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Negative curvature – a drawn triangle's angles add up to less than 180°; such 3-dimensional space is locally modeled by a region of a hyperbolic space H 3. Curved geometries are in the domain of non-Euclidean geometry. An example of a positively curved space would be the surface of a sphere such as the Earth.
On this usage, comoving and proper distances are numerically equal at the current age of the universe, but will differ in the past and in the future; if the comoving distance to a galaxy is denoted , the proper distance () at an arbitrary time is simply given by = where () is the scale factor (e.g. Davis & Lineweaver 2004). [2]
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 .
The Milne universe is a special case of a more general Friedmann–Lemaître–Robertson–Walker model (FLRW). The Milne solution can be obtained from the more generic FLRW model by demanding that the energy density, pressure and cosmological constant all equal zero and the spatial curvature is negative.
Three-dimensional anti-de Sitter space is like a stack of hyperbolic disks, each one representing the state of the universe at a given time. [a]In mathematics and physics, n-dimensional anti-de Sitter space (AdS n) is a maximally symmetric Lorentzian manifold with constant negative scalar curvature.
Roblox (/ ˈ r oʊ b l ɒ k s / ⓘ, ROH-bloks) is an online game platform and game creation system developed by Roblox Corporation that allows users to program and play games created by themselves or other users. It was created by David Baszucki and Erik Cassel in 2004, and released to the public in 2006. As of August 2020, the platform has ...
In general, dark energy is a catch-all term for any hypothesized field with negative pressure, usually with a density that changes as the universe expands. Some cosmologists are studying whether dark energy which varies in time (due to a portion of it being caused by a scalar field in the early universe) can solve the crisis in cosmology. [7]
In geometry, curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved. These coordinates may be derived from a set of Cartesian coordinates by using a transformation that is locally invertible (a one-to-one map) at each point. This means that one can convert a point given in a Cartesian ...