Download The geometry of Minkowski spacetime: an introduction to the by Gregory L. Naber PDF

By Gregory L. Naber

ISBN-10: 0387978488

ISBN-13: 9780387978482

It's the purpose of this monograph to supply an advent to the unique thought of relativity that's mathematically rigorous and but spells out in significant aspect the actual value of the math. specific care has been exercised in preserving transparent the excellence among a actual phenomenon and the mathematical version which purports to explain that phenomenon in order that, at any given aspect, it's going to be transparent no matter if we're doing arithmetic or attractive to actual arguments to interpret the maths.

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Extra resources for The geometry of Minkowski spacetime: an introduction to the mathematics of the special theory of relativity

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Since the Finslerian metric function is assumed to be single-valued, there should exist a one-to-one correspondence between u a and the unit vectors f Therefore, ua , like Ii itself, may be treated as zerodegree homogeneous functions of yi. This remark suggests the idea that a parametrical representation of the indicatrix may be obtained through a set of N - 1 scalars a = 1,2, ... e. ua(x, ky) = ua(x,y), k >0. 93) 34 Chapter 1 (ii) The matrix having entries oualoi is of the highest rank: rank(oualoi) = N - 1.

22) is differentiated with respect to yn, we find hkn = 2Q~klmlihjn + Q~khnmlilj. 19). 17), can be proved in the same way. Therefore, we get the following PROPOSITION 4. 19) are equivalent. 17) is equivalent to B~nk substitution of the obvious equality 0 2 (F2gij)/oy moyn = 2gmn g ij - 4YmCnij - 4Yn Cmij - = O. 26) is called the T-tensor. 27) A Finsler space is said to satisfy the T-condition if the T-tensor vanishes 7 • In such a case, we shall also say that the metric function satisfies the T-condition.

Let us confine ourselves to considering one of them, say the sector c Mx formed by all the vectors ym EM x for which yms~(x) > 0 for any value of the index A. (x)ym) N ] liN . 30) Obviously, a Finsler space with such a metric function is based on the notion of volume, the lengths of vectors in this space being measured by Ndimensional volumes. 31) which is called the Berwald-Moor metric functions. 30) will be called the Ijorm Berwald-Moor metric function in agreement with the terminology adopted in the next section.

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