|
In physics and astronomy, the Reissner–Nordström metric is a static solution to the Einstein-Maxwell field equations, which corresponds to the gravitational field of a charged, non-rotating, spherically symmetric body of mass ''M''. The metric was discovered by Hans Reissner and Gunnar Nordström. These four related solutions may be summarized by the following table: where ''Q'' represents the body's electric charge and ''J'' represents its spin angular momentum. ==The metric== In spherical coordinates (''t'', ''r'', θ, φ), the line element for the Reissner–Nordström metric is : where ''c'' is the speed of light, ''t'' is the time coordinate (measured by a stationary clock at infinity), ''r'' is the radial coordinate, is a 2-sphere defined by : ''r''S is the Schwarzschild radius of the body given by : and ''rQ'' is a characteristic length scale given by : Here 1/4πε0 is Coulomb force constant.〔Landau 1975.〕 In the limit that the charge ''Q'' (or equivalently, the length-scale ''r''''Q'') goes to zero, one recovers the Schwarzschild metric. The classical Newtonian theory of gravity may then be recovered in the limit as the ratio ''r''S/''r'' goes to zero. In that limit that both ''rQ''/''r'' and ''r''S/''r'' go to zero, the metric becomes the Minkowski metric for special relativity. In practice, the ratio ''r''S/''r'' is often extremely small. For example, the Schwarzschild radius of the Earth is roughly 9 mm (3/8 inch), whereas a satellite in a geosynchronous orbit has a radius ''r'' that is roughly four billion times larger, at 42,164 km (26,200 miles). Even at the surface of the Earth, the corrections to Newtonian gravity are only one part in a billion. The ratio only becomes large close to black holes and other ultra-dense objects such as neutron stars. 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「Reissner–Nordström metric」の詳細全文を読む スポンサード リンク
|