Tuesday, 22 August 2017

Colliding black holes inside a computer

When we see a picture of scientists in lab or at a research centre, we notice that there are computers everywhere. And we think that they use these computers to analyze the data from the experiments in particle physics or cosmology. But there are lots of other things that are done with the aid of these computers, like landing of a rover, communication with a satellite orbiting mars, etc. 

SpaceX/Dragon CRS-12 Launches to the International Space Station

I was curious how physicists, cosmologists, and mathematicians use computers to solve problems. Like how the simulations of colliding black holes or galaxies is produced. How can it reveal something which has not happened yet? Like how our sun will explode at the end of its life and become a white dwarf.

The stars we see at night are just a small part of our galaxy. And our closest star, the sun can be seen throughout the day.

But how a black hole looks like?

We know that the planets are illuminated by star. Similarly Black holes are illuminated by the accretion disc surrounding them. So how does a black hole look like with its accretion disc? 

First computer images of the appearance of a black hole surrounded by an accretion disc were obtained by J.P. Luminet in 1979.

He had to produce the final image by hand using the numerical data.


Almost 38 years have passed since then. 
So now we should have a real picture of black holes, right?

But still we do not have one.

Although the simulations of black hole have become more beautiful and precise, and Luminet’s original work has now been done with a computer and shows 3D model of similar picture he created with his own hands.

And the black hole Gargantua in the movie INTERSTELLAR with its distorted accretion disc due to gravitational lensing is also now a famous visualization of such black holes.


But we do not have to be disappointed, because the Event Horizen Telescope, which is a large collection of telescopes, has started working on it and within few years we’ll see the first picture of a black hole!

Saturday, 27 May 2017

Black Hole (Gargantua) and Event Horizon Telescope

Murph's bookshelf, Blight, Wormhole, Gargantua (The Black hole), Singularity, Tesseract, Bulk Beings... 
So many misconceptions were cleared after reading the Awesome book by Kip Thorne.
One of the best things about the movie Interstellar is the Awesome and Fascinating view of Gargantua, the black hole...
And the Tesseract is just unbelievable!!

I am writing some beautiful lines straight from the book which I found really interesting and also eye-opening!

Tuesday, 28 February 2017

Black holes

“Astronomy is older than physics. In fact, it got physics started, by showing the beautiful simplicity of the motion of stars and planets, the understanding of which was the beginning of physics. But the most remarkable discovery in all of astronomy is that the stars are made of atoms of the same kind as those on earth.*
Richard Feynman 

How can a star turn into a Black Hole? From an object that shines due to nuclear fusion to something which does not allow light itself to escape from it. It becomes something so mysterious that cosmologists need to combine one of the greatest theories – General theory of relativity and Quantum mechanics to understand what is inside it. 

As Michael describes in his video "Travel INSIDE a black hole", theoretically anything, you, me or the Earth you are sitting right now can become a black hole if you shrink it under the Schwarzschild Radius. fortunately there is no means of doing it. But a star can do it at the end of its life.

But how? How can a star turn into a black hole.
To understand it we have to see what happens inside a star.

Stars emit electromagnetic radiation during nuclear fusion.
In our Sun during nuclear fusion Hydrogen nuclei fuse into Helium nuclei and produce electromagnetic radiation which we feel as heat. Photosynthesis starts as the radiation falls on leaves.
Thus everything we eat here on earth is just Bottled Sunshine!

Here are some of my favourite lines from Carl Sagan’s book “cosmos”,

It was more awesome to listen it in his beautiful voice in the video series Cosmos Episode 2 - One Voice in the Cosmic Fugue

Stars are very stable due to the thermal equilibrium that exists between the outward pressure and gravitational force. Outward pressure is maintained by heat generated in the nuclear reactions. But as more heavier elements form in the center of star, different layers start forming, star begins to swell and becomes a red giant. In the end it collapses into a dense core.

This is how we are told that the stars die, but its still described as one of the unsolved problems of physics"What is the exact mechanism by which an implosion of a dying star becomes an explosion?"

So, every star becomes a black hole in the end?
No, two things are important for a star to become a black hole,
  1.     Chandrashekhar limit
  2.     Schwarzschild radius

If a star’s mass is less than 1.4 times the mass of sun (Chandrashekhar limit), it will settle down to a white dwarf, which will remain stable due to the balance between gravitational force and Pauli Exclusion Principle which is the repulsion between electrons. That is the the dense core left at the end will be so dense, it will have only electrons!

But if its mass is above Chandrashekhar limit, it will become a neutron star which is stable by the Pauli Exclusion Principle followed by neutrons. The dense core will be made of neutrons! But if the mass of a star is more than 10 or 20 times that of the sun it will collapse in on itself to a point! This is what is called a BLACK HOLE!

So what is inside a black hole?

We don't know!

One of the solutions of Einstein’s field equations is “Schwarzschild metric”. It describes spacetime surrounding a non-rotating massive object. Schwarzschild black holes which are simplest kind of black holes are described using this metric.


Schwarzschild metric described by Matthew O'Dowd of PBS space time,

Metric is another word to describe the distance between two points in space. Metric can be different for different space. 
In spherical polar coordinate system the Schwarzschild metric is,

In the above equation, 2m=Rs (Schwarzschild Radius).
According to this metric, there is a Schwarzschild Radius surrounding a black hole where the escape velocity is greater than speed of light. This Schwarzschild Radius is actually whats written in many books as event horizon of a NON-ROTATING black hole.

As nothing can travel faster than light, this region surrounding a black hole looks black.

Usually when we see a picture of a black hole, we see the surroundings distorted and the black hole itself shown literally black. But as we know, all these images are not real. But they tell us what really is true. What we actually see when we look at a picture like this is the Schwarzschild radius or the sphere, from which nothing can escape, not even light.


And because of black hole's immense gravity, the galaxy behind it also