In Jacobson's theory, space is thermodynamic. But what about the temperature of electromagnetic radiation?

Question

Following Jacobson ( https://arxiv.org/abs/gr-qc/9504004 ), Padmanabhan, Verlinde and others, space is due to microscopic degrees of freedom. They are unspecified, but have temperature and entropy.

I have a question nagging me. The temperature $T$ they talk about is related the the local gravitational acceleration $a$, and obeys $T = 1/a$ (with suitable constants added). In usual situations on earth, the temperature values are very low. In usual situations, say in a kitchen oven, the temperature is much higher by many orders of magnitude.

So let me put it bluntly: why does a kitchen oven not disturb gravity? It is much hotter, including the electromagnetic radiation in it.

I know that it sound like a facetious question - but I really want to understand this. Alternatively, I could also ask the following: why does the cosmic background radiation not disturb or influence gravity in the universe?

Answer 1

Relativity supplies the answer. A kitchen oven has energy (T being proportional to E) so does indeed 'disturb gravity', just not very much compared to your mass-energy (E=mc2 simplifying) waiting for dinner to cook.

As to the cosmic microwave background, well it also affects gravity as much as its energy i.e. negligible