• 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
5,054 questions , 2,207 unanswered
5,348 answers , 22,725 comments
1,470 users with positive rep
818 active unimported users
More ...

  Penrose diagram of Janus black holes

+ 3 like - 0 dislike

Recently I'm interested in the Janus black holes, it's a solution of three dimensional Einstein-scalar action which can be embedded in ten dimensional type IIB supergravity with appropriate ansatz. And its metric is

$$ds^2=f(\mu){\rm cos}^2\mu ds_{BTZ}^2=f(\mu)(-d\tau^2+d\mu^2+r_0^2{\rm cos}^2\tau d\theta^2),$$

so it's time dependent, and function $f(\mu)$ is consisted of some Jacobi elliptic functions which have similar shape as $1/{\rm cos}^2\mu$ but with longer period than $\pi/2$, and its spatial asymptotic infinity is $\pm\mu_0>\pi/2$. So the penrose diagram is elongated horizontally: Penrose diagram of Janus black hole

But it confuses me that the coordinate transformation is unchanged as the old BTZ black hole ($t$,$r\rightarrow t,r^*\rightarrow U,V\rightarrow\mu,\tau$), so the original time $t$ and space $r$ can't reach $\pm\mu_0$. So what I want to ask is that how can we draw the penrose diagram above if there is no coordinate transformation to cover the whole region.

The original paper is https://arxiv.org/abs/hep-th/0701108, thank you for any help.

This post imported from StackExchange Physics at 2019-04-13 07:44 (UTC), posted by SE-user Jiahui Bao
asked Feb 15, 2019 in Theoretical Physics by Jiahui Bao (15 points) [ no revision ]

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