Black Holes and Neutron Stars

They are the final stage of massive stars’ lives, where such stars become either black holes or neutron stars after a supernova explosion. This happens when a massive star exhausts its nuclear fuel, causing its core to collapse under gravity, which then rebounds and triggers a massive explosion that ejects the star’s outer layers.

Black Holes:
The star continues collapsing through different barriers until even neutrons are crushed, and the structure of matter itself collapses. The star shrinks infinitely, producing extremely strong gravity “according to general relativity,” pulling everything in and allowing nothing to escape, not even light. There are four types of black holes: intermediate black holes, primordial black holes, stellar black holes, and supermassive black holes.

One of the key features of black holes is the event horizon, which is the boundary beyond which nothing can escape gravity.
The singularity is the region at the center of the black hole where density and gravity become infinite. At this point, all known laws of physics break down, and modern and classical theories alike fail to describe what actually happens there.

Neutron Stars:
After a supernova explosion, the core of the star collapses, and protons and electrons combine under extreme pressure to form neutrons. This collapse creates a neutron star with incredibly high density. Although a neutron star may have a mass similar to that of the Sun, its radius is only about 10–20 km, making it extremely dense.
The gravity on the surface of a neutron star is extraordinarily strong, capable of accelerating nearby objects to extremely high speeds, sometimes approaching the speed of light. This intense gravitational pull results from the star’s extremely high density.

Thus, neutron stars are unique cosmic objects where enormous mass is packed into a very small volume, producing strong gravitational effects that can significantly accelerate nearby matter to near-light speeds.

Star Life Cycle

Scientists often compare the life sequence of stars to the life of a human.
Stars have a beginning and an end. They are born inside nebulae and pass through a phase of youth and old age.

After billions of years of a star’s life, it begins to die. If the star is a low-mass star, hydrogen fusion starts, and when it is exhausted, the fusion process stops, and the star begins to contract.

After the star has used up its nuclear fuel, it expands and becomes a red giant, goes through several stages, then becomes a white dwarf. After trillions of years, the white dwarf gradually cools until it loses all its thermal energy and becomes a black dwarf. There are also medium-mass and high-mass stars, which we will discuss in the coming days.

Quantum Mechanics

It is one of the branches of physics that studies the phenomena that occur at the atomic and subatomic levels, where classical physics, such as Newton’s laws, is unable to explain the behavior of tiny particles. In quantum mechanics, particles such as electrons, protons, and photons are treated as having dual properties, meaning they behave as both particles and waves at the same time.

Quantum mechanics developed thanks to the work of Max Planck, who introduced the quantum theory, followed by Einstein’s research on the photoelectric effect, then Niels Bohr, Heisenberg, Schrödinger, and other scientists who advanced the theory more deeply.

There are key concepts in quantum mechanics:
(Uncertainty Principle, Wave Function, Quantum Superposition, Quantum Entanglement)

Theory of (Soft Hair on Black Holes)

In the past, the scientist Stephen Hawking had a hypothesis that a black hole could never retain the information of the body or anything it attracts.

But in 2016, Stephen Hawking presented his last scientific contribution in collaboration with some scientists, stating that a black hole can in fact retain the information of everything it attracts.
But how?
And why was the first hypothesis modified?

In reality, his first hypothesis contradicted the principles of quantum mechanics when it claimed that information is destroyed..!

For this reason, Stephen Hawking presented this modification: information is preserved in the event horizon of the black hole, but not inside it. This also matches the theory of relativity when it states: everything that enters a black hole cannot escape from it — including information, of course!

Therefore, all the information of the objects attracted by the black hole remains preserved in its event horizon (stored in a quantum way).

Differentiation

Differentiation is a mathematical process that aims to calculate the instantaneous rate of change of a function, or in other words, the slope of the tangent line to the curve of the function at a specific point.

The instantaneous change of a function means the change that occurs in the function at a particular moment.

For example, if you calculate the speed of a car by dividing the total distance it traveled by the total time (this is called the average rate of change).
But if you calculate the distance the car traveled in a very small period of time to know the exact speed at a “specific point” (this is called the instantaneous rate of change), it is measured using differentiation.

Before differentiation was developed, scientists like

Archimedes

studied equations in different ways to reach results. But in the 17th century, the two scientists

Newton

and

Leibniz

developed differentiation (and also integration) in many ways and for different applications.

To understand how differentiation is studied in its original form:

1. First, the concept of the Limit, which is fundamental in differentiation. To calculate the slope of the tangent line, we use this definition:
f'(x) = lim(Δx → 0) [f(x + Δx) - f(x)] / Δx
2. Second, the rules of differentiation, which are six main rules.

From these basic concepts, many advanced methods have been developed, but these remain the foundation.

Differentiation is also used in many fields such as physics, artificial intelligence, engineering, and many others.

Integration

Integration is a mathematical process used to calculate the area under a curve, the volume, the mass, or any varying quantity — in other words, “any quantity that gradually accumulates over time until it becomes something final.”

Now let us explain the phrase “calculate the area under a curve.” Imagine you want to calculate the distance a car travels in a certain amount of time. For example, how far can the car travel in half an hour? If the car’s speed is constant, we can simply use the formula:

Distance=Speed*Time

But in the case where the car’s speed is increasing and not constant, we need to use integration to calculate the distance it covered in that time (half an hour).

Integration originated from the need of scientists to study the volumes of irregular bodies and the areas of curved shapes.

Integration gradually developed through the work of Newton and Leibniz. Before them, Archimedes used the idea of dividing objects into small parts to calculate areas and volumes — a concept similar to integration, but in a primitive way without modern symbols. Later, integration advanced further when Riemann introduced what is called Riemann sums.

Now, let us see how integration is studied. There are several stages:

1.Multiple integrals: used to calculate volumes or quantities in higher dimensions.
2.Indefinite integrals: the reverse of differentiation, they give you the original function before it was derived.
3.Definite integrals: used to calculate the area under a curve between two points.
4.Methods of integration: such as substitution, integration by parts, and numerical integration.

Integration is applied in various fields such as physics, engineering, statistics, medicine, and many others.

Quantum Entanglement

It is a strange phenomenon in quantum mechanics, where it states that when particles are formed, they can exist in overlapping states such that their conditions become inseparably connected regardless of the distance between them. This means that measuring the state of one particle immediately reveals the state of the other particle, even if the distance between them is extremely large.

Quantum Superposition

It is a principle in quantum mechanics that indicates particles have the ability to exist in multiple states at the same time before being measured. This means that a particle can simultaneously be in different energy states, positions, or spin states. Once the particle’s state is measured, the quantum superposition collapses. An example of this is Schrödinger’s cat. After measurement, the particle settles into one of the possible states.

The Theory of Electrodynamics in the Framework of Relativity

Before Albert Einstein and before the theory of special relativity, electricity and magnetism appeared as if they were separate phenomena. But after Einstein introduced his theory and the Lorentz transformations, it was revealed that electricity and magnetism are two sides of the same coin, called electromagnetic fields.

Let us take an example to clarify the idea further:
Suppose you are an observer watching a wire with moving electrons. If you, the observer, are at rest relative to the wire, you will see a magnetic field around it.

However, if you move (run) at the same speed as the electrons, you will see the electrons as stationary and the positive ions moving (relative to you). In this case, you will observe an electric field.

In other words, depending on the reference frame, you observe something different.

But what does relativity have to do with all of this?
Relativity plays the fundamental role here because of Lorentz transformations, which showed the change in length measurements (contraction). This contraction alters the distribution of charges, and therefore, if an electric field appears in one frame of reference, it will appear as a magnetic field in another.

In summary, those who established and developed this theory were James Clerk Maxwell, Albert Einstein, and Hendrik Lorentz, and finally Hermann Minkowski, who expressed everything in the language of spacetime, making it simpler within relativity.