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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?

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    $\begingroup$ Welcome to Physics SE :) Adding a reference might facilitate potential answerers to reply :) $\endgroup$ – Sanya Aug 17 '16 at 22:09
  • $\begingroup$ thank you :) it's Antony Zee's book : Einstein Gravity in a Nutshell. $\endgroup$ – Milou Aug 17 '16 at 22:18
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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.

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  • $\begingroup$ Thank you, that was helpful :) AdS as said in the book is a "gravity container" ot "tin can", so could we say that the importance of the boundary itself is that by this boundary we can understand the bulk which contains gravitational waves? and doing so we may reveal some gravity's properties? Or am I misunderstandings the link to gravity? $\endgroup$ – Milou Aug 19 '16 at 13:57
  • $\begingroup$ sorry gravitational field* $\endgroup$ – Milou Aug 19 '16 at 14:00
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    $\begingroup$ I am presuming you are replacing wave with field. That is the case. The AdS is a stationary gravity field that maps its information to the boundary. This is a basis for the AdS/CFT correspondence. $\endgroup$ – Lawrence B. Crowell Aug 21 '16 at 12:54

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