Introduction to the mathematics of general relativity: Difference between revisions

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:<math>s^2 = \Delta r^2 - c^2\Delta t^2 \,</math>{{spaces|5}}(spacetime&nbsp;interval),
 
where {{math|''c''}} is the speed of light, and {{math|Δ''r''}} and {{math|Δ''t''}} denote differences of the space and time coordinates, respectively, between the events. The choice of signs for {{math|''s''<sup>2</sup>}} above follows the [[sign convention#Relativity|space-like convention (−+++)]]. A notation like {{math|Δ''r''<sup>2</sup>}} means {{math|(Δ''r'')<sup>2</sup>}}. The reason {{math|''s''<sup>2</sup>}} is called the interval and not {{math|''s''}} is called the interval is that {{math|''s''<sup>2</sup>}} can be positive, zero or negative.
 
Spacetime intervals may be classified into three distinct types, based on whether the temporal separation ({{math|''c''<sup>2</sup>Δ''t''<sup>2</sup>}}) or the spatial separation ({{math|Δ''r''<sup>2</sup>}}) of the two events is greater: time-like, light-like or space-like.