Return to Special Relativity

Unit I assumes that the reader has an understanding of Algebra, Linear Algebra and some understanding of Calculus, both in integration and differentiation.

Every author has his own conventions, his own way of doing general relativity. When mixing equations from this book with equations from other authors of relativity, make sure to account for the differences in definitions and conventions as needed.

This book will use the following conventions. The space-time signature will be (+ - - -). Where the word mass or the letter m is used unqualified it will be defined as invariant as discussed in the section on mass. Greek superscripts and subscripts will be indices running 0,1,2,3 where 0 will represent the time index. Indices i and j will only be spatial indices running 1,2,3. A comma will represent a partial derivative. In other words F^l,_r will mean ¶F^l/¶x^r.

The Einstein summation convention will be used in the following way. Unless otherwise stated, whenever a product of quantities or a single quantity appears where one index is high and the other is low summation over the repeated index will be implied. Also recall, that for Greek indices they run 0,1,2,3 , but the indices i and j will only run 1,2,3. For instance the expression

R^l_mln

means

R⁰_m0n + R¹_m1n + R²_m2n + R³_m3n

For another example

P_iPⁱ = P₁P¹ + P₂P² + P₃P³

Unless otherwise stated an index that is repeated but both are high, or both are low, then summation is not implied. For instance T^mm will simply be the mm element of T^mn. There is no summation here.