Quantum calculus - Revision history

en>Mogism: /* References */Cleanup/Typo fixing, typo(s) fixed: , → , (2) using AWB

2014-10-29T18:28:07Z

References: Cleanup/Typo fixing, typo(s) fixed: , → , (2) using AWB

← Older revision		Revision as of 20:28, 29 October 2014
Line 1:		Line 1:
	~~{{Unreferenced stub\|auto=yes\|date=December 2009}}~~		Hi there. Allow me begin by introducing the writer, her name is Sophia. Credit authorising [http://C045.Danah.Co.kr/home/index.php?document_srl=1356970&mid=qna real psychic] is where my main earnings comes from. [http://Myfusionprofits.com/groups/find-out-about-self-improvement-tips-here/ free online tarot card readings] To perform lacross is one of the things she loves most. My spouse and I live in Kentucky.<br><br>Also visit my site ... psychic readings; [http://Www.taehyuna.net/xe/?document_srl=78721 Privacy of Data: This tool is built-with and functions-in Client Side JavaScripting, so only your computer will see or process your data input/output.a cool way to improve],
	~~In the theory of Lorentzian manifolds, spherically symmetric spacetimes admit a family of nested round spheres~~. ~~In each of these spheres, every point can be carried to any other~~ by ~~an appropriate rotation about~~ the ~~center of symmetry.~~

	~~There are several different types of coordinate chart which are ''adapted'' to this family of nested spheres~~, ~~each introducing a different kind of distortion~~. ~~The best known alternative is the~~ [~~[Schwarzschild coordinates\|Schwarzschild chart]], which correctly represents distances within each sphere, but (in general) distorts radial distances and angles~~. ~~Another popular choice is the [[isotropic coordinates\|isotropic chart]], which correctly represents angles (but in general distorts both radial and transverse distances)~~. ~~A third choice is the '''Gaussian polar chart''', which correctly represents radial distances, but distorts transverse distances and angles~~. ~~In all three possibilities, the nested geometric spheres are represented by coordinate spheres, so we can say that their ''roundness'' is correctly represented~~.

	==~~Definition==~~
	~~In a Gaussian polar chart (on a static spherically symmetric spacetime), the~~ [~~[line element]] takes the form~~
	:~~<math>ds^2 =~~ -~~f(r)^2 \, dt^2 + dr^2 + g(r)^2 \, \left( d\theta^2 + \sin(\theta)^2 \, d\phi^2 \right), </math>~~
	~~:<math>~~-~~\infty < t < \infty, \, r_0 < r < r_1, \, 0 < \theta < \pi, \,~~ -~~\pi < \phi < \pi<~~/~~math>~~

	~~Depending on context, it may be appropriate to regard f, g as undetermined functions~~ of the ~~radial coordinate~~. ~~Alternatively, we can plug~~ in ~~specific functions (possibly depending on some parameters) to obtain an isotropic coordinate chart on a specific Lorentzian spacetime~~.

	~~==Applications==~~
	~~Gaussian charts are often less convenient than Schwarzschild or isotropic charts~~. ~~However, they have found occasional application in the theory of static spherically symmetric perfect fluids~~.

	=~~=See also==~~
	*[[static spacetime]],
	*[[spherically symmetric spacetime]],
	*[[static spherically symmetric perfect fluid]]s,
	*[[Schwarzschild coordinates]],
	*[[isotropic coordinates]],
	*[[frame fields in ~~general relativity]]~~, ~~for more about frame fields and coframe fields~~.

	~~{{DEFAULTSORT:Gaussian Polar Coordinates}}~~
	~~[[Category:Coordinate charts in general relativity~~]]
	~~[[Category:Lorentzian manifolds]]~~


	~~{{Relativity-stub}}~~

en>DumbBOT: removing a protection template from a non-protected page (info)

2013-04-26T13:17:59Z

removing a protection template from a non-protected page (info)

← Older revision		Revision as of 15:17, 26 April 2013
Line 1:		Line 1:
	~~Hi there~~, ~~I am Alyson Pomerleau and I believe it seems fairly good when you say it~~. ~~One~~ of the ~~extremely~~ best ~~issues~~ in the ~~world for him~~ is ~~performing ballet~~ and he'~~ll be starting some thing else alongside with it. Ohio~~ is ~~where his house is and his family loves it~~. ~~I am currently~~ a ~~journey agent.~~<br><br>~~Also visit my blog~~ ... ~~[http://findyourflirt~~.~~net/index.php?m~~=~~member_profile&p~~=~~profile&id~~=~~117823 free psychic reading~~]		{{Unreferenced stub\|auto=yes\|date=December 2009}}
			In the theory of Lorentzian manifolds, spherically symmetric spacetimes admit a family of nested round spheres. In each of these spheres, every point can be carried to any other by an appropriate rotation about the center of symmetry.

			There are several different types of coordinate chart which are ''adapted'' to this family of nested spheres, each introducing a different kind of distortion. The best known alternative is the [[Schwarzschild coordinates\|Schwarzschild chart]], which correctly represents distances within each sphere, but (in general) distorts radial distances and angles. Another popular choice is the [[isotropic coordinates\|isotropic chart]], which correctly represents angles (but in general distorts both radial and transverse distances). A third choice is the '''Gaussian polar chart''', which correctly represents radial distances, but distorts transverse distances and angles. In all three possibilities, the nested geometric spheres are represented by coordinate spheres, so we can say that their ''roundness'' is correctly represented.

			==Definition==
			In a Gaussian polar chart (on a static spherically symmetric spacetime), the [[line element]] takes the form
			:<math>ds^2 = -f(r)^2 \, dt^2 + dr^2 + g(r)^2 \, \left( d\theta^2 + \sin(\theta)^2 \, d\phi^2 \right), </math>
			:<math>-\infty < t < \infty, \, r_0 < r < r_1, \, 0 < \theta < \pi, \, -\pi < \phi < \pi</math>

			Depending on context, it may be appropriate to regard f, g as undetermined functions of the radial coordinate. Alternatively, we can plug in specific functions (possibly depending on some parameters) to obtain an isotropic coordinate chart on a specific Lorentzian spacetime.

			==Applications==
			Gaussian charts are often less convenient than Schwarzschild or isotropic charts. However, they have found occasional application in the theory of static spherically symmetric perfect fluids.

			==See also==
			*[[static spacetime]],
			*[[spherically symmetric spacetime]],
			*[[static spherically symmetric perfect fluid]]s,
			*[[Schwarzschild coordinates]],
			*[[isotropic coordinates]],
			*[[frame fields in general relativity]], for more about frame fields and coframe fields.

			{{DEFAULTSORT:Gaussian Polar Coordinates}}
			[[Category:Coordinate charts in general relativity]]
			[[Category:Lorentzian manifolds]]


			{{Relativity-stub}}

212.64.8.16 at 14:17, 29 February 2012

2012-02-29T14:17:15Z

New page

Hi there, I am Alyson Pomerleau and I believe it seems fairly good when you say it. One of the extremely best issues in the world for him is performing ballet and he'll be starting some thing else alongside with it. Ohio is where his house is and his family loves it. I am currently a journey agent.<br><br>Also visit my blog ... [http://findyourflirt.net/index.php?m=member_profile&p=profile&id=117823 free psychic reading]