gravity due to: curvature of space-time, a force proportional to mass, or a change of refractive index? I think that it is more useful to think of these as several different, but equivalent ways of thinking about what is happening. JRSpriggs (talk) 01:01, 28 March 2016 (UTC)

## Why are those equations called "Einstein" field equations here ?

Those equations were introduced as "Hilbert field equations" at my university and many - maybe most - scientific papers also call them Hilbert field equations. I wonder, why they are called "Einstein field equations" here ? This doesn't seem to reflect the scientific consensus. --Lambda C (talk) 01:42, 10 July 2016 (UTC)

Perhaps you should consider attending another university. YohanN7 (talk) 14:02, 11 July 2016 (UTC)

## The integral form of the equations?

It is unclear whether there is an integrated form of these equations? For example, see here. — Preceding unsigned comment added by 178.120.182.18 (talk) 12:22, 2 January 2017 (UTC)