What is anti-de Sitter space-time?
Conversely, the simplest negatively curved spacetime is called anti-de Sitter space. It is similar to hyperbolic space except that it also contains a time direction. Unlike our universe, which is expanding, anti-de Sitter space is neither expanding nor contracting. It looks the same at all times.—
Is anti-de Sitter space hyperbolic?
The metric on anti-de Sitter space is that induced from the ambient metric. It is nondegenerate and, in the case of q = 1 has Lorentzian signature. When q = 0, this construction gives a standard hyperbolic space.
Is our universe a de Sitter space?
The current observations indicate that the universe is expanding in an accelerated rate, and may approach de Sitter space asymptotically (Perlmutter 1999). The discovery of a nonzero cosmological constant suggests that our universe asymptotes to a de Sitter space-time in the infinite future (I+).
Is de Sitter space asymptotically flat?
Only spacetimes which model an isolated object are asymptotically flat. An even simpler generalization, the de Sitter-Schwarzschild metric solution, which models a spherically symmetric massive object immersed in a de Sitter universe, is an example of an asymptotically simple spacetime which is not asymptotically flat.
Is there anti space?
Abstract: Further investigation of the second ‘space’ reveals that it is, in effect, an ‘antispace’, which contains the same information as real space but in a less accessible form. …
Are AdS globally hyperbolic?
AdS is not a globally hyperbolic spacetime. In non-globally hyperbolic manifolds knowledge of equations of motion and of initial data is not enough to determine the time evolution of physical quantities.
How does time behave in space?
The general theory of relativity suggests that space-time expands and contracts depending on the momentum and mass of nearby matter. Four gyroscopes were pointed in the direction of a distant star, and if gravity did not have an effect on space and time, they would remain locked in the same position.
What does de Sitter space look like?
In de Sitter space-time, where the cosmological constant has a positive value, the universe is shaped like a sphere. And when the cosmological constant is negative, you get AdS space-time, which has a saddle shape.
Is de Sitter space flat?
These are flat (Minkowski) spacetime, de Sitter spacetime (obtained when the cosmological constant is positive) and Anti-de Sitter spacetime (when the cosmological constant is negative).
Why is space time flat?
On a cosmic scale, the curvature created in space by the countless stars, black holes, dust clouds, galaxies, and so on constitutes just a bunch of little bumps on a space that is, overall, boringly flat. is easily explained, too: spacetime is curved, and so is space; but on a large scale, space is overall flat.
Is time difference in space?
Time dilation goes back to Einstein’s theory of special relativity, which teaches us that motion through space actually creates alterations in the flow of time. Time is measured differently for the twin who moved through space and the twin who stayed on Earth.
Why is AdS not globally hyperbolic?
However, AdS spacetime fails to be globally hyperbolic, so a classical field satisfying a hyperbolic wave equation on AdS spacetime need not have a well defined dynamics. In the present paper, we reduce the analysis of electromagnetic, and gravitational perturbations in AdS spacetime to scalar wave equations.
How is an anti-de Sitter space similar to a de sitster space?
An anti-de Sitter space in general relativity is similar to a de Sitter space, except with the sign of the spacetime curvature changed.
Is the universal cover of anti-de Sitter space periodic?
Thus, the anti-de Sitter space contains a conformal Minkowski space at infinity (“infinity” having y-coordinate zero in this patch). In AdS space time is periodic, and the universal cover has non-periodic time. The coordinate patch above covers half of a single period of the spacetime.
How is de Sitter space related to Euclidean geometry?
De Sitter space in general relativity de Sitter space involves a variation of general relativity in which spacetime is slightly curved in the absence of matter or energy. This is analogous to the relationship between Euclidean geometry and non-Euclidean geometry.
Where did Albert Einstein and Willem de Sitter work?
Willem de Sitter and Albert Einstein worked together closely in Leiden in the 1920s on the spacetime structure of the universe.