Mathematical Principles of Theoretical Physics

7.2. STARS 431

core

Figure 7.2: Circulation in a shell layer causing blast.

In particular, the huge explosion has no imploding force, and will not generate a new black
hole.

The analysis in Steps 1-6 above provides the supernova exploding mechanism, and clearly
provides the power resource of the explosion.
In addition, by (7.2.12) and (7.2.16) we have

α=

1

1 −δr^2 /r 02 −η(r)

, η(r) =

1

2 r

∫r

0

r^2 ψ′φ′

α ψ

dr for 0≤r≤r 0.

We can verify that

(7.2.62) η(r)> 0 for 0<r<r 0.

In fact, by (7.2.17) and (7.2.12) we have

(7.2.63) η( 0 ) = 0 , η(r 0 ) = 0.

Therefore,ηhas an extremumr( 0 <r<r)satisfying

η′(r) = 0.

Letη=^1 rf. Then
η′(r) = 0 ⇒ f(r) =ear (a=constant).

Hence, at the extremumr,ηtakes a positive value

(7.2.64) η(r) =

1

r

f(r) =ea> 0 for 0<r<r 0.

Thus, (7.2.62) follows from (7.2.63) and (7.2.64).
The fact (7.2.62) implies that the criticalδ-factorδcfor the supernova explosion is less
than one, i.e.δc<1.