When I look at electric or magnetic fields, each of them has a constant that defines how a field affects or is affected by a medium. For example, electric fields in vacuum have a permittivity constant $ϵ_0$ embedded in the electric field expression of a point charge: $E = q/4π ϵ_0r^2$. However, if I put this point charge in some dielectric that has a different permittivity constant $ϵ$, the value of the electric field changes. On a similar note, magnetic fields behave very similar but have the permeability constant $μ_0$ instead.
From my understanding, I believe that this is not the case for gravitational fields since the universal gravitational constant $G$ is consider to be a fundamental constant. So I am assuming that even though gravitational fields do operate in different types of mediums, this somehow doesn’t affect the gravitational field value. My question is why is this the case, that is, why isn’t there a permittivity-type constant for gravitation?
Answer
Permittivity $\varepsilon$ is what characterizes the amount of polarization $\mathbf{P}$ which occurs when an external electric field $\mathbf{E}$ is applied to a certain dielectric medium. The relation of the three quantities is given by
$$\mathbf{P}=\varepsilon\mathbf{E},$$
where permittivity can also be a (rank-two) tensor: this is the case in an anisotropic material.
But what does it mean for a medium to be polarized? It means that there are electric dipoles, that units of both negative and positive charge exist. But this already gives us an answer to the original question:
There are no opposite charges in gravitation, there is only one kind, namely mass, which can only be positive. Therefore there are no dipoles and no concept of polarizability. Thus, there is also no permittivity in gravitation.
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