• Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.


PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback


(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,075 questions , 2,226 unanswered
5,347 answers , 22,743 comments
1,470 users with positive rep
818 active unimported users
More ...

  Is the Hawking radiation of a charged black hole thermal?

+ 10 like - 0 dislike

Suppose you have a Schwarzschild black hole of mass $M$ and angular parameter $a = 0$ (no rotation).

Question: is it possible to throw a charge $Q$ at a faster rate than it will be re-radiated? Will the radiation profile be still thermal?

If it is thermal, it would mean that even big, cold black holes would emit a lot of energy in the form of electromagnetic radiation just to be able to get rid of the extra charge? A thermal spectra that starts at $511\: \mathrm{KeV}$ (the energy of the lowest charged particles and has very little emitted power at lower energies) would be a very weird thing to call 'thermal'.

There is a differential expression for the increase in temperature as a small charge (compared to the black hole mass) is added to the black hole that one obtains by taking the formula 11.2.17 in this page (Modern Relativity, 2005, David Waite) and deriving against $e$ and $M$ and taking

$$ \delta T = ( \frac{\partial T}{\partial e} + \frac{c^2}{G} \frac{\partial T}{\partial M} ) \delta e$$

so this gives a profile for the variation of black hole temperature with charge.

Question: Is it correct to conclude that you can estimate the overall Hawking radiation of a relatively small black hole ($M \approx 10^{18} Kg$) by adding electric charge at a faster rate than it will be re-emitted by the thermal spectra?

Or is the spectra totally non-thermal, and the radiation will favour throwing away charged particles, while being electromagnetically cold?

This post imported from StackExchange Physics at 2016-07-10 09:14 (UTC), posted by SE-user lurscher

asked Dec 14, 2012 in Astronomy by CharlesJQuarra (555 points) [ revision history ]
edited Jul 10, 2016 by Dilaton
You probably have to solve the charged Dirac field in that metric. You should find more elections being emitted then positrons.

This post imported from StackExchange Physics at 2016-07-10 09:14 (UTC), posted by SE-user Prathyush
The real question is: how does Hawking radiation thwart our attempts at making a super-extramal hole by charging it up and allowing it to radiate, relying on the 511keV cutoff to prevent it losing charge as it loses mass?

This post imported from StackExchange Physics at 2016-07-10 09:14 (UTC), posted by SE-user Kevin Kostlan

This post imported from StackExchange Physics at 2016-07-10 09:14 (UTC), posted by SE-user Count Iblis

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights