Expected value of perfect information - Revision history

76.91.110.207: /* Example */

2014-03-18T04:49:52Z

Example

← Older revision		Revision as of 06:49, 18 March 2014
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	~~In the mathematical description of [[general relativity]],~~ the '~~''Boyer–Lindquist coordinates''' are~~ a ~~generalization of the coordinates used for the metric of a [[Schwarzschild black hole]] that can be used~~ to ~~express the metric of a [[Kerr black hole]]~~.		Hello. Let me introduce the writer. Her title is Refugia Shryock. It's not a typical factor but what she likes performing is foundation jumping and now she is attempting to make money with it. California is our birth location. Managing individuals is his occupation.<br><br>Look into my page [http://test.ithink-now.org/content/think-f83d96d08fe71e25bf80a6cb59048a18 test.ithink-now.org]

	~~The coordinate transformation from Boyer–Lindquist coordinates <math>r, \theta</math>, <math>\phi</math> to cartesian coordinates x, y, z~~ is ~~given by~~
	~~::<math>{x} = \sqrt {r^2 + a^2} \sin\theta\cos\phi</math>~~
	~~::<math>{y} = \sqrt {r^2 + a^2} \sin\theta\sin\phi</math>~~
	~~::<math>{z} = r \cos\theta \quad </math>~~

	~~The line element for a black hole with mass <math>M</math>, angular momentum~~ <~~math~~>J<~~/math~~>~~, and charge <math>Q</math> in Boyer–Lindquist coordinates and [~~[~~natural units]] (<math>G=c=1</math>) is~~

	:~~:<math> ds^2 = -\frac{\Delta}{\Sigma}\left(dt - a \sin^2\theta d\phi \right)^2 +\frac{\sin^2\theta}{\Sigma}\Big((r^2+a^2)d\phi - a dt\Big)^2 + \frac{\Sigma}{\Delta}dr^2 + \Sigma d\theta^2 <~~/~~math>~~

	~~where~~

	~~::<math> \Delta = r^2 - 2Mr + a^2 + Q^2 </math>~~
	~~::<math> \Sigma = r^2 + a^2 \cos^2\theta </math>~~
	~~::<math> a = J/M </math>, the angular momentum per unit mass of the black hole~~

	~~Note that in natural units <math>M<~~/~~math>, <math>a</math>, and <math>Q</math> all have units of length. This line element describes the [[Kerr-Newman metric]].~~

	~~The Hamiltonian for~~ test ~~particle motion in Kerr spacetime was separable in Boyer–Lindquist coordinates~~. ~~Using Hamilton~~-~~Jacobi theory one can derive a fourth constant of the motion known as [[Carter constant\|Carter's constant]]~~.<ref name="carter_1968">{{cite journal \| last = Carter \| first = Brandon \| authorlink = Brandon Carter \| year = 1968 \| title = Global structure of the Kerr family of gravitational fields \| journal = Physical Review \| volume = 174 \| issue = 5 \| pages = 1559–1571 \| bibcode=1968PhRv..174.1559C \| doi=10.1103/~~PhysRev.174.1559}}<~~/~~ref>~~

	~~==References ==~~
	~~{{reflist\|1}}~~
	*Boyer, R. H. and Lindquist, R. W. ''Maximal Analytic Extension of the Kerr Metric''. J. Math. Phys. ~~8, 265~~-~~281, 1967.~~
	*Shapiro, S. L. and Teukolsky, S. A. ''Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects''. ~~New York: Wiley, p. 357, 1983.~~

	~~{{DEFAULTSORT:Boyer-Lindquist coordinates}}~~
	~~[[Category:Black holes~~]]
	~~[[Category:Coordinate charts in general relativity]]~~


	~~{{relativity-stub}}~~

en>Lugia2453: Reverted edits by 140.80.199.91 (talk) (HG 3)

2014-01-06T20:31:31Z

Reverted edits by 140.80.199.91 (talk) (HG 3)

← Older revision		Revision as of 22:31, 6 January 2014
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	~~The writer is recognized by~~ the ~~title~~ of ~~Numbers Lint~~. ~~To gather badges~~ is ~~what her family members~~ and ~~her enjoy. Hiring~~ is ~~his profession. California is exactly~~ where ~~I've always been living and I love every working day residing here.~~<br><br>~~Also visit my blog post~~: ~~[http~~://~~Glskating.com~~/~~groups~~/~~stay~~-~~yeast~~-~~infection~~-~~free~~-~~with~~-~~these-helpful-suggestions/ std testing at home]~~		In the mathematical description of [[general relativity]], the '''Boyer–Lindquist coordinates''' are a generalization of the coordinates used for the metric of a [[Schwarzschild black hole]] that can be used to express the metric of a [[Kerr black hole]].

			The coordinate transformation from Boyer–Lindquist coordinates <math>r, \theta</math>, <math>\phi</math> to cartesian coordinates x, y, z is given by
			::<math>{x} = \sqrt {r^2 + a^2} \sin\theta\cos\phi</math>
			::<math>{y} = \sqrt {r^2 + a^2} \sin\theta\sin\phi</math>
			::<math>{z} = r \cos\theta \quad </math>

			The line element for a black hole with mass <math>M</math>, angular momentum <math>J</math>, and charge <math>Q</math> in Boyer–Lindquist coordinates and [[natural units]] (<math>G=c=1</math>) is

			::<math> ds^2 = -\frac{\Delta}{\Sigma}\left(dt - a \sin^2\theta d\phi \right)^2 +\frac{\sin^2\theta}{\Sigma}\Big((r^2+a^2)d\phi - a dt\Big)^2 + \frac{\Sigma}{\Delta}dr^2 + \Sigma d\theta^2 </math>

			where

			::<math> \Delta = r^2 - 2Mr + a^2 + Q^2 </math>
			::<math> \Sigma = r^2 + a^2 \cos^2\theta </math>
			::<math> a = J/M </math>, the angular momentum per unit mass of the black hole

			Note that in natural units <math>M</math>, <math>a</math>, and <math>Q</math> all have units of length. This line element describes the [[Kerr-Newman metric]].

			The Hamiltonian for test particle motion in Kerr spacetime was separable in Boyer–Lindquist coordinates. Using Hamilton-Jacobi theory one can derive a fourth constant of the motion known as [[Carter constant\|Carter's constant]].<ref name="carter_1968">{{cite journal \| last = Carter \| first = Brandon \| authorlink = Brandon Carter \| year = 1968 \| title = Global structure of the Kerr family of gravitational fields \| journal = Physical Review \| volume = 174 \| issue = 5 \| pages = 1559–1571 \| bibcode=1968PhRv..174.1559C \| doi=10.1103/PhysRev.174.1559}}</ref>

			==References ==
			{{reflist\|1}}
			*Boyer, R. H. and Lindquist, R. W. ''Maximal Analytic Extension of the Kerr Metric''. J. Math. Phys. 8, 265-281, 1967.
			*Shapiro, S. L. and Teukolsky, S. A. ''Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects''. New York: Wiley, p. 357, 1983.

			{{DEFAULTSORT:Boyer-Lindquist coordinates}}
			[[Category:Black holes]]
			[[Category:Coordinate charts in general relativity]]


			{{relativity-stub}}

en>Arms & Hearts: Added {{ref improve}} and {{technical}} tags to article (TW)

2012-06-27T16:38:00Z

Added {{ref improve}} and {{technical}} tags to article (TW)

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