Anti-de Sitter space
The anti- de Sitter space ( AdS ) is a spacetime with negative cosmological constant. The naming was made as a counterpart to de Sitter space, named after the Dutch astronomer Willem de Sitter. The energy form of anti - de Sitter space is attractive in contrast to the dark energy of the de Sitter space.
The anti- de Sitter space is similar to the hyperbolic space plus a time dimension. In contrast to our universe, an anti -de- Sitter space neither expand nor contract - he looks at all times regardless of (steady state).
Despite this difference, the anti - de Sitter space turns out to be very useful in the search for quantum theories of space-time and gravitation. Thus, the universe is in the Randall - Sundrum models, a five-dimensional anti - de Sitter space.
The special physical properties
If you float freely anywhere in such a space, one has the impression to reside at the bottom of the gravitational potential: any object that you flings away, comes back like a boomerang. Even more surprising is that the time does not depend until the return of the force of the throw: the object away on his tour, although the more, the more momentum you give him, but the return time is always the same. When sending out a flash of light, consisting of photons with the maximum possible speed, so he moves away infinitely far and yet returns in finite time back. The reason for this peculiar phenomenon is a kind of time contraction, which increases with the distance from the observer.
The anti- de Sitter space and the holographic theory
If we represent the hyperbolic space as a disk, then adjusts the anti - de Sitter spacetime of a stack of disks that form a cylinder. Along the cylinder axis the time passes. A hyperbolic space can have more than two dimensions. The anti- de Sitter space with its three spatial dimensions similar to our space-time most, creates a three-dimensional projection of these disks as a cross -section of the four-dimensional cylinder.
In the four-dimensional anti - de Sitter space is the limit of the space - in relation to the universe - at any time a spherical surface. This limit is the hologram of the holographic theory. This raises the idea that a quantum theory of gravity in the interior of such a space is equivalent to an ordinary quantum field theory of point particles that applies on the edge. If so, you can use a relatively well controllable " Quantenteilchentheorie " to define a quantum theory of gravity, about which we know virtually nothing.