# Assuming only rest mass as source of gravity and real observations

PAllen
2019 Award
PPN goes too far. If i understand correctly, it even exclude special relativity effects.
I'm interested in gravitational effects.
This is not true. The post Newtonion limit assumes weak gravity and slow speeds. The 1PN formalism describes this limit. However, the PPN methodology has been extended well beyond 3.5PN order, allowing consideration of fairly strong gravity and relativistic orbital motions. See section 4.1 of the following for minimum PN levels required for different cases:

http://relativity.livingreviews.org/Articles/lrr-2006-3/ [Broken]

Last edited by a moderator:
Dale
Mentor
Hi Quantum Immortal,

This comment by WBN is particularly important in this context.
When one combines special relativity with Coulomb's law one obtains the Maxwell equations
Note, that when one does combine special relativity with Coulomb's law the source of the field goes from being a scalar (the charge density) in Coulomb's law to being a four-vector (the four current) in Maxwell's equation. In other words, the process of "relativising" increased the rank of the tensor of the source.

The same thing happens with gravity. The rank of the source tensor increases for the relativistic theory compared to the non-relativistic theory.

Hi Quantum Immortal,

This comment by WBN is particularly important in this context.
Note, that when one does combine special relativity with Coulomb's law the source of the field goes from being a scalar (the charge density) in Coulomb's law to being a four-vector (the four current) in Maxwell's equation. In other words, the process of "relativising" increased the rank of the tensor of the source.

The same thing happens with gravity. The rank of the source tensor increases for the relativistic theory compared to the non-relativistic theory.
Yea, i have some understanding of electromagnetism.
i think this is playing with semantics. Or a philosophical difference if you want. A current is just a moving charge. It didn't transform to something completely different. It is still a charge. For movement, you don't need a new theory, special relativity should suffice.

Magnetism is just an imbalance in electrostatics due to relativistic length/time contractions of the currents ( =special relativity). We can experience the effects of these tiny contractions at slow speeds because electrostatics is extremely strong inside mater.

Yes, i admit my OP is a bit messy
When i said that the source is just the rest mass i meant it to be like the electric charge in electrmagnetism. The rest mass can have a current/move, and special relativity still applies.
I'm not asking about special relativity effects though, only stuff that are purely GR.

PeterDonis
Mentor
2019 Award
I think that you are just seeing the non relativistic models for these things.
Assuming that only rest mass is a source of gravity *is* non-relativistic; as has been said several times already in this thread, "rest mass" in the sense you appear to be using the term is not covariant, but the source of gravity has to be covariant in a relativistic theory.

You forget that the materials will just hit there limits eventually. Electrons eventually combine with protons to form neutrons, then neutrons merge to form a quark plasma, then sub quark physics takes over. Eventually you get a BH.....

I have hard believing, that there is some type of matter that can withstand arbitrary amounts of pressure.
In relativity, it's true that it is currently believed that any physically reasonable type of matter must obey what are called "energy conditions", one of which is, more or less, that the pressure can't be greater than the energy density. This does place a limit on the kinds of equation of state that matter can have, which places a limit on how dense a piece of matter can be and still support itself against gravity with some kind of pressure.

However, it is perfectly possible to have a stress-energy tensor that violates the energy conditions and still gives a self-consistent solution in GR. In fact, our best current belief is that the effective stress-energy tensors generated by quantum fields do violate the energy conditions in some physically relevant scenarios. One of them is Hawking radiation by black holes; another is the Casimir effect, in which vacuum fluctuations between two uncharged conducting plates create a small attractive force between the plates--this has actually been measured.

Having said all that, let me go back to a comment a little earlier in your post:

It seams to me, that the mass limits simply get increased.
*If* you could somehow concoct a relativistic theory in which only rest mass, not pressure, was a source of gravity, but which still obeyed the energy conditions I referred to above, then yes, I think you would still get a mass limit for objects like white dwarfs and neutron stars, but it would be a significantly higher limit than the one we actually observe. However, I'm not sure you could concoct a consistent theory of this type, for reasons which I and others have already given multiple times in this thread.

Dale
Mentor
i think this is playing with semantics. Or a philosophical difference if you want. A current is just a moving charge.
If that is playing with semantics then so is your worry about the stress energy tensor. A stress is just a moving momentum flux. The various components of the stress energy tensor have a similar relationship to each other as to charge and current density.

Furthermore, the point remains that current (regardless of its connection to charge) is not part of Coulombs law. To get a relativistically invariant theory form Coulombs law you have to increase the rank of your source tensor as well as add the other equations which describe those additional components.

With gravity it is the same.

I think that what you should be doing is trying to understand the stress energy tensor. You realize that charge and current are related, but don't seem to understand that the various components of the SET are also similarly related.