Falling into a Black Hole

Parts of a black hole and the fate of an object that falls into one

Hello fellow enthusiasts, it is great to see you again.

As is obvious from the title, this article is in continuation to my previous article on the Black Holes. Today, we would be talking about the parts of a black hole and the fate of objects that fall into it. I hope you are as excited as I am. So, let’s begin.

A beautiful depiction of a black hole, because, why not?

We will begin with some basics, starting with the knowledge of what the various parts of a black hole are.

1.      Singularity: Singularity is the point in space where the mass of a black hole is supposed to be concentrated. The point has zero volume and an infinite density. It is the hole part of the black hole. (The very existence of a singularity in a physical world is mindblowing. It makes for an interesting point of discussion.)

2.      Event Horizon: The event horizon is a sphere of zero thickness around the singularity. It is marked by the surface at which the gravitational pull of a black hole is so strong that even light cannot escape. For escaping the event horizon your velocity should be greater than the speed of light. And which according to the General Theory of Relativity is impossible. So, no escape! It makes up the black part.

3.      Photon Sphere: The Photon sphere is the region around a black hole with gravity so strong the photons start to revolve around it. It is a point where light doesn’t necessarily get sucked inside the black hole, but doesn’t necessarily return. Its thickness equals one-half times that of the Schwarzschild radius (or the radius of the event horizon).

4.   Ergosphere: The region around a black hole where it is not possible to remain stationary is called an ergosphere. It exists only in rotating black holes. Its shape is that of an oblate spheroid - bulged at the equator and flattened at poles. Since the Ergosphere is outside the Event Horizon, it’s possible to escape the black hole from here. When the object leaves, it leaves with extra energy accumulated from the spinning black hole.

Accretion Disk: Material, such as gas, dust, and other stellar debris that has come close to a black hole but not quite fallen into it, forms a flattened band of spinning matter around the event horizon called the accretion disk. An accretion disk is most clearly visible in a quasar. It may or may not be present in all the black holes. 

Parts of a black hole

So, it was as far as parts of a black hole goes. Now, let’s jump to the fun part!

What would happen if we fall into a black hole?

As we will study later but we now take it for its word, gravitational fields bend space-time. A star situated behind our sun would appear a bit displaced due to this warping of space. But what happens when a massive object as massive as an entire galaxy or a black hole comes in between? We would see a distorted, smudged, or smeared image. If we are looking at a galaxy, say A, and galaxy B is in between, galaxy A would look to us like a ring or smudge around galaxy B. This phenomenon is known as gravitational lensing.

Gravitational Lensing by a black hole

This is one phenomenon we needed to know before we could proceed. Let's get going!

For simplicity, we will take an uncharged, non-rotating black hole that is not already feeding. As we approach this black hole, distortion of the sky grows greater and greater (due to gravitational lensing). A large part of our field of view looking forward into the black hole is filled with darkness. When half of our field of view is filled with darkness, we have reached the photon sphere (where the photons orbit the black hole here, remember?). If we could theoretically stop for a moment and look sideways, we would see the back of our own heads. As the light has travelled from our back and after revolving around the black hole came to us again.

Photon Sphere

The gravitational field also warps time. For an observer looking at us, time would appear moving slow. This is the phenomenon of time dilation. For them, our approach to the black hole would seem to get slower and slower, until we reach a point – The Event Horizon. Space and time are so warped up here we have only one direction of motion, and that is inside it. We can only move in the forward direction. And as for the observer, we would appear frozen in space. 

The light coming from our body would get increasingly red-shifted until we disappear (The wavelength would keep on increasing even if it is not in the visible region. Our information or the information of any object that has fallen into the black hole would be preserved on its surface. Thus, information is conserved. This statement has more meaning than it appears now. Its significance will be better visible when I would talk about Hawking Radiation). They would not see us actually get past the event horizon.

Astronaut frozen in space

But for us, things would be completely different. We would continue our journey inside the event horizon, to our inevitable death!

