flat space


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flat space

[¦flat ‚spās]
(mathematics)
A Riemannian space for which a coordinate system exists such that the components of the metric tensor are constants throughout the space; equivalently, a space in which the Riemann-Christoffel tensor vanishes throughout the space.
References in periodicals archive ?
However, this is not true, because the [p.sub.i] are at point x' in the curved space, while the coefficients in the transformation (18) are at point x in the flat space. To know the global coordinate transformations x(x') and x'(x) would amount to solve in fact the equations of motion.
the line-element thereof) produced by the founders of the black hole problem, but represents the perspective of a real observer whose location is in the real Schwazschild space itself (inhomogeneous and curved), not by quantities in an abstract flat space tangential to it at the point of observation (as it was previously, in the classical solution).
However, the introduction of a curvilinear coordinate system does not convert the original flat space into a curved one.
In mathematics, the Riemannian space is often embedded in a higher dimensional flat space [5].
The fundamental metric tensor of an Euclidean space is as well a constant, so values of [[??].sub.[mu][nu]], taken in the vicinities of a point of the pseudo-Riemannian space, converge to values of [g.sub.[mu][nu]] in the flat space tangential at this point.
This is also a most important feature of the Milne kinematic model universe in the flat space. Thus, this model universe replaces a very short inflationary period of the universe expansion with a continuous steady-state expansion and matter creation in the spirit of Hoyle.
Moreover, similar to the cases in the AdS space and dS space, the specific heat capacity of the black hole in the asymptotically flat space can be expressed as [c.sub.v] ~ [(T - [T.sub.c]).sup.-2/3] [29], where [T.sub.c] denotes the critical temperature.
"If quantum gravity in a flat space allows for a holographic description by a standard quantum theory, then there must by physical quantities, which can be calculated in both theories -- and the results must agree," says Grumiller, who collaborated with colleagues from the University of Edinburgh, Harvard, IISER Pune, MIT and the University of Kyoto to carry out the research.
Papapetrou, "Einstein's theory of gravitation and flat space," Proceedings of the Royal Irish Academy Section A, vol.
Anywhere there is a large flat space covered with light debris, this innovative tool now offers homeowners, businesses, and property managers a great way to make quick work of time-consuming cleanup.
Whereas both Gbur's and Saccoccio's surfaces resolve in flat space, Ferris achieves a sense of depth through layering.
The drive provides plenty of flat space for children to play out in safety and ample parking.