7.2. STARS 429
and (7.2.55) follows.
5.Shock wave.As the total energyERof the star is invariant, we haved
dtER= 0.
It follows from (7.2.55) that
(7.2.56) Pr=0 onr= 1 (i.e.on the boundaryR).
On the other hand, the physically sound boundary condition for the star with variable radius
is
(7.2.57)
∂Pr
∂r=0 onr= 1 ,which means that there is no energy exchange between the starand its exterior. Thus, (7.2.56)
and (7.2.57) imply that there is a shock wave outside the star near the boundary.
Remark 7.13.Formula (7.2.55) is very important. In fact, due to the boundary condition
(7.1.81) andev/^2 ≃ 1 /
√
1 −δ, in the star shell layer, (7.2.55) can be approximately written
as
(7.2.58) ρPr=−
√
1 −δ
4 πR^2d
dtMr forR−r>0 small,whereδ= 2 Mr 0 G/c^2 R. This shows that a collapsing supernova is prohibited to shrink into
a black hole(δ= 1 ). In fact, the strongest evidence for showing that black holes cannot be
created comes from the relativistic effect of (7.2.14), which provides a huge explosive power
in the star shell layer given by
(7.2.59)
ν δ^2
1 −δPr→∞ asδ→ 1 (Pr 6 = 0 ).HerePris the convective momentum different from the contracting momentumPrin (7.2.58);
see Section7.3.3for details.
Remark 7.14.One difficulty encountered in the classical Einstein gravitational field equa-
tions is that the number of unknowns is less than the number ofequations, and consequently
the coupling between the field equations and fluid dynamic andheat equations become trou-
blesome.
7.2.6 Mechanism of supernova explosion
In its late stage of life, a massive red giant collapses, leading to a supernova’s huge explosion.
It was still a mystery where does the main source of driving force for the explosion come
from, and the current viewpoint, that the blast is caused by the large amount of neutrinos
erupted from the core, is not very convincing.
The stellar dynamic model (7.1.78)-(7.1.84) provides an alternative explanation for su-
pernova explosions, and we proceed in a few steps as follows: