Merging timelike and spacelike surfaces

In summary, "Merging timelike and spacelike surfaces" explores the mathematical and physical implications of combining surfaces that represent different causal structures in spacetime. The study examines how these surfaces can interact, leading to new insights in general relativity and the geometry of spacetime. It emphasizes the significance of understanding the transitions between timelike and spacelike regions, which can influence the behavior of particles and the propagation of signals in relativistic contexts. The findings may have applications in theoretical physics, particularly in the study of black holes and cosmological models.
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TL;DR Summary
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
 

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