A Merging timelike and spacelike surfaces

Click For Summary
The discussion revolves around a proposed method for determining boundary length by smoothly merging timelike and spacelike surfaces that are homologous to the boundary and possess a well-defined first derivative at the merging point. A key question raised is whether this merging procedure can be applied in the context of thermal AdS, particularly when the boundary is located at infinity. Participants are exploring the implications of this approach for understanding the geometry of spacetime. The feasibility of this method in thermal AdS could provide insights into the behavior of boundaries in such geometrical frameworks. Overall, the conversation highlights the intersection of mathematical theory and physical applications in the study of spacetime surfaces.
codebpr
Messages
6
Reaction score
0
TL;DR
How to merge spacelike and timelike surfaces in the case of thermal AdS?
In the following paper, there is a statement which says:

We propose to determine the boundary length by merging smoothly the timelike and spacelike surfaces in such a way that they are homologous to the boundary and have a well-defined first derivative at the merging point.

Can this procedure be done in the case of thermal AdS, where the boundary is at infinity?


[1]: https://arxiv.org/abs/2404.01393
 

Thread 'The Einstein Clock aka Light Clock'

Hello, everyone, hope someone will resolve my doubts. I have posted here some two years ago asking for an explanation of the Lorentz transforms derivation found in the Einstein 1905 paper. The answer I got seemed quite satisfactory. Two years after I revisit this derivation and this is what I see. In the Einstein original paper, the Lorentz transforms derivation included as a premise that light is always propagated along the direction perpendicular to the line of motion when viewed from the...
View full post »

Similar threads

I Synchronous Reference Frame: Definition and Usage
Replies
16
Views
3K
A Connectedness of Boundary Points in Schwarzschild Penrose Chart
Replies
7
Views
2K
I Is this a closed spacelike curve?
Replies
5
Views
2K
I Black hole horizon for different observers
Replies
24
Views
2K
A Interior volume of a black hole
Replies
23
Views
3K
I How many apparent horizons could the Universe have?
Replies
12
Views
2K
B Further Understanding Simultaneity Conventions
2
Replies
51
Views
4K
A Current status of Tom Banks' Holographic space time?
Replies
2
Views
3K
I ER=EPR baby steps: causation or not?
Replies
3
Views
3K
I Kinematic Decomposition for "Rod and Hole" Relativity Paradox
2
Replies
78
Views
6K