Our view of the whole universe would get compressed into a smaller and smaller point behind us. We may die before we actually reach the event horizon by hitting a firewall (A black hole firewall is a hypothetical phenomenon where an observer falling into it encounters high-energy quanta (plural for quantum; which is the minimum amount of any physical entity involved in an interaction) at or near the event horizon). If we enter a black hole, large enough, we can remain for hours going inside it before it starts hurting. And why would it hurt? The answer is, as we approach singularity, the gravitational field gets so strong that even a small distance of say 1 cm would have a difference of millions of times of gravitational pull. The molecules in our body will be torn apart and we would get stretched to billions of pieces. In fact, this phenomenon has a special name! Spaghettification. 

You die either way

Here, we will die! Actually, we would not be alive to see what happens to us as we reach the singularity. We would never be alive to see a naked singularity. The singularity always exists in the future for us. This way in which the Universe protects or “censors” a black hole from being observed gives rise to a hypothesis – The Cosmic Censorship Hypothesis. The naked singularity and cosmic censorship hypothesis make for our next topic of discussion.

But, the question remains, what happens when our remains finally reach singularity?

We actually don’t know. We may get sucked into the singularity and completely disappear against all the laws of physics.

or

As another theory suggests, we may enter a wormhole. These are shortcuts in space-time. Inside a wormhole, we can travel faster than the speed of light from one point in the Universe to the other. It makes use of theories involving other dimensions. It is something like “Doraemon’s anywhere door”. This also a potential candidate for an interesting discussion. But, of course, you know we can’t cover it here. (As we would get completely off-topic plus the word limit…) So, let's be hopeful future articles bring more about them.

I hope you enjoyed reading this article as much as I enjoyed writing it. I'll sign off now, but before that,

We are doomed.

here, I present to you our doom. :)

See you later!

The amazing mystery of the black holes

Black Holes

Today, we will talk about one of the most mysterious bodies of our Universe – The Black Hole. Yes, The Black Hole! The place where a singularity comes into the picture, laws of physics break, time stops, the space-time warps and what not!

Black Hole - Just look at this magnificence!

But such is the binding by the word limit and the need to keep it short and simple, we cannot discuss as much as we would wish to. Thus, we would talk very briefly about black holes in this article, mainly their formation and some of their properties. Topics related to it, such as its parts, nature of particles around it, the fate of us if we fall into one, its death, etc. would come following. So, let’s start!

To understand a black hole, to define it, we have to look at its origin.

As we know, stars keep on burning and releasing enormous amounts of energy due to nuclear fusion which takes place in its core. Hydrogen fuses to form helium giving a huge amount of energy. The energy in the form of radiation pushes against gravity. Thus, preventing the massive crust from collapsing into the core. This maintains a delicate balance between the two forces.

Balancing the two forces

But what happens when all the fuel is consumed?

For a star that has about one half the mass of the sun is too small and too cool to fuse helium to carbon. Thus, it ends up becoming a white dwarf made of helium. Stars between one half to four times the mass of the sun are massive and hot enough to fuse carbon to oxygen. Carbon and oxygen fuse more or less at the same time and a white dwarf made of carbon and oxygen is obtained. Due to a large amount of heat and pressure, we may have a white dwarf made of diamonds! Stars with masses greater than four times the mass of the sun are massive and hot enough to fuse oxygen to silicon. Stars that have earned the title of “supergiant” are so massive and hot that they begin fusing silicon into a solid core of iron.

White Dwarf

Lucy - A diamond star 4000 Km across

Fusing silicon to iron takes more energy than it gives off. Thus, the balance between radiation energy and gravity is broken. The star begins to shrink under its own gravity. If the iron core builds up to 1.4 times the mass of the sun, it cannot survive the pressure and collapse. In some cases, matter slams into the core resulting in shock waves that trace back and blow the star apart, ending it in a supernova. A supernova releases incredible amounts of energy and is responsible for the formation of heavier elements in our Universe.

