The Stefan-Boltzmann law says that a black body radiates energy at a rate $\sigma T^4$ per unit surface area, where $\sigma$ is the Stefan-Boltzmann constant.
I have always assumed this is an upper limit, i.e. no body can ever lose heat faster than this due to radiation. However, the Wikipedia article linked above claims that this limit can be exceeded for some metamaterials. The reference cited for this seems not to be super-famous, and since it's such a surprising result I'd like to check I've understood it.
To make my question as concrete as possible, let me set up a hypothetical experiment: suppose I have an infinitely conductive metal sphere of radius $r_1$, which contains a nuclear reactor that keeps its surface always at a fixed temperature $T$. Surround this physical sphere with an imaginary sphere of radius $r_2>r_1$. Inside this imaginary sphere we can place any kind of apparatus we want, but it's not allowed to stick out of the imaginary sphere, and it must operate in steady state, i.e. it can't have any power source besides the temperature difference between the metal sphere and its surroundings.
This whole thing is to be placed in empty space, far away from any stars, and the goal is to extract energy from the metal sphere and radiate it away at as high a rate as possible. (Any spectrum of radiation is acceptable - it doesn't have to be black body radiation.)
The obvious solution is to surround the metal sphere with an infinitely conductive sphere of radius $r_2$, with a completely black surface. This will extract heat from the metal sphere and radiate it away at a rate $4\pi r_2^2 \sigma T^4$. The question is, is it possible, in principle, to do better than this?
If it's not possible, then is Wikipedia's reference wrong, or is it just claiming something else (and if so what)? If it is possible, then how can this be achieved, and is there any fundamental limit to how fast a body can radiate?