phymath999: （Riemann）构造了一种最著名的、最抽象的纯粹分析理论。rigid body

Saturday, July 11, 2015

（Riemann）构造了一种最著名的、最抽象的纯粹分析理论。rigid body

最后的沉思

classnet.yizhong.xm.fj.cn/zyw/up/wlwx/8010077.PDF - 轉為繁體網頁

2008年5月2日 - （Riemann）构造了一种最著名的、最抽象的纯粹分析理论。为了说明它们的 ...... 理想黑体，但是却存在着克服这种困难的方法。我们可以把白炽体放 ...

http://www.researchgate.net/post/How_can_black_holes_emit_black_body_radiation_when_the_only_things_that_emits_black_body_radiation_are_black_bodies

"Bernard Lavenda

The correct metrics of constant curvature are given in Robertson-Noonan eqns (14.12), Relativity and Cosmology. Hyperbolic distance is arctanh, not arcsinh as in Landau and Lifshitz (111.12), Classical Theory of Fields. The latter is the circumference of a hyperbolic circle of radius r, i.e. 2 pi R sinh r/R, where R is the absolute constant of the geometry (31.5) Busemann and Kelly, Projective Geometry and Projective Metrics. It was even known to Einstein that the ratio of the circumference of a rotating disc to the radius was greater than 2 pi. In the RW metric at constant r, you would get the ratio equal to 2 pi for k=-1 (constant negative curvature). So RW is wrong and is not to be found in the Robertson-Noonan monograph except in the forward by Fowler.
The Schwarzschild solution is inconsistent. The outer solution has non-constant curvature while the inner solution has constant curvature. There is no matching condition on the boundary. It goes from M/r->rho r^2, i.e., from constant mass M to constant density rho. In Moller, eqn (79) of Ch. XI, the \Lambda term is negative, cf. (98) and the spatial geometry of the inner solution is given by (104) with 2m missing. This I interpret as going from one of constant mass to one of constant density. Moreover, the inner solution (104) does not agree with the Riemann metric (14-10) in Roberston-Noonan. The historical evolution is Riemann->Beltrami->Poincare. These are known metrics of constant curvature, and I showed that it is the Beltrami metric that characterizes a uniformly rotating disc. One of the major results is that you cannot have local observers at the (inertial) center and on the periphery communicating their time differences and thereby knowing their positions on the disc. This is what Einstein contended who did not realize that as you move about on the disc your rulers and clocks will shrink or enlarge with you so that you have no way of knowing where you are in reference to someone else. It will also take you an infinite time to reach the boundary of the disc. Any theory of relativity must reduce to these metrics in the constant curvature limit so that there was no reason for looking for new metrics that would be solutions to Einstein's equation in the constant curvature limit. "

Theory of Relativity - Page 240 - Google Books Result

https://books.google.com/books?isbn=0486319229

W. Pauli - 2013 - ‎Science

Pressure gravitational, 203, 205. in ideal gas, 140. radiation, 97, 138. scalar, 133. Principle of Least Action, ... Riemann—Christoffel tensor, see Curvature tensor.

[PDF]Riemannian geometry in thermodynamic ﬂuctuation theory

guava.physics.uiuc.edu/.../Ruppeiner%20Riemannian%20geometry%20i...

Properties of the Riemannian curvature tensor. A. Fluctuations with ... ﬂuctuation theory 624 C. Ideal gas ...... 1904 to assist in understanding blackbody radiation.

How can black holes emit black body radiation when the ...

www.researchgate.net/.../How_can_black_holes_emit_blac...

ResearchGate

The Schwarzschild solution requires the Ricci tensor to vanish, but then we learn ... (temperature is the average kinetic energy of molecular motion) Black body ...

The Riemann Legacy: Riemannian Ideas in Mathematics and ...

https://books.google.com/books?isbn=9401589399

Krzysztof Maurin - 2013 - ‎Mathematics

Riemannian Ideas in Mathematics and Physics Krzysztof Maurin ... that the spectrum of black body radiation does not asymptotically depend on the shape of ... Perhaps the best insight into this kind of problems is provided by the theory of diffusion ... equations for expressions built from components of curvature tensor Rijkl.

Unified Grand Tours - Contents

www.unifiedgrandtours.org/contents.html

2.1.3 Summary and examples. 2.2 Tensors. 2.3 Extra Geometrical Structures. 2.3.1 The affine connection. 2.3.2 Geodesics. 2.3.3 The Riemann curvature tensor.

[PDF]arXiv:1408.4531v4 [gr-qc] 7 Jan 2015

arxiv.org/pdf/1408.4531

arXiv

by H Pejhan - ‎2014 - ‎Cited by 2 - ‎Related articles

Jan 8, 2015 - of expectation values of the energy-momentum tensor, and in ... that the hole produces black-body radiation which its temperature exactly coincides with the result obtained ... are defined on the total space, while the average values of the ..... of the Riemann curvature tensor, Rµνρτ , and its contractions [29].

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