Kartik Prabhu
replied to a post on Twitter with
The electric potential (which is the analog of surface gravity) is indeed constant as I showed in my thesis (Sec. 3 Theorem 1). The electric flux E.n is more analogous to the area element/ Noether charge which need not be constant.
Send me (Learn more)

Replies

Steve McCormick
replied on Twitter with
Thanks guys! I knew I could count on Twitter :) My gut feeling is that static -> nice/symmetric etc. so it hard to imagine a solution with varying flux, but the comparison to area element makes it seem more reasonable. Do you know of explicit examples where it’s nonconstant?
Kartik Prabhu
replied on Twitter with
I also expect static to imply that the electric flux/area element is constant, but I really have no idea how to show that without using global results like Birkhoff’s theorem or uniqueness (in the stationary case). Somehow our guts know about global results that our brains don’t!
Steve McCormick
replied on Twitter with
Yeh, that’s sort of what I’m thinking as well — Some weird stuff can happen if you allow for strange asymptotics, and this is harder to grasp intuitively. For example, there can be toroidal horizons, which could give counterexamples (?) 🤷🏻‍♂️
Kartik Prabhu
replied on Twitter with
anything violating the uniqueness theorems would be fair game: asymptotics, higher dimensions, modified gravity… But getting an explicit counter-example seems pretty hard. Would be nice to have some local existence proof though not sure how to even approach that!
Steve McCormick
replied on Twitter with
Yeah, I might ask around. I am beginning to feel like it’s not actually true without assuming global properties though. If it were something you could prove locally, then there aren’t really *that* many ways you could approach it. So I feel if it were true, it’d be known by now