Quantcast
  • 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.

News

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

Attributions

(propose a free ad)

Site Statistics

145 submissions , 122 unreviewed
3,930 questions , 1,398 unanswered
4,853 answers , 20,624 comments
1,470 users with positive rep
501 active unimported users
More ...

What does SUSY have to do with the stability of black holes?

+ 3 like - 0 dislike
208 views

In this comment, Lumo says that

"Once SUSY is broken, it must be possible for all black holes to decay, to avoid black hole remnants"

I dont understand this remark, does it mean that if one has unbroken SUSY, stable black holes can exist but they are not black hole remnants? I just realize that I am somewhat confused about the difference between stable black hole remnants and stable (in particular microscopic) black holes too ...

asked Aug 26, 2014 in Theoretical Physics by Dilaton (4,295 points) [ no revision ]

1 Answer

+ 3 like - 0 dislike

Well, it has to do with the fact that some black holes within supersymmetric theories arises as BPS states of the theory, right? BPS states enjoy a lot of good properties. I am not sure if it applies to all supersymmetric black holes but let me give you an example which I have heard of.

In specific a Reissner-Nordström black hole which is a solution of the Einstein-Maxwell theory can be embedded in a $\mathcal{N}=2$ supegravity (not sure if it applies to any $d$) by adding some spinor-vector fields and taking the limit that they are 0. Now, this is indeed a supersymmetric solution since it possesses Killing spinors and by asking the variation $\delta_{\epsilon} \psi_{\mu \alpha}$ w.r.t. the supersymmetric parameter $\epsilon$ is zero you end up with half the supersymmetries being independent. Ok (things are a bit more messy but not dramatic), then only four Killing spinors are left, half of the total number, and these four transformations which do not act trivially correspond to four fermionic collective modes. Thus our black-hole is part of the $\mathcal{N}=2$ supergravity hypermultiplet which contains a supercharge $Z$ (seriously, think about it as a $\mathcal{N}=2$ susy), and this can be expressed as

$$Z = p-iq$$

where $p,q$ are the electric and magnetic charges of the theory. Now the Reissner-Nordström black hole mass is given by $M_{RN} = (q+p)^{1/2} = |Z|$. Thus we can say that this black hole solution is invariant under half the supersymmetries, it is a BPS state because of the BPS bound on its mass and lives in a short-multiplet thus it is a protected state and absolutely stable. 

I hope that this gives you a clear indication that BPS black holes are stable and if susy is broken they can lose this stability. You can find nice information in Ortin's book.

answered Jan 5, 2015 by conformal_gk (3,535 points) [ no revision ]
Thanks conformal_gk, I like this illustrative example and your nice explanations :-)

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:
p$\hbar$ysics$\varnothing$verflow
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).
To avoid this verification in future, please log in or register.




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

Your rights
...