# Linearized Gravity: Bimetric Theory of General Relativity?

• I
• dsaun777
In summary, the conversation discussed the concept of linearized gravity in general relativity and its relation to bimetric theory. It was clarified that linearized gravity does not involve two physical metrics, but rather expresses the metric in a useful form. The benefits of bimetric theory over adding another dimension to general relativity were also discussed, with the conclusion that there are no proponents of this theory present. Finally, the possibility of different speeds for electromagnetic radiation and gravitational waves was mentioned, with a reference to a specific paper.

#### dsaun777

Is the linearized gravity that describes the gravitational waves of general relativity a bimetric theory of gravity? Your adding the flat spacetime metric of minkowski spacetime to the perturbed metric, usually denoted h, to arrive at g.

dsaun777 said:
Is the linearized gravity that describes the gravitational waves of general relativity a bimetric theory of gravity?
No.

dsaun777 said:
Your adding the flat spacetime metric of minkowski spacetime to the perturbed metric, usually denoted h, to arrive at g.
No, you're expressing the metric g, to linear order, as a sum of the flat metric and the perturbation. That doesn't mean there are two metrics in the theory. It just means you're expressing the single metric in a useful form given that the perturbation is small.

• vanhees71
PeterDonis said:
No.

No, you're expressing the metric g, to linear order, as a sum of the flat metric and the perturbation. That doesn't mean there are two metrics in the theory. It just means you're expressing the single metric in a useful form given that the perturbation is small.
How does this differ from bimetric theory? What's the benefit of a bimetric theory over just adding another dimension to General
Relativity?

dsaun777 said:
How does this differ from bimetric theory?
A bimetric theory says there are two different physical metrics. In linearized gravity there is only one physical metric, g.

• vanhees71
dsaun777 said:
What's the benefit of a bimetric theory over just adding another dimension to General
Relativity?
I'm not sure what you mean by "adding another dimension to General Relativity", since that has nothing to do with what linearized gravity does.

As for the benefits of bimetric theory, you would have to ask its proponents.

• vanhees71
PeterDonis said:
I'm not sure what you mean by "adding another dimension to General Relativity", since that has nothing to do with what linearized gravity does.

As for the benefits of bimetric theory, you would have to ask its proponents.
Are there any proponents of the theory here? I'm not suggesting linearized gravity does have any to do with higher dimensions.

dsaun777 said:
Are there any proponents of the theory here?
Not that I'm aware of. If you can give a specific reference to a paper that describes the bimetric theory of gravity you are interested in, you might have a better chance of getting the attention of someone who knows about it.

Bimetric theories have been used to explore the possibility of different speed for EM radiation and gravitational waves, i.e. as test theories. Here is an example:

https://arxiv.org/abs/gr-qc/0403060

• vanhees71 and PeterDonis
PeterDonis said:
Not that I'm aware of. If you can give a specific reference to a paper that describes the bimetric theory of gravity you are interested in, you might have a better chance of getting the attention of someone who knows about it.
No specific paper in general. I just wanted to have some people interject their thoughts on a variable a speed of gravity or speed of light.