Supernova

When a large star implodes, its weight is enough to squash atoms in its core, down to its nuclei. This results in an ultra-dense neutron star. We can imagine the density of neutron stars to be that of a mountain being crushed into the size of a marble! Neutron stars due to their ultra-density can withstand enormous amounts of pressure. But if enough matter falls upon it, above a critical threshold, they will collapse into absolute nothingness! And when that happens, a black hole is born. Mass is packed into a single point known as a singularity. (Singularity is a point with infinite density and our general understanding of physics fail here.)

Neutron Star

A decent-sized black hole is called a stellar-mass black hole with a diameter of an asteroid. There are also super-massive black holes with mass millions to billions of times the mass of the sun. We have one at the centre of every galaxy, including our Milky Way! It offers a great insight into the formation of these galaxies as they must have been interdependent.

An artist's depiction of the black hole at the centre of the Milky Way Galaxy

A common idea about a black hole is that it is made up of matter very compact. But this is wrong! The matter gets completely destroyed. It no longer exists. Yet it leaves behind one of its most powerful legacies – The Gravity!

According to Albert Einstein, gravity is not the force that attracts two objects but it is the warping of space-time around a massive object. A black hole is a deep puncture in space-time. The energy of matter is converted into energy of warped space-time.

Gravity as described by General Theory of Relativity

One more misconception that is widely held is about the size of a black hole. A black hole has no actual size. It is a singularity. The black boundary that you often see in the pictures, represents the part of the black hole, where the gravitational pull is so strong even light cannot escape (And as light is necessary for an object to be visible the region appears black). The boundary of the black part is called the event horizon. But, the radius of the event horizon does depend upon the mass of the black hole. To give it a name, this radius is the Schwarzschild radius. It can be calculated for any mass as

Radius = 2GM/c² 

               Where    G is the Gravitational constant.

                              M the mass

               And,       c is the speed of light.

Thus, r = 1.48*10^-30 M meter.

Or, we can say that if we crush a body into its Schwarzschild radius, we will obtain a black hole!

Event Horizon, Singularity and the Schwarzschild Radius

Well, that was all for the day. I hope you liked the article. Don't forget to calculate your Schwarzschild radius!

Bis später!

The Mighty Quasar

Quasars

QSO or Quasi-stellar objects, commonly known as quasars are one of the most magnificent celestial bodies! They have a supermassive black hole, a solar system sized whirlpool of super-heated plasma that shines brighter than an entire galaxy and jets of near light-speed particles that fill the universe with giant radio plumes. It’s no wonder it attracts so many astronomers and cosmologists!

A Quasar

A Quasar as Wikipedia defines is an active galactic nucleus of very high luminosity. A Quasar consists of a supermassive black hole surrounded by an orbiting accretion disk of gas. As gas in the accretion disk falls towards the black hole, energy is released in the form of electromagnetic radiation.

This must be a complex definition to understand at this stage. So, here I come.

To understand it more, we have to take a look at its history first.

In the 1950s, when the first radio telescopes pointed to the sky they noticed a fat blob of radio signals. But the telescopes back then had a very low spatial resolution. Thus, the source could not be located. It was only in 1963 that astronomers had a chance. In an event known as a lunar occultation, (If the moon happens to cross the line of sight to a source, the source is said to be occulted. The drop in intensity of a radio source as it is blocked by the moon and the rise when the moon has moved out of its way gives an accurate indication of when it was occulted and, since the position of the moon in the sky is accurately known, it is possible to have an accurate estimate of the direction to the radio source.) the moon passed in front of one of these brightest of radio blobs. The Parkes radio telescope in Australia was trained for it. The timing of occultation allowed astronomers to identify a tiny star-like point of bluish light as the source of radio emission. The astronomers observed this “star” and split the observed light into a spectrum. The spectrum looked nothing like the spectrum of stars ever observed. One thing to be noted was that the spectrum was red-shifted, which meant that the wavelength of this light stretched out, as it travelled through the expanding universe. That meant the quasar discovered (named 3C 273) was very far away, about two billion light-years, to gain the red-shift observed. Yet, to be as bright as it was observed after travelling so long a distance meant the object that the light came from was emitting many galaxies worth of light from a seemingly impossible small region of space.

