Black Holes

 Black Holes - a very deep topic

Looking into black holes may give us a clue to the speed of causality. They are definitely an extreme object and change everything including time. Let’s start with how black holes are made.

Making a Black Hole

In order to make a black hole a given amount of mass would have to be compressed so that its mass would fit into the Schwarzschild radius. In order to do this the force applied to the matter at the core would have to exceed the force exerted by the combination of the force generated by thermal energy (random motion of the matter), and the electromagnetic repulsive force and then the nuclear repulsive force. The core of a nuclear fusion reactor, a normal star, is held apart by the vibration of its particles, the electromagnetic and the strong nuclear force, depending on the depth of the measurement and the size of the star. The heat is generated by a combination of the energy of the force from gravity and the energy released by nuclear fusion reactions when lighter particles form to make heavier ones.

Once the repulsive force of the electrons is overcome, when the atoms turn into plasma, then the nucleus will have a repulsive force generated by the protons, which I assume for now is the same as the repulsive force between electrons, but as you approach the 1 femtometer (1*10^-15 meters) distance then the strong nuclear force takes over and these nucleic particles will bond. This is a fusion reaction. This bonding only occurs up to about 0.7 femtometer then the weak force becomes repulsive. The graph shows the empirically derived function of force verses distance of this force.

The nuclear force is the force between protons and neutrons, subatomic particles that are collectively called nucleons. The nuclear force is responsible for binding protons and neutrons into atomic nuclei. Neutrons and protons are affected by the nuclear force almost identically. Since protons have charge +1 e, they experience a strong electric field repulsion (following Coulomb's law) that tends to push them apart, but at short range the attractive nuclear force overcomes the repulsive electromagnetic force.

The nuclear force is powerfully attractive between nucleons at distances of about 1 femtometer and, as shown in the graph, rapidly decreases to zero at distances beyond about 2.5 fm. But at distances less than 0.7 fm the nuclear force becomes repulsive. This repulsive force needs to be overcome in order to create a singularity. If it is not overcome, if there is not enough gravitational force to compress even more, then the star will become a neutron star.

The forces that bond the quarks together inside the protons and neutrons (hadrons) is still the strong nuclear force but at these distances they become very strong. For example, the force..

F = hc/[2πr²]

where h is Planck’s constant 6.26070040*10^-34 Joule-seconds

..and c is the speed of light in a vacuum C=2.997910⁸*m/sec

Here is time again showing up as the speed of light. The strength demonstrated here is many orders of magnitude greater. This is the bonding force of the quarks inside the nucleon. Note that this graph shows the attractive force of the nucleic material and greater attraction is a larger positive number where the nuclear force in the first graph shows the repulsive force at positive.

To get to this distance though one needs to overcome the barrier at about 0.7 fm. Notice that a femtometer is 10²⁰ larger than a Planck’s length. The question arises; do the quarks bind together when a black hole is formed or is there some kind of exclusion similar to that of the Pauli exclusion of atoms’ electrons where quarks can only bond in certain triplets?

I am not sure how these forces combine into one mathematical model. As far as I am concerned there should be a clear mathematical model that demonstrates the nuclear strong force and distance between bodies, but my understanding is not there yet. Let’s call this ‘to be done’.

Back to Black Holes

When a star has burned out its fuel supply it will undergo a contraction that can be stopped only if it reaches a new state of equilibrium. Depending on the mass during its lifetime, these stellar remnants can take one of three forms:

• White dwarfs, in which gravity is opposed by electron degeneracy pressure

• Neutron stars, in which gravity is opposed by neutron degeneracy pressure and short-range repulsive neutron–neutron interactions mediated by the strong force

• Black hole, The pressure of gravity has overcome the strong nuclear force that repels the nucleons

Black Holes are the universe's strangest and most fascinating objects - Dr Becky explains all, and why nearly everything you know about them is wrong.

Right now, you are orbiting a black hole. The Earth goes around the Sun, and the Sun goes around the centre of the Milky Way: a supermassive black hole - the strangest and most misunderstood phenomenon in the galaxy.

In A Brief History of Black Holes University of Oxford astrophysicist, Dr Becky Smethurst charts the scientific breakthroughs that have uncovered the weird and wonderful world of black holes, from the collapse of massive stars to the iconic first photographs of a black hole in 2019.

Schwarzschild Radius Calculation

Any mass can become a black hole if it collapses down to the Schwarzschild radius - but if a mass is over some critical value between 9 and 10 solar masses (this number needs to be verified) and has no fusion process to keep it from collapsing, then gravitational forces alone make the collapse to a black hole singularity inevitable. Down past electron degeneracy, on past neutron degeneracy and then on past the Schwarzschild radius to collapse toward zero spatial extent - the singularity. The Schwarzschild radius (event horizon) just marks the radius of a sphere past which we can get no particles, no light, no information back out of the hole. Following is a formula modeling the Schwarzschild radius.

r_s = 2MG/c²

where..

G is the gravitational constant: G=6.67428*10^-11 m³/(kg*sec² )

M is the mass of the object in kg

C is the speed of light in a vacuum C=2.997910⁸ m/sec

rs is in meters

This calculation does not show how massive an object, like a star, needs to be to become a black hole but it does show the size that the event horizon would be if that mass became a black hole.

If all of the visible non-dark matter mass in the universe 3*10⁵² were to collapse into a black hole, then its Schwarzschild radius would be 4.4558 * 10²⁵ meters.

The Schwarzschild radius of the planet Earth is 8.8732 millimeters and the sun is 2.954 km.

Time Dilation

When a sphere collapses to a singularity from its own point of view, an outside observer sees the sphere appear to freeze at its horizon because as it collapses it becomes more and more redshifted hence fainter to the outside observer according to the following formula that models the time dilation in and about an object with mass. This is due to the time dilation that happens at the singularity and its surrounding space due to gravitation’s distortion of time-space

T_d = √(1-2MG/(rc²))

Time dilation in a gravity well is calculated where Td is the ratio of the time inside the well to the time outside the well far away from the influence of gravity.

According to Einstein's theory, for larger stars than ours, roughly double the mass of our Sun, no known form of cold matter (normal matter) can provide the force needed to oppose gravity in a new dynamical equilibrium. Hence, the collapse continues with nothing to stop it.

Once a body collapses to within its Schwarzschild radius it forms what is called a black hole, meaning a space-time region from which not even light can escape. It forms a singularity that is confined within the event horizon bounding the black hole, so the space-time region outside will still have a well behaved geometry, with strong but finite curvature, that is expected to evolve towards a rather simple form describable by the historic Schwarzschild metric in the spherical limit and by the more recently discovered Kerr metric if angular momentum is present.

So if an object is to fall into a black hole it would, relative to the outside observers, become frozen in time due to gravity affecting the dilation of time. Take note though that the frequency of the light would be extremely red shifted and would not be visible. This freezing of time occurs when the position of the object in question is equal to the Schwarzschild radius and anything inside the Schwarzschild radius would have a time dilation of an imaginary number as the square root would be that of a negative number. What does this mean?

When the denominator of the time dilation equation ri * c2 becomes less than its denominator 2 * G * M then the root becomes a negative one. This tells us that time is moving in another dimension.

By the star physicist and author of multiple #1 Sunday Times bestsellers, a major and definitive narrative work on black holes and how they can help us understand the universe.

At the heart of our galaxy lies a monster so deadly it can bend space, throwing vast jets of radiation millions of light years out into the cosmos. Its kind were the very first inhabitants of the universe, the black holes.

Today, across the universe, at the heart of every galaxy, and dotted throughout, mature black holes are creating chaos. And in a quiet part of the universe, the Swift satellite has picked up evidence of a gruesome death caused by one of these dark powers. High energy X-ray flares shooting out from deep within the Draco constellation are thought to be the dying cries of a white dwarf star being ripped apart by the intense tides of a supermassive black hole – heating it to millions of degrees as it is shredded at the event horizon.

They have the power to wipe out any of the universe’s other inhabitants, but no one has ever seen a black hole itself die. But 1.8 billion light years away, the LIGO instruments have recently detected something that could be the closest a black hole gets to death. Gravitational waves given off as two enormous black holes merge together. And now scientists think that these gravitational waves could be evidence of two black holes connecting to form a wormhole – a link through space and time. It seems outlandish, but today’s physicists are daring to think the unthinkable – that black holes could connect us to another universe.

At their very heart, black holes are also where Einstein’s Theory of General Relativity is stretched in almost unimaginable ways, revealing black holes as the key to our understanding of the fundamentals of our universe and perhaps all other universes.

Join Professors Brian Cox and Jeff Forshaw in exploring our universe’s most mysterious inhabitants, how they are formed, why they are essential components of every galaxy, including our own, and what secrets they still hold, waiting to be discovered.