Search results
Results from the WOW.Com Content Network
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 .
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.
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.
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.
Penrose diagram of an infinite Minkowski universe, horizontal axis u, vertical axis v. In theoretical physics, a Penrose diagram (named after mathematical physicist Roger Penrose) is a two-dimensional diagram capturing the causal relations between different points in spacetime through a conformal treatment of infinity.
Some physicists, such as Lawrence Krauss, Stephen Hawking or Alexander Vilenkin, call or called this state "a universe from nothingness", although the zero-energy universe model requires both a matter field with positive energy and a gravitational field with negative energy to exist. [2] The hypothesis is broadly discussed in popular sources.