QUASAR 3C 273

One more factor that contributed to the estimation of a quasar’s size was the fact that many quasars exhibit rapid variation in their light and radio output. This fact places a limit on their physical size; for, if an object exhibits variability on a characteristic time scale T, its size must be limited by ~ cT, where c is the speed of light. This limitation arises from the special relativistic result that no physical disturbance can propagate with a speed greater than c.

This made quasars very compact. A quasar may emit comparable energy to that of a galaxy per unit time from a volume whose linear extent may be only a few light hours!

This huge amount of energy from a seemingly small region in space invited several hypotheses. Some claimed the light was coming from a swarm of neutron stars. Some proposed possibility of an advanced alien civilization harnessing their entire galaxy’s power. But it was only in the 1980s when the most satisfying explanation came.

For a quasar to form, we need a black hole of mass millions to billions of times the mass of our sun. And every decent-sized galaxy has one such black hole at its core including our Milky Way!

So, what happens when this black hole decides to feed?

A swarm of gases is driven into a galactic core, which may happen when galaxies merge and grow. So, this swarm of gases approaches the attracting black hole at incredible speeds. It is swept up into a raging whirlpool around the black hole which we call an accretion disk. Here, the energy of the motion of these gases is turned into heat. The heat glow of the accretion disk travels to the ends of the universe. Some gas is swallowed, causing the black hole to grow. However, a lot of it does not make it to the event horizon. Some are converted directly into energy and radiated as light and this same light drives powerful wind of gas back out into the surrounding galaxy. In some cases, for reasons, we fully don’t understand some of that gas can also be paralleled and channelled into jets that erupt from the poles of the quasar. This might be due to the magnetic field of a rapidly growing black hole.

The exact appearance of this phenomenon depends largely on our viewing angle. When the jets are perpendicular to our view, we see a radio galaxy.

Radio Galaxy Hercules A

If they are at an angle, we see a quasar and when staring right down the barrel of the jet we see a blazer.

Blazar

These are the same objects viewed from three different angles.

Each burst of quasar activity in a given galaxy probably lasts for only ten million years or so but is enough for making considerable changes in the entire galaxy.

Our Milky Way Galaxy has such a black hole at its core. It might have been roaring in the past but is silent now. Perhaps, in a few billion years, when it will collide with its closest neighbour, the Andromeda Galaxy and their cores will merge it will roar again, reminding The universe of its existence…

Collision scenario for Milky Way and Andromeda Galaxy Encounter

So, that was all about the enigmatic quasar for now – the brightest and one of the most beautiful phenomena of the Universe. <3

Thanks for reading!

It's all undefined!

  

Singularity

This is our first blog. So, let's start with some basics. Because, why not? So, here we go...

Mathematics defines a singularity as a point where a given mathematical object such as a function is not defined. The function reaches an undefined value such as infinity or is non-differentiable at the point.

Singularity

We can see this from an example of the function, 1/x. As x approaches zero the value of the function increases significantly. At zero, the value is not defined or we say that it reaches infinity. In Mathematics, we escape such situations by not defining function at these points. But what happens when we try to apply these equations in our real, practical life? What do these results imply?

There might be one of these two possibilities: Either mathematics is not describing reality if we look too closely or, we may claim the reality in actuality has infinities!

Let us try to understand the probability of the existence of these singularities from some examples and physical equations.

Let us take the case of a vortex flow, the velocity of fluid particles spinning in the whirlpool is inversely proportional to the distance of fluid particles from the centre of the vortex. As the fluid reaches the centre of the vortex (or its radius approaches zero) its velocity approaches infinity. At a radius equal to zero or at the centre of the vortex an infinite velocity is expected. But in actual this phenomenon is restricted by many factors.  Like the size of water molecules (2.75 angstroms), repulsion between atoms, electrons etc. Thus, the infinite velocity is not reached and singularity (at r = 0) does not exist in this example, as proposed by the mathematical equation.

A vortex

Let us take another example.

Suppose, we are walking on the equator at such a speed that we can cross all the time zones in a 24-hour span. We would complete a full circle of the earth in 24 hours. Now, if we move northwards, say near the north pole, at 60 degrees latitude, and move with the same speed, we would cross all the time zones twice in the same 24-hour span. At a latitude of 89.4 degrees this count increases to 100. As we get closer to the north pole, the number of times we cross the time zones at the same speed and same time interval increases steeply. At the north pole, as we all know all the time zones intersect at a point, the no. of times we cross the time zones reaches infinity, whatever that may mean.

But if instead of seeing these time zones on a globe, we use a map; we will see these time zones as parallel non-intersecting lines with no singularity. Thus, singularity is removed by a mere change of coordinates. This type of singularity is called co-ordinate singularity, i.e., a mere change in co-ordinates can bring or remove a singularity.

An artist's hilarious depiction of co-ordinate singularity

Let's take the example of something all of us are most interested in - The case of Gravitational Singularity!

If we take Newton’s laws of gravitation, we see that the gravitational force between two bodies is inversely proportional to the square of the distance between them. When the two bodies approach each other, the gravitational force between them increases. For a finite body, the whole mass can be supposed to be concentrated at the centre of gravity. When we reach that point, we are most probably inside the body and all the mass is over us. But, what if the whole mass was concentrated on one point?

The point would have infinite density and a point near to that would experience infinite gravitational pull. This infinite force would lead to infinite acceleration, thus, breaking the laws of physics. This point is the gravitational singularity!

Artist's rendering of a black hole sucking matter from a blue giant companion star.

Thus, we can define gravitational singularity as a point where infinite density develops as infinite space-time approaches it. This was the case with Newton’s law of Gravitation! But, as we know, Newton’s law of Gravitation is actually not that universal and it gives wrong answers where the gravitational pull is too strong, like near a star or a black hole. But what happens when we take into consideration the General Theory of Relativity?

Actually, it gives even more singularities!

For understanding this we need some high-level mathematics which is outside the scope of this blog. We use Schwarzschild Metric. This is obtained when we solve Einstein field equations for the simple case of a spherically symmetric mass in an empty universe. When we simplify it to allow movements towards or away from a massive object, this equation reduces to

This allows us to compare two points or events in space-time around a massive object from the perspective of different observers. 

Here, ∆s is the space-time interval, r_s is the Schwarzschild radius, ∆t is the time interval and ∆r is the change in position. 

As it can be seen, we can obtain about two singularities from this equation. One when r = 0, and one when r = r_s. The first case is similar to as given by Newton’s law of Gravitation. However, the second case is that of the event horizon (Event horizon is a boundary in space-time where the gravitational pull becomes so great, that escape is impossible, even for light. We will talk about it more in further articles). This is the case of a co-ordinate singularity and not an actual singularity and can be resolved by Eddington- Finkelstein tortoise co-ordinates (Big name? I know). Once, the event horizon is crossed, we still have a central singularity to deal with. Unfortunately, this cannot be done away with a simple change in coordinates. So, this gives rise to the most obvious question. Does this point of singularity actually exist? Actually, Einstein’s theory and the Schwarzschild solution derived from it, suggests it must exist. The apparent inevitability of this singularity may be evidence that general relativity is incomplete.

The two singularities predicted by the equation

So, I would leave this topic here only, for now. Hope it was useful and you liked and enjoyed reading it. Will see you soon. Till then, bye.

Danke!