Allowed fields in General Relativity

[kent davidge]

How do you know what fields can be coupled with the gravitational field? Is there a general procedure for knowing it or we have to try out and see whether it makes sense or not?

 

[Vanadium 50]

Can you defined "coupled with"?

 

[kent davidge]

Can you defined "coupled with"?

Interacting with each other

 

[martinbn]

Can you give an example of a field that cannot?

 

[Vanadium 50]

Interacting with each other

If it's not worth your time to write a complete sentence explaining what exactly you are looking for, how do you expect to get a good answer?

 

[haushofer]

We do know that coupling gravity to spins exceeding 2 gives problems, see e.g.

https://en.m.wikipedia.org/wiki/Higher-spin_theory

 

[kent davidge]

If it's not worth your time to write a complete sentence explaining what exactly you are looking for, how do you expect to tet a good answer?

And your lazy when you read my question instead of thinking about it, you claim it's incomplete.

We do know that coupling gravity to spins exceeding 2 gives problems, see e.g.

https://en.m.wikipedia.org/wiki/Higher-spin_theory

Thank you, that's an adequate type of answer.

 

[PeterDonis]

And your lazy when you read my question instead of thinking about it, you claim it's incomplete.

Your response was incomplete; "interacting with each other" is just as vague as "coupled with".

 

[PeterDonis]

that's an adequate type of answer

Sort of. It explains why fields of spin higher than 2 (even if they could consistently exist, which the other theorems referred to in that article indicate they can't) can't be consistently coupled to gravity. But it doesn't tell you anything about which fields of spin 2 or lower can couple to gravity. To really adequately answer the latter question, you need to come up with a precise definition of what "coupled with" (or "interacting with") means.

 

[Vanadium 50]

And your lazy when you read my question instead of thinking about it

You're right. Why is the onus on the reader to figure out what you mean rather than for you to write it clearly? Put another way, exactly how much more valuable do you think your time is than ours?

To really adequately answer the latter question, you need to come up with a precise definition of what "coupled with" (or "interacting with") means.

Exactly. Is this about trivial couplings, such as the fact that fields have energies associated with them? Or more than that?

 

[pervect]

What's usually referred to as "the coupling" can be derived from the Lagrangian, though I don't recall the details anymore. I'm not sure if this is what the OP is asking about, however.

For example equation 15 in "Kinetic energy and the equivalence principle", https://arxiv.org/abs/gr-qc/9909014. This calculates "the coupling", but it doesn't define it.

 

[sweet springs]

Any other field that has something to do with energy and momentum would have to relate with gravity through Einstein equation.

 

[PeterDonis]

Any other field that has something to do with energy and momentum

Which is any other field, period.

would have to relate with gravity through Einstein equation

On this view, "couples to gravity" simply means "has a stress-energy tensor", which any other field has, as above. But this does not address issues like the one raised above, about fields with spin greater than 2 not being able to consistently couple to gravity (such fields can still have a stress-energy tensor). So I don't think this works as an answer to what "coupling" means for this discussion.

 

[sweet springs]

Which is any other field, period.

Any field with energy and momentum other than gravitational field, e.g. electromagnetic field.

ut this does not address issues like the one raised above, about fields with spin greater than 2 not being able to consistently couple to gravity (such fields can still have a stress-energy tensor).

I have no idea how to deal with gravity and quantum object like particle spin. Thanks.

 

[Vanadium 50]

I got beat up for asking what the OP meant, but here we are, three days later, still trying to figure it out.