Here it is necessary to confirm that the spatial axes of D₁ are those axes fixed with their zero at the centre of the gravitational source, and whose radial variable outside the source is represented in this series of papers by the parameter s. It does not mean axes attached to localised space.

For the situation external to the source, the relationship between these axes has been established as [1] Eq(4.18). An alternative form for it can be developed very easily starting once again from the equivalence of (3.3) and (3.9). thus

from which a can be obtained in terms of v_s as

Inserting (A.2) into [1] Eq(4.18) then gives

and s is then determined in terms of r as

which shows that the relationship between lengths on the respective axes of D₁ and D₀ outside the source, to be a simple relativistic one.

The comparable relationship within the source cannot exhibit any form of discontinuity at the boundary, i.e. the surface of the source. Therefore, this relationship must hold both at this boundary, and within the source. Thus with u_i from (3.31) re-written as

where

and if (3.9), with v_is substituted for v_s, is equated to (A.5) and the above process applied, the result is

This importantly shows that s_i = 0 when r_i = 0.

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