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Re: Tidal Gravity And Spacetime Curvature

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Posted by Zephram Cochrane/">Zephram Cochrane on September 22, 1999 06:17:30 UTC

Some consider space-time curvature to be the case where all the components of the Reimann tensor vanish. If this were your definition of curvature then I wouldn't refer to the gravitational field as curvature, I would then refer to gravitation as space-time geometry instead. I say this because there are space-times in which all the components of the Reimann tensor are zero and yet there is an acceleration or gravitational field present (such is the case for a uniform gravitational field). There are two different kinds of tidal forces, shearing and stressing. For example the oceans nearest to the moon are more attracted to the moon then the oceans far from it. This causes stressing (it pulls them apart). On the other hand the oceans on one side of the earth perpendicular to the direction of the moon are just as far from the moon as oceans on the other side, also perpendicular to the direction to the moon. Even though the acceleration due to gravity is just as great at both oceans the direction is slightly different. They each have a small component of acceleration toward each other. This causes shearing.

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