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In Newton's theory of gravitation and in various relativistic classical theories of gravitation, such as general relativity, the tidal tensor represents #''tidal accelerations'' of a cloud of (electrically neutral, nonspinning) test particles, #''tidal stresses'' in a small object immersed in an ambient gravitational field. ==Newton's theory== In the field theoretic elaboration of ''Newtonian gravity'', the central quantity is the gravitational potential , which obeys the Poisson equation : where is the mass density of any matter present. Note that this equation implies that in a vacuum solution, the potential is simply a harmonic function. The ''tidal tensor'' is given by the ''traceless part'' : of the Hessian : where we are using the standard ''Cartesian chart'' for E3, with the Euclidean metric tensor : Using standard results in vector calculus, this is readily converted to expressions valid in other coordinate charts, such as the ''polar spherical chart'' : : 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「tidal tensor」の詳細全文を読む スポンサード リンク
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