/sci/ - Science & Math

[PKM No.3213626]

Gravity is a property of energy. (energy has gravity)
Gravity is also a form of energy. (Gravitational potential energy)
How does this work? Thinking through this leads to gravity having gravity of it's own, which has gravity of it's own etc.
Can someone explain this to me?

[Anonymous No.3213629]

Your wrng and nobody knows thread

[Anonymous No.3213643]

>>3213626
Gravitational potential is not potential energy. It is when a particle enters the potential, part of it's energy gets transformed into potential E from kinetic E.

[Anonymous No.3213650]

Gravitational potential energy does not mean gravity is a form of energy. Gravity is a force.

Since now you know that gravity is not energy, you can sleep soundly knowing that gravity does not have it's own gravity.

[Anonymous No.3213659]

>>3213643
Or you can stick to only kinetic energy but the particle will fly on longer trajectory (since space curved). After you project the whole thing from curved surface into flat you will get that the object will be shorter as well (lower wavelength higher f).

But for the sake of simplicity and similarity to another analogies it's better to stick to kinetic and potential energies.
- please correct me if I'm wrong.

[PKM No.3213674]

Okay then. Different question. Energy has gravity. Therefore photons have gravity. Could a singularity made entirely of photons exist?

[Anonymous No.3213773]

>>3213626
The fact that the gravitational field (Christoffel Symbols, if you will) is itself a potential for particles and therefore recouples to the gravitational field itself is taken into account by the einstein field equation by them being nonlinear - in contrast to say...most other equations in classical machanics - which therefore fulfill the superposition principle (Newton, Maxwell, Schrödinger, however not Boltmann (that mutherfucker))

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

http://upload.wikimedia.org/math/3/f/5/3f50fd206f2fe543a6a8a3e687cf74c3.png

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

here you see something in the sense of

R(g)=T

where R is a function of the spacetime metric (the fundamental variable in general relativity which brings the Christoffel Symbols and therefore the "force")

T is the energy(-tensor), your photons for example.

since R is "g^2" (it's much more complicated than that of course) the equations are nonlinear and therefore
>Thinking through this leads to gravity having gravity of it's own, which has gravity of it's own etc.
is kinda true.
R is
http://en.wikipedia.org/wiki/Riemann_tensor
which is a function of R

However, if there is really only empty space then gravity has no energy in the direct sense, i.e. there is no T(g) (and only T).
So yes, there is this effect, but not in this way.

In the case that T=0 (really just gravity), you have an Einstein manifold

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

If you have an electric field F, then T=F^2
see
http://en.wikipedia.org/wiki/Electromagnetic_stress-energy_tensor

If you find a solution with
R(g)=T=F^2, where g is singular, then yes, you have singularity from Photons only - but I don't know about such a solution (there are view solutions of the Einstein equation, due to the nonlinarity)

[Anonymous No.3213787]

Boltzmann*
(and oops, I'm not implying the Schrödinger equation is classical)

and I just saw the Christoffel symbold wiki page
http://en.wikipedia.org/wiki/Christoffel_symbols
is a bit technical. whatever, relevant for this discussion is the part
>In general relativity, the Christoffel symbol plays the role of the gravitational force field with the corresponding gravitational potential being the metric tensor.
where the metric g is
http://en.wikipedia.org/wiki/Metric_tensor

and
>R(g)=T
was supposed to be a shortcut for
http://upload.wikimedia.org/math/3/f/5/3f50fd206f2fe543a6a8a3e687cf74c3.png

[Anonymous No.3213796]

I don't know if anyone knows what state things are in after they enter a black hole (aka: singularity).

Light (aka: energy) gets sucked into black holes. However, know that all energy has an associated amount of mass, albeit maybe not rest mass.

[Anonymous No.3213813]

>>3213773
>>3213787

Wow, that made me wet for math/physics. My co-worker just finished general relativity, super jealous.

[Bruised !crow0v0ifw No.3213848]

<span class="math"> R_{\mu \nu} + \frac{R}{2} g_{\mu \nu} = T_{\mu \nu} [/spoiler]
The traditional energy and momentum information is contained within <span class="math"> T_{\mu \nu} [/spoiler]. Although this does not incorporate gravitating energy-momentum which are contained, as >>3213773 said, in the Christ-awful symbols (which are part of the Ricci Tensor).
If you want to write the total energy of the system in terms of a single tensor (pseudotensor) see http://en.wikipedia.org/wiki/Landau-Lifshitz_pseudotensor .

>Thinking through this leads to gravity having gravity of it's own, which has gravity of it's own etc.
It does, but the effects converge, not diverge. You could probably prove this via some fiddling of the Landau-Lifshitz pseudotensor.

[Anonymous No.3213849]

Don't think too hard about it. Since there isn't a unifying theory it means something isn't actually right. Most everyone agrees what's weird is gravity. And it's a completely abstract concept so....sure gravity has it's own gravity....whatever, doesn't matter as long as the functions work.

[Anonymous No.3213917]

Do you guys know how to express gravitational field emitted by a photon? Because apparently if there are photons flying parallel to each other they don't affect each other by gravitational interaction - is that true?

[Anonymous No.3213935]

>>3213917
Actually I just realize it makes sense. Frequency of two parallel photons with respect to each other is zero, hence momentum. hence energy hence no gravit. field. But for an outside moving observer there would have been gravit field.

Which brings me next question do photons lose energy as they travel through space due to emitting gravitational waves?

[Anonymous No.3214020]

>>3213935
The word photon is a bit difficult if you talk about classical general relativity, since there the electromagnetic field is not quantized: You would be talking about a plane wave or so. However, if the momentum is fixed, like with a photon, then the plane wave exp(ikx) is pretty much non-localized.

Anyway, I don't know the solutions by heart, but if you really have only photons/electromagnetic field and no currents or charge densities, then

http://upload.wikimedia.org/math/1/1/c/11cca0c5c0d7949ff9a6ce0dbfdf597a.png

this is "obviously" traceless

T^\mu_\mu=0

therefore, plugging that into

http://upload.wikimedia.org/math/3/f/5/3f50fd206f2fe543a6a8a3e687cf74c3.png

you see that R (curvature tensor, here R is rather R_\mu\nu but I was sloppy above) is traceless, i.e. R=0 (ricci scalar is zero), and so light alone doesn't really change spacetime too much. There is a reason why all the black hole solutions, high curvature, have mass in the middle.

don't know if you know what a trace is though, so this might not help

[Anonymous No.3214029]

okay, I'm sorry since actually there a now three curvatures R floating around (Riemann curvatur, Ricci curvature and Ricci scalar), with 4, 2 and 0 indices.

[Anonymous No.3214212]

>>3214020
But can a planar wave lose energy due to emitting gravitational waves in general? I mean assuming the planar wave was travelling for a very long time (10^6 10^10 years)
is it possible that the astronomical red shift is partially contributed by this phenomena? - I still assume that universe expands etc. not questioning the big bang theory since red shift is not the only experimental evidence of it. But it might be still interesting to know whether there is any such distortion or not.

[ႼЋïŁႣƧტƿḩЄƦṥ !Scone2booQ No.3214269]

>>3213626
Gravity is potential energy. Potential energy is negative energy. It it is the negative energy that balances out the positive energy in the form of matter (or any other form). So no, gravity doesn't have its own gravity, because it is not positive energy.