I was reading a chapter about Anti-de Sitter space-time, it was mentioned that it has a boundary and this boundary is its most striking feature. Note that they weren't taking about the AdS/CFT correspondence.They mentioned that this boundary is important to understand gravity Could someone please explain more why is it that important to have a boundary? And how is it related to gravity?
I have not read this book. The boundary of the AdS is a conformal boundary and it maps "infinity" to a finite region. The boundary of AdS is the similar to the x-axis for the Poincare half plane, where arc or geodesics approach or leave as their parameter approaches infinity. It is also a region where there is a reduction of space, similar to the Lorentz contraction of a body approaching an event horizon. As a result the boundary contains all the information in the bulk region or interior of the spacetime.