I
received a comment / question from a certain Clemetine Simon Cabelti who asked
below my blog post here:
https://scientificlogic.blogspot.com/2023/05/spiritual-meaning-of-left-behind-vs.html
It
reads:
“I
read with tremendous interest all your articles especially about the mystery of
life, all of them benefitted and have interested me a lot. Gives us tremendous
amounts of food for spiritual thoughts.
May I ask you a very difficult question in astronomy that has always puzzled me
when scientists say that a black hole is so dense that even light cannot
escape. How is it possible for a star to be so dense that light cannot escape
from it? Is there a way to prove this
I hope you can prove this is possible for us. Waiting for your answer in
anticipation
Thank you”
CSC.
May
20, 2023, at 11:21 AM
Thank
you for your inquiry, Clementine.
I
am not really an expert in astrophysics, or in Einstein General Theory of
Relativity. But I shall try my best within my means and knowledge in astronomy.
First
of all, a black hole is a region
of spacetime where gravity is so strong that nothing, not
even light or other electromagnetic waves would be able to
escape it. The theory of general relativity predicts that a
sufficiently compact mass can deform spacetime to form a black
hole. The boundary of no escape is called the event horizon
which is enclosed by the Schwarzschild radius or
the gravitational radius.
One
of the terms used with black holes is "photon sphere", the radius of
the orbit of light around the black hole. For 3 solar masses this radius
is 13.5 km = 3/2 x the event horizon
radius. The event horizon radius is also called
the Schwarzschild radius.
For
example, the photon sphere for a black hole with 5 times the mass of Sun or
solar mass is, 22.5 km.
In
simple words, when a star or any object collapses until its radius is less than
a certain value it will become a black hole.
This
radius is defined by the quantity of mass surrounding its radius. The
Schwarzschild radius was named after the German astronomer Karl
Schwarzschild calculated this exact solution for the theory of general
relativity in 1916.
The
Schwarzschild radius (Rs) is given as
Rs =
2GM / c2
where G is
the gravitational constant (6.6743 × 10-11 m3 kg-1 s-2), M is
the object mass, and c is the speed of light (299,792,458
metres per second), and one solar mass =1.9891 × 1030 kilograms
The
Schwarzschild radius (Rs) may also be simplified as:
2954.27 metres per solar
mass
This means, the
Schwarzschild radius of a star with the same mass as our Sun is 2.954 km (2954 m) or about 3 km.
Similarly, the Schwarzschild radius (Rs) 3 times the mass of the
Sun
= 2.954 x 3 = 8.862 km (8862
m)
5 times the mass of the Sun:
2.954 x 5
= 14.77 km (14770 m)
But
before we go further into calculations, let us look at some data first:
The
mass of Sun = 1.9891 × 1030 kilograms
The
mass 3 times that of sun = 5.9673 x 10 30 kg
The
mass 5 times that of sun = 9.9455 x 10 30 kg
Let
us now try to calculate how light or any object is going to escape under the
gravity of masses. We call this ‘velocity of escape’ and is given by:
Ve = √ (2GM / r)
Where:
Ve =
escape velocity
G
= universal gravitational constant = 6.6743 × 10-11 m3 kg-1 s-2
M
= mass in kg. of the body attempting to escape
r
= distance in metres from the center of the mass such as a black hole.
Hence,
the velocity of escape of light for a star 3 times the solar mass that has
already collapsed into a black hole would be:
√
2(6.6743 × 10-11 m3 kg-1 s-2).3(1.9891 × 1030 kilograms) / 8862 m
= 2,99,806,416 m /s
This is 1.000046559 times
faster than the velocity of light at 299,792,458 m
/ second.
Let us now look at a black
hole with a mass 5 times that of the Sun. The mass is 9.9455 x 10 30 kg.
For light to escape from a
black hole of 5 solar masses, its velocity has to be:
√
2(6.6743 × 10-11). (9.9455 x 10 30)
/ 14,770 m
=
299,806,416 m /s
This
is also 1.000046559 faster than light itself.
Let us now have a look at one of the
most gigantic stars astronomers have ever discovered. It is the Westerhout 49-2 (W49-2)
star, a very massive and luminous star in the H II
region Westerhout 49.
It
has a luminosity 4,365,000 times that of the Sun, and has a temperature of
about 35,500 Kelvin with a radius of over 55.29 times that of the Sun. It lies
at a distance of 36,200 light years away. It has a solar mass of 250 (4.97 x
10 32 kg).
Such
a massive star probably can last for only a few million years more when its
nuclear fuel runs out before collapsing into a black hole, or it may explode
into a supernova.
Supermassive stars,
with masses more than 10 times that of our Sun are possible progenitors of
supermassive black holes in galactic nuclei. Because of their short nuclear
burning timescales, such objects can be formed only when matter is able to
accumulate at a rate exceeding that of our Sun. It will take a star at least 3
times our solar mass for it to become a black hole.
It
is unlikely a star with a mass the size of our Sun will explode into a
supernova or turn into a black hole when its nuclear fuel runs out. Our
star will grow to be a red giant in about 10 billion years. It will be so large
that it will envelope the inner planets, including our Earth. That's when the
sun will become a red giant, and will remain as one for about a billion
years.
Then,
the hydrogen in her outer core will deplete, leaving an abundance of helium.
That element will then fuse into heavier elements, like oxygen and carbon. However,
in this nucleosynthesis of the elements she would not emit much energy. Once
all the helium disappears, the forces of gravity will take over, and the sun
will shrink into a white dwarf. She will not have sufficient mass to
accrete further into a black hole. All the outer material will dissipate,
leaving behind a planetary nebula.
In
1944, Walter Baade categorized groups of stars within the Milky
Way into stellar populations. In the abstract of the article by
Baade, he recognizes that Jan Oort originally conceived this type of
classification in 1926.
Baade
observed that bluer stars were strongly related with the spiral arms, and
yellow stars dominated near the central galactic bulge and
within globular star clusters. He divided the stars into two main
divisions as population I and population II, with
another newer, hypothetical division called population III added
in 1978. We shall talk about the Hertzsprung-Russell diagram (HR diagram)
shortly after this.
Among
the population types, significant differences were found with their individual
observed stellar spectra. These were later shown to be very important and were
possibly related to star formation from their
observed kinematics, stellar age, and even galaxy
evolution in both spiral and elliptical galaxies.
These three population classes practically divided stars by their chemical
composition or telling us the elements (metals) within.
By
definition, each population group shows the trend where decreasing metal
content indicates increasing age of stars. Hence, the first stars in the
universe (very low metal content) were classed as population III, old
stars (low metallicity) as population II, and recent stars (high
metallicity) as population I.
The Sun is
considered population I, a recent star with a relatively high 1.4%
metallicity. In chemistry, as in astrophysics, areas of sciences that I am
familiar with, we normally consider any element heavier
than helium to be a "metal", including
chemical non-metals such as oxygen.
"When
a star dies, it ejects its stellar envelopes of gas and dust into space. A
chemical analysis of these star dusts tells us about their life, their fuel
contents before dying.
Astronomers
estimate that the sun has at least 8 – 10 billion more years to go before it
dies. By then all humanity will long be gone. The Sun is now at her mid-age
since her creation 4.603 billion years ago.
One
of the most important tools we use to study when stars were evolved is by
looking at the Hertzsprung-Russell diagram (HR
diagram) is The HR diagram tells us much about stellar evolution,
especially their ages by looking at their luminosities. The HR diagram was
developed in the early 1900s by Ejnar Hertzsprung and Henry Norris Russell. It
plots the temperature by looking at their colours or spectral types of the
stars against their luminosity to determine their absolute
magnitude (the observational HR diagram, also known as a colour-magnitude
diagram). By examining their brightness, we can determine their ages
We can tell the stages of their evolution by their luminosities, and from these
measurements we can determine their masses and ages, their internal structure
and how it produces energy. Their changes in their stage of evolution will show
up by their changes in the temperature and luminosity that will be placed
indifferent regions on the HR diagram. By merely looking at the positions they
are placed in the HR diagram we can tell their internal structure and
evolutionary stage.
For
instance we can tell our Sun is in her middle age by looking at her position
among other stars in the main sequence that stretches from the upper
left (hot, luminous stars) to the bottom right (cool, faint stars) in the HR
diagram. It is here in the main sequence that stars spend about 90% of their
lives fusing hydrogen into helium in their cores to give us
light. Main sequence stars have a Morgan-Keenan luminosity
class labelled V. Some of the classes we give on the age of these
stars are:
- The
red giant and supergiant stars (luminosity
classes I through III). They occupy the region above the
main sequence. They have low surface temperatures and
high luminosities which, according to the Stefan-Boltzmann law,
tell us they have large radii. They enter this evolutionary stage once
they have exhausted the hydrogen fuel in their cores and have started to
burn helium and other heavier elements.
- The
white dwarf stars (luminosity class D) are the final
evolutionary stage of low to intermediate mass stars. They are placed at
the bottom left of the HR diagram. These stars are very hot but have low
luminosities due to their small size.
As
already mentioned, our Sun is placed on the main sequence with a
luminosity of 1 and a temperature of around 5,400 Kelvin.
As
astronomers, we normally use the HR diagram either to understand how stars are
evolved by looking at their luminosities and temperatures or to investigate the
properties of a collection of stars or how much fuel they still have and how
long more they can last.
For
instance, by plotting a HR diagram for either a globular or open cluster of
stars, we can estimate the age of the cluster from where stars appear to turn
off the main sequence. The HR diagram is very useful for us to tell us
much about the evolution of stars, their ages and their fate. That is one of
the ways we can tell that the Sun is of middle age, and she has another 8 – 10
billion years more to go before she turns into a red giant to engulf our Earth
and beyond.
Suppose
a supermassive star like Westerhout 49-2 (W49-2) I have already mentioned
turns into a black hole after exhausting its hydrogen nuclear fuel. What
happens? Its current estimated mass is 4.97 x 10 32 kg
with a Schwarzschild radius of 2.954 x 55.29 = 162.33 km (163326 m).
Let’s
check this out, what would be its velocity of escape?
√
(2. (6.6743 × 10-11).(solar mass) / Schwarzschild radius
√ (2. (6.6743 × 10-11).(4.97 x 10 32 )
/163,326 m]
=
637,335,913 m /s.
Theoretically,
this would be 2.1 times faster than light. It would never be possible because
the limit of all speeds is the speed of light at 299,792,458 m / second. Hence
light itself remains trapped within the photon sphere at the Schwarzschild
radius.
The
velocity of escape for light in Einstein General
Theory of Relativity is given as
=
c√ (Rs / R), and this is the same as in Newton equation: √=2GM/ R.
Einstein
derived it from the relativistic energy formula, which is more complicated and
lengthier to explain here, and we shall not dwell into that.
This
is as far as light, matter, space and time are concerned where we are all
trapped because we are all material and physical. But the soul has no mass,
dimension nor the kind of energy that we know. It cannot be trapped by any
black hole no matter how massive, how black or how dark. Einstein General
Relativity does not apply to the soul at all. It just flies out from the
deepest and the darkest chasms on physical death to the body. See explanation
here:
https://scientificlogic.blogspot.com/search?q=does+soul+have+mass
https://scientificlogic.blogspot.com/2023/03/the-conveyers-belt-of-time-and-life.html
Summary:
When
a star with about 3 or more solar masses collapses into a black hole, its
escape velocity beyond the event horizon, defined by its Schwarzschild radius,
will exceed that of light, such that it cannot escape except it orbits round
and round the photon sphere which is about 3/2 x the event horizon radius.
Remember, nothing can travel faster than light. In theory if it tries, it will
remain trapped with the Schwarzschild radius, and may orbit around the photon
sphere.
I
hope I managed to explain in a very simple way without using too much
astrophysics or mathematics.
Thank
you for your inspiration, interest and your question.
Lim
jb
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