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In general relativity, an electrovacuum solution (electrovacuum) is an exact solution of the Einstein field equation in which the only nongravitational mass-energy present is the field energy of an electromagnetic field, which must satisfy the (curved-spacetime) ''source-free'' Maxwell equations appropriate to the given geometry. For this reason, electrovacuums are sometimes called (source-free) Einstein-Maxwell solutions. ==Mathematical definition== In general relativity, the geometric setting for physical phenomena is a Lorentzian manifold, which is physically interpreted as a curved spacetime, and which is mathematically specified by defining a metric tensor (or by defining a frame field). The curvature tensor of this manifold and associated quantities such as the Einstein tensor , are well-defined even in the absence of any physical theory, but in general relativity they acquire a physical interpretation as geometric manifestations of the gravitational field. We also need to specify an electromagnetic field by defining an electromagnetic field tensor on our Lorentzian manifold. These two tensors are required to satisfy two following conditions # The electromagnetic field tensor must satisfy the ''source-free'' curved spacetime Maxwell field equations and # The Einstein tensor must match the electromagnetic stress-energy tensor, . The first Maxwell equation is satisfied automatically if we define the field tensor in terms of an electromagnetic potential vector . In terms of the dual covector (or potential one-form) and the electromagnetic two-form, we can do this by setting . Then we need only ensure that the divergences vanish (i.e. that the second Maxwell equation is satisfied for a ''source-free'' field) and that the electromagnetic stress-energy matches the Einstein tensor. 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「electrovacuum solution」の詳細全文を読む スポンサード リンク
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