Tidal Gravitational Accelerations near an Arbitrary Timelike Geodesic in Schwarzschild Space

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Abstract
It is suggested that a ``physical'' definition of a singularity in a space-time manifold might be that it is a point where the relative accelerations of nearby timelike geodesics become infinite. Along an arbitrary timelike geodesic in Schwarzschild space, we construct an orthonormal tetrad of 4-vectors which are used to define ``elevator coordinates'' in a neighborhood of the geodesic. We use these coordinates to determine the tidal gravitational accelerations near the geodesic, and we point out that these accelerations are finite (and continuous) at r = 2m, the ``Schwarzschild surface,'' although they are unbounded as r approaches 0.

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