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
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] , 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
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Whereas both Gbur's and Saccoccio's surfaces resolve in flat space
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The drive provides plenty of flat space
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