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The Friedmann–Lemaître–Robertson–Walker (FLRW) model using Friedmann equations is commonly used to model the universe. The FLRW model provides a curvature of the universe based on the mathematics of fluid dynamics, that is, modeling the matter within the universe as a perfect fluid. Although stars and structures of mass can be introduced ...
In other words, the energy (relative to the origin) of a co-moving particle in free-fall is conserved. General relativity merely adds a connection between the spatial curvature of the universe and the energy of such a particle: positive total energy implies negative curvature and negative total energy implies positive curvature.
Alternatively, as before, k may be taken to belong to the set {−1 ,0, +1} (for negative, zero, and positive curvature respectively). Then r is unitless and a(t) has units of length. When k = ±1, a(t) is the radius of curvature of the space, and may also be written R(t). Note that when k = +1, r is essentially a third angle along with θ and φ.
General relativity is a theory of the nature of time, space and gravity in which gravity is a curvature of space and time that results from the presence of matter or energy. Energy and mass are equivalent (as expressed in the equation E = mc 2). Space and time values can be related respectively to time and space units by multiplying or dividing ...
The ΛCDM model assumes that the shape of the universe is of zero curvature (is flat) and has an undetermined topology. In 2019, interpretation of Planck data suggested that the curvature of the universe might be positive (often called "closed"), which would contradict the ΛCDM model.
Curved spaces play an essential role in general relativity, where gravity is often visualized as curved spacetime. [2] The Friedmann–Lemaître–Robertson–Walker metric is a curved metric which forms the current foundation for the description of the expansion of the universe and the shape of the universe.
For example, the Gaussian curvature of a cylindrical tube is zero, the same as for the "unrolled" tube (which is flat). [1] [page needed] On the other hand, since a sphere of radius R has constant positive curvature R −2 and a flat plane has constant curvature 0, these two surfaces are not isometric, not even locally. Thus any planar ...
In mathematical physics, n-dimensional de Sitter space (often denoted dS n) is a maximally symmetric Lorentzian manifold with constant positive scalar curvature.It is the Lorentzian [further explanation needed] analogue of an n-sphere (with its canonical Riemannian metric).