# Tag Info

### Einstein field equations from covariant derivative of a general linear gauge transformation

None. Nothing of this has anything to do with gravity. Your equation for "R" defines the gauge field curvature $F_{\mu\nu}$, not the Riemann curvature $R_{\alpha \beta\mu\nu}$.
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### Is space-time made of something?

General relativity can be viewed another way than space-time curvature: e=mc2 therefore gravitation energy has mass that follows Newton. Of course, this is a feedback situation: when gravitational ...
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### Does solving Einstein's field equation depend on Newtonian equations?

I recently heard, that there is a derivation of the field equations not using the Newtonian limit. The one I know of uses it though. We get $g_{00}=1-\frac{2\Phi}{c^2}$ out of the Newtonian limit of ...
Accepted

### Does solving Einstein's field equation depend on Newtonian equations?

When Einstein derived his equations the Newtonian limit (and it may be taken also in the present of sources) was an important check for the theory. It is also useful to understand the limits of the ...
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### Does solving Einstein's field equation depend on Newtonian equations?

If, in some limit, GR didn't reduce down to $\kappa \nabla ^{2}\phi = \rho$ for some constant kappa, (where $\phi$ is a gravitational potential such that ${\vec g} = {\vec \nabla}\phi$), then it ...
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### Is space-time made of something?

In theoretical physics there is always a 'choose your battles' judgement call to make. My favorite example in the history of physics is Newton proposing the inverse square law of gravity. Many of his ...
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### Is space-time made of something?

In a nutshell, General Relativity is an interpretation of gravity where instead of mass simply being attracted to mass, mass exists within a conglomeration of space and time and causes it to curve. ...
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### Is space-time made of something?

What exactly is the "spatial points" that can be curved? As far as we know, spacetime is not made of “things”. When we talk about curvature we are not talking about a material “thing” that ...
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### Can 1D beings in 1+1D determine if they are in a curved universe?

Are you assuming that the 1D beings can only learn by sensory stimulus? Assuming they have sufficient mathematics, why couldn't a 1D being determine that it was living in a single dimension of a ...

### Can 1D beings in 1+1D determine if they are in a curved universe?

There is no intrinsic curvature in 1D. If you work out the math you find that there are $n^2(n^2−1)/12$ independent components of the curvature tensor in $n$ dimensions. For 1D that is zero, and for ...
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### What should be the shape of spacetime to repel opposite masses from one another?

If you have a positive and a negative mass the negative mass will repel the positive one and the positive one will attract the negative one, so together they will form a runaway pair. The ...
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1 vote

### Could the curvature of spacetime, as in general relativity, result from the interaction of quantum fields?

Is it possible that the curvature of spacetime, as in general relativity, results from the interaction of those quantum fields with the fields of quantum matter? I find this phrasing a little weird, ...
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### Einstein field equations in empty space, question about non-zero curvature

It is a good question. Suppose there is only empty space, and nothing changes, no field no nothing, then what? ... well, as nothing changes there is no time (because time ... is change). For there to ...
1 vote

### Could the curvature of spacetime, as in general relativity, result from the interaction of quantum fields?

I'm gonna write a pretty quick and not much detailed answer, but to give you a quick idea. The first taught thing to quantize gravity is actually, that its quantum field behaves as a spin 2 particle ...
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### Why are distances to event horizons linear with mass when gravitational effects fall off as $1/r^2$?

Forget black holes, just think about Newtonian physics. The escape speed from some radius around a spherically symmetric mass is just where the sum of the kinetic and potential energy is zero. This ...
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### Why are distances to event horizons linear with mass when gravitational effects fall off as $1/r^2$?

Let's say that a 2 kg dumbbell is hanging 100 m above event horizon. Let's say that when said dumbbell is dropped into the hole the mass of the hole increases by 100 grams. (This can happen ...
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### Is space — as opposed to space-time — curved by a gravitating mass?

"Can we relatively freely rotate our 4 dimensional coordinate system for the universe's spacetime such that what was space before (time fixed, say at zero) is rotated "into" the time ...
Accepted

### Is space — as opposed to space-time — curved by a gravitating mass?

A few facts: In a 4-dimensional manifold such as spacetime you can pick any timelike direction and call it time in the vicinity of any given event. Directions orthogonal to this will then make up '...
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