Pedro Lauridsen Ribeiro

less info
575 reputation
26
bio website cmcc.ufabc.edu.br/…
location Cotia, Brazil
age 35
visits member for 1 year, 9 months
seen Sep 17 at 17:53

I'm a professor at the Center of Mathematics, Computation and Cognition of the Federal University of the ABC, Santo André, Brazil.


Jun
26
awarded  Enlightened
Jun
26
awarded  Nice Answer
Jun
11
revised AdS Space Boundary and Geodesics
added small clarification
Jun
11
revised AdS Space Boundary and Geodesics
corrected fomulae, simplified argument
Jun
11
revised AdS Space Boundary and Geodesics
corrected fomulae
Jun
11
revised AdS Space Boundary and Geodesics
Corrected final form of geodesic equation in $H_m$, improved explanation, corrected formula
Jun
11
revised AdS Space Boundary and Geodesics
Corrected final form of geodesic equation in $H_m$
Jun
11
revised AdS Space Boundary and Geodesics
improved explanation of the covering map, added short explanation
Jun
11
revised AdS Space Boundary and Geodesics
improved explanation of the covering map
Jun
11
revised AdS Space Boundary and Geodesics
Improved explanation at the end
Jun
11
revised AdS Space Boundary and Geodesics
small rewording, added clarification
Jun
11
revised AdS Space Boundary and Geodesics
small rewording
Jun
10
revised AdS Space Boundary and Geodesics
Improved explanation at the end
Jun
10
revised AdS Space Boundary and Geodesics
Added description of metric and conformal infinity of $AdS_4$, small typo corrected
Jun
10
revised AdS Space Boundary and Geodesics
covering map formula corrected, small rewording
Jun
10
revised AdS Space Boundary and Geodesics
some indices corrected, some minor rewordings
Jun
10
comment AdS Space Boundary and Geodesics
@user13223423 I've added enough details to my answer to make it self-contained.
Jun
10
revised AdS Space Boundary and Geodesics
Added major details to answer, to compensate for lack of access to reference given in the comments.
Jun
9
comment AdS Space Boundary and Geodesics
The argument in O'Neill's book actually comprises geodesics of all causal characters - timelike geodesics in the fundamental domain of $AdS_4$ behave as in my above comment, whereas null geodesics therein are one of the two connected components of the intersection of the hyperboloid with a null 2-plane through the origin. In particular, all null geodesics are also null geodesics in the ambient space $\mathbb{R}^{2,3}$. When lifted to the universal covering, complete null geodesics remain in a single sheet. Since this geodesic is complete but not closed, it must escape to conformal infinity.
Jun
9
comment AdS Space Boundary and Geodesics
@user13223423 It has just came to my attention, and I apologize in advance if my impression is mistaken - are you sure your form of the metric is correct? Shouldn't $f(r)$ be $r^2+m$ $(m>0)$ and $d\zeta^2=d\theta^2+\sin^2\theta d\phi^2?$ As far as I remember, $f(r)=r^2-m$ in your formula (with $\sin$ instead of $\sinh$) yields the four-dimensional de Sitter ($dS_4$) metric.