Gravity and Electromagnetic Radiation: Exploring the Relationship

[Denton]

Does electromagnetic radiation have its own gravitational field ~ If you were to convert the mass of the Earth into gamma rays (possibly with antimatter) and contain it inside some sort of reflective box, would the effects of the Earth's gravity remain, or does converting matter into energy 'destroy' gravity.

On a side note, would placing a black hole adjacent and at a particular distance away from another black hole flatten their respective gravitational wells and normalise them?

 

[Dale]

If you were to convert the mass of the Earth into gamma rays (possibly with antimatter) and contain it inside some sort of reflective box, would the effects of the Earth's gravity remain, or does converting matter into energy 'destroy' gravity.

Yes, the gravity would remain. In GR the source of the gravitational field (curvature of spacetime) is not mass specifically, but rather the stress-energy tensor. Mass has a lot of energy, but it is not the only form of energy.

 

[element4]

(Im just repeating what DaleSpam said, just in different words. Sorry if its too "pedagogical", in the negative sense.)

In Einsteins General theory of relativity, gravitation is not just a force (like in Newtonian gravity, which is the lowest order approximation) but rather the geometric structure of the 4-dimensional space-time. If spacetime curves, we have gravitation, if its flat, there is no gravitation!

The curvature of spacetime is caused by energy and momentum density. It doesn't matter where the energy is from. If you for example have some charge, with mass=0, the electromagnetic field will "bend" the spacetime and then gravitation will occur! (Note, without any mass). And the same thing with electromagnetic radiation (poyting vector).

In our "everyday experience" the gravitation duo to mass is by far the most dominating (because there is for example much more mass on the planets, that charge), and that's why humans in very long time thought that gravitation was only present if mass was present!

It must be said that gravitation is a very weak force, because the spacetime requires LOTS of energy before it will curve!

 

[JinChang]

This is very interesting topic since it's similar to one of my past post where I asked if gravity can exist without mass.

If the cause of the gravity is stress-energy-tensor, then would it not imply that gravity should be "relative" to the stress-energy-tensor of its surroundings (i.e. space-time fabric)? Or, is there a true "empty" stress-energy-tensor region where one can safely say that no gravity exists. I guess this question is somewhat similar to the OP's second question.

Also, I read somewhere that "pressure" is involved when it comes to referring to gravity in terms of stress-energy-tensor. Not sure how that fits in. Anyone care to explain, preferably in layman's terms?

 

[element4]

Also, I read somewhere that "pressure" is involved when it comes to referring to gravity in terms of stress-energy-tensor. Not sure how that fits in. Anyone care to explain, preferably in layman's terms?

Pressure can get involved in the simple cosmological models describing the universe as a whole, where galaxies, clusters of galaxies and even clusters of clusters of galaxies is seen as point particles!
One would usually postulate that the universe is (globally) homogeneous and
isotropic, then describe it as a perfect fluid (no viscous effects). The idea is similar to how we describe gases. The energy-momentum tensor can have the form (taken from fluid mechanics)

$$T_{\mu}_{\nu} = pg_{\mu}_{\nu} + (p+\rho)U_{\mu}U_{\nu}$$​

where p is pressure, $$\rho$$ is the density, $$U_{\mu}$$ is the 4-velocity (in co-moving coordinates, $$U^{\mu} = (1,0,0,0)$$) and $$g_{\mu}_{\nu}$$ is the stress tensor (describing the curvature of spacetime). Thats a way pressure can get involved (bear in mind, that its because we want to describe the universe as as whole. If we wanted to describe the curvature of spacetime duo to very few "objects", pressure would not get involved).

For further information, you can search for "The cosmological standard model".

 

[Dale]

If the cause of the gravity is stress-energy-tensor, then would it not imply that gravity should be "relative" to the stress-energy-tensor of its surroundings (i.e. space-time fabric)?

The whole reason for using tensors is that tensors are "absolute" in the sense that all frames agree on them, not "relative" to a given frame.

 

[Naty1]

Does light influence space?

yes...if you take "space" to be something...Some here say space is "nothing" and so would say "curvature" is only a mathematical representation. I prefer to think of space as "something" where vacuum energy (and the cosmological constant) resides...

Because light is electromagnetic energy, it will slightly influence the curvature of space.

Or, is there a true "empty" stress-energy-tensor region where one can safely say that no gravity exists.

Mathematically you can describe such a region; in practice there is always some form a gravitational influence present due to mass,energy and or pressure...hence some curvature. If you consider a small enough region (akin to taking a derivative dx) such that curvature is negligible (space is flat) then for practical purposes you can ignore gravity...this follows from "local" frames in general relativity...

 

[The Dagda]

How could you measure a region where there is no energy or particles anyway? In space gravitation is never 0, it can approach it but never reach it except hypothetically.