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.
W3Counter Web Stats

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

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 β tools

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

Attributions

(propose a free ad)

Site Statistics

206 submissions , 164 unreviewed
5,106 questions , 2,251 unanswered
5,412 answers , 23,072 comments
1,470 users with positive rep
822 active unimported users
More ...

  How to calculate the extrinsic curvature of boundary of AdS2

+ 1 like - 0 dislike
7696 views

I have a simple but technical problem:

How to calculate the extrinsic curvature of boundary of  AdS2?


The boundary of AdS2 metric
ds2=dt2+dz2z2
is given by (t(u),z(u)).
The induced metric on the boundary is
ds2bdy=gαβdxαdxβ=gαβxαyaxβybdyadyb==gαβeαaeβbdyadyb=habdyadyb


For Ads2 case, ds2bdy=huududu where huu=z2+t2z2

My calculation is the following:

1) compute normal vecotr (nt,nz)

From the orthogonal relation eαanα=o and unit norm condition gαβnαnβ=1, we have nt=zzt2+z2,nz=ztt2+z2

2) compute the extrinsic curvature K=αnα

K=αnα=1g[t(gnt)+z(gnz)]=1g[1tu(gnt)+1zu(gnz)]

I tried some times but I can not reprodue the result in the paper.
My question is whether there are some mistakes in the formulas I used above.

asked Jul 15, 2017 in Theoretical Physics by C Thone (110 points) [ revision history ]
edited Jul 17, 2017 by C Thone

1 Answer

+ 0 like - 0 dislike

Obviouly, the last step is not correct.

You can see 

https://arxiv.org/pdf/1703.10969.pdf

for the correct calculation of K. 

answered Jan 3, 2021 by anonymous [ 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):
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol in the following word:
pysicsOverflow
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
...