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Definition Of "Tidal Force Tensor" For "zc"

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Posted by pmb on February 27, 2000 02:48:53 UTC

Since "zc" has made it clear to us that he is unfamiliar with the various synonyms for the Rieman tensor this post is intended to rectify the situation. References are provided in case one wishes to verify this information.  Hopefully this will prevent this misunderstanding from continuting. Different authors/relativists use different terms to mean the same thing.

References ========================================

OH = Gravitation and Spacetime - Second Edition,  Ohanian,  Ruffini

MTW = Gravitation - Misner, Thorne and Wheeler

First the synonyms

[MTW - page 224] Reimann tensor = Reimann curvature tensor

[OH - page 659] Reimann curvature tensor = Curvature tensor

[OH - page 54] Reimann tensor = Tidal Force Tensor

================================================

In Newtonian gravity the term tidal force tensor is defined in terms of the Newtonian gravitational potential U as {note: U,k  is the partial derivatire of U with respect to xk, :   U,kl is the partial derivative of U,k  with respect to xl )

Rk0l0 = c-2 U,kl

The tidal forces acting on a body in a gravitational field are given in terms of this tensor. In General Relativity the existance of spacetime curvature is determined by the non-vanishing of a tensor caller the Riemann curvature tensor, the components of which are often denoted as Rmnab. In the weak field limit the components Rm0a0 of the Riemann tensor are equal to c-2 U,kl . The other components can then be determined by measuring the components in several other frames. Thus  Rm0a0   is derived from  Rk0l0. Therefore the Riemann tensor is refered to as the tidal force tensor in general relativity since spaceitme curvature and tidal gravity are the same thing in differenent languages. The former in terms of relativity and the later in terms of Newtonian gravity. In the weak field limit the tidal force tensor reduces to the tidal force tensor in Newtonain gravity [ See OH page 344]

zc  = Please check your facts before you claim that something doesn't exist. If you see a person using a term which you've never seen before then ask them about it.

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