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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Gravitational redshift ： ウィキペディア英語版 Gravitational redshift In astrophysics, gravitational redshift or Einstein shift is the process by which electromagnetic radiation originating from a source that is in a gravitational field is reduced in frequency, or redshifted, when observed in a region of a weaker gravitational field. This is a direct result of gravitational time dilation - as one moves away from a source of gravitational field, the rate at which time passes is increased relative to the case when one is near the source. As frequency is inverse of time (specifically, time required for completing one wave oscillation), frequency of the electromagnetic radiation is reduced in an area of a lower gravitational field (i.e., a higher gravitational potential). There is a corresponding reduction in energy when electromagnetic radiation is red-shifted, as given by Planck's relation, due to the electromagnetic radiation propagating in opposition to the gravitational gradient. There also exists a corresponding blueshift when electromagnetic radiation propagates from an area of a weaker gravitational field to an area of a stronger gravitational field. If applied to optical wavelengths, this manifests itself as a change in the colour of visible light as the wavelength of the light is increased toward the red part of the light spectrum. Since frequency and wavelength are inversely proportional, this is equivalent to saying that the frequency of the light is reduced towards the red part of the light spectrum, giving this phenomenon the name redshift. ==Definition== Redshift is often denoted with the dimensionless variable $z\backslash ,$, defined as the fractional change of the wavelength〔 See for example equation 29.3 of ''Gravitation'' by Misner, Thorne and Wheeler. 〕 $z=\backslash frac$ where $\backslash lambda\_o\backslash ,$ is the wavelength of the electromagnetic radiation (photon) as measured by the observer. $\backslash lambda\_e\backslash ,$ is the wavelength of the electromagnetic radiation (photon) when measured at the source of emission. The gravitational redshift of a photon can be calculated in the framework of general relativity (using the Schwarzschild metric) as $\backslash lim\_z(r)=\backslash frac\}\}-1$ with the Schwarzschild radius $r\_s=\backslash frac$, where $G$ denotes Newton's gravitational constant, $M$ the mass of the gravitating body, $c$ the speed of light, and $R\_e$ the distance between the center of mass of the gravitating body and the point at which the photon is emitted. The redshift is not defined for photons emitted inside the Schwarzschild radius, the distance from the body where the escape velocity is greater than the speed of light. Therefore this formula only applies when $R\_e$ is larger as $r\_s$. When the photon is emitted at a distance equal to the Schwarzschild radius, the redshift will be infinitely large and it can't escape to any finite distance from this Schwarzschild sphere! When the photon is emitted at an infinitely large distance, there is no redshift. In the Newtonian limit, i.e. when $R\_e$ is sufficiently large compared to the Schwarzschild radius $r\_s$, the redshift can be approximated by a binomial expansion to become $\backslash lim\_z\_\backslash mathrm(r)=\backslash frac\backslash frac\; =\; \backslash frac$ The redshift formula for the frequency $\backslash nu\; =\; c/\backslash lambda$ (and therefore also for the energy $h\backslash nu$ of a photon) can simply deduced from the wavelength-formula above to be $\backslash lim\_\backslash nu\_r=\backslash nu\_e\backslash sqrt\}$ with $\backslash nu\_e$ the emitted frequency at the emission point and $\backslash nu\_r$ the frequency at distance $r\; >\; R\_e$ from the center of mass of the gravitating body causing this gravitational potential. Moreover we get from the law of energy conservation $h\backslash nu\_\backslash infty=h\backslash nu\_1\backslash sqrt\}\; =\; h\backslash nu\_2\backslash sqrt\}$ the general case for a photon of frequency $\backslash nu\_2$ emitted at distance $R\_2$ to observer distance $R\_1$ (measured as distances from the gravitational center of mass) the equation $\backslash nu\_1\; =\; \backslash nu\_2\backslash sqrt\}$ as long as $R\_1,\; R\_2\; >\; r\_s$ holds. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Gravitational redshift」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.