In the formula for the Unruh effect, temperature (of a photon gas mostly) is proportional to the acceleration of some classical observer. But how can that be? Temperature is a scalar, while acceleration is a vector. The cause of the effect obviously preferres one spatial direction, and Rindler coordinates reflect that. I have looked into an article explaining the Unruh effect in some detail (https://arxiv.org/pdf/1304.2833.pdf). This article explicitely states to restrict itself to 1+1 – dimensional spacetime, and so do some other sources I found. So, for the Unruh experiment taking place in our full spacetime, what is the distribution of the photons in 3-dimensional position space as well as in 3-dimensional momentum space? In contrast, Hawking temperature appears as quite plausible to me. But I assume that for black holes which are not spherically symmetric, i.e. rotating ones, temperature varies over the latitude. Is that right? Thank you in advance for any answers.