Curved space often refers to a spatial geometry which is not "flat", where a flat space has zero curvature, as described by Euclidean geometry.[1] Curved spaces can generally be described by Riemannian geometry, though some simple cases can be described in other ways. Curved spaces play an essential role in general relativity, where gravity is often visualized as curved space.[2] The Friedmann–Lemaître–Robertson–Walker metric is a curved metric which forms the current foundation for the description of the expansion of space and shape of the universe.[citation needed] The fact that photons have no mass yet are distorted by gravity, means that the explanation would have to be something besides photonic mass. Hence, the belief that large bodies curve space and so light, traveling on the curved space will, appear as being subject to gravity. It is not, but it is subject to the curvature of space.
^"The Feynman Lectures on Physics Vol. II Ch. 42: Curved Space". www.feynmanlectures.caltech.edu. Retrieved 2024-01-18.
geometry. Curvedspaces can generally be described by Riemannian geometry, though some simple cases can be described in other ways. Curvedspaces play an...
embedding space, it is not necessary that a surface be embedded in a higher-dimensional space in order to be curved. Such an intrinsically curved two-dimensional...
formula, too, is readily generalized to curved spacetime by replacing partial derivatives with their curved-manifold counterparts, covariant derivatives...
mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be...
Newtonian gravitation is a theory of curved time. General relativity is a theory of curved time and curvedspace. Given G as the gravitational constant...
quantum field theory in curved spacetime (QFTCS) is an extension of quantum field theory from Minkowski spacetime to a general curved spacetime. This theory...
geometry, the Peano curve is the first example of a space-filling curve to be discovered, by Giuseppe Peano in 1890. Peano's curve is a surjective, continuous...
The Hilbert curve (also known as the Hilbert space-filling curve) is a continuous fractal space-filling curve first described by the German mathematician...
the Dirac equation in curved spacetime is a generalization of the Dirac equation from flat spacetime (Minkowski space) to curved spacetime, a general Lorentzian...
geometry is used as a model of physical space, it is known as curvedspace. Even in curvedspace, Minkowski space is still a good description in an infinitesimal...
The curvedspace diamond structure is a patented modular building system representative of a diamond crystal enlarged 8 billion times. These playground...
three-dimensional Euclidean space, which is flat. However, in mathematics Newton's laws of motion can be generalized to multidimensional and curvedspaces. Often the term...
up to less than 180°; such 3-dimensional space is locally modeled by a region of a hyperbolic space H3. Curved geometries are in the domain of Non-Euclidean...
solve this problem by transforming the time-sliced flat-space path integral to curvedspace using a multivalued coordinate transformation (nonholonomic...
which space is conceived as curved, rather than flat, as in the Euclidean space. According to Albert Einstein's theory of general relativity, space around...
together, the curvature and the torsion of a spacecurve are analogous to the curvature of a plane curve. For example, they are coefficients in the system...
Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, in Euclid's Elements, it was the three-dimensional...
accelerated along a curved path. de Sitter precession, a general-relativistic correction accounting for the Schwarzschild metric of curvedspace near a large...
that their equations of motion will take the same form in curvedspace that they do in flat space. A physical law expressed in a generally covariant fashion...
theoretical physicist Walter Gordon in 1923 to study the geometrical optics in curvedspace-time filled with moving dielectric materials. Let ua be the normalized...
Relativistic energy and momentum Space-time Curvedspace Chapters: The Theory of Gravitation (Vol. I, Chapter 7) CurvedSpace (Vol. II, Chapter 42) Electromagnetism...
}=g_{\rho \zeta }R^{\zeta }{}_{\sigma \mu \nu }.} One can see the effects of curvedspace by comparing a tennis court and the Earth. Start at the lower right corner...
given points in a curvedspace, assumed to be a Riemannian manifold, can be defined by using the equation for the length of a curve (a function f from...
projection of a geodesic of the curved four-dimensional (4-D) spacetime geometry around the star onto three-dimensional (3-D) space. The full geodesic equation...
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