The Concepts of Space and Time pp 431-432 | Cite as
Geometrical Physics
Chapter
Abstract
The geometrical theory of gravitation characterizes gravitational force in terms of a curvature of space-time. We mean by the curvature of space that unit measuring rods will not serve to build a Cartesian lattice system. The curvature of space-time means that the separation of two world points can not be expressed as
, where dx, dy, dt are determined by unit rods, and clocks which are regulated by the principle of the constancy of the velocity of light. In curved space-time one introduces a Gaussian coordinate system which is characterized by the components of the fundamental metrical tensor, g 11, 9 12, etc.
$$d{s^2} = d{x^2} + d{y^2} + d{z^2} - {c^2}d{t^2}
$$
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© Springer Science+Business Media Dordrecht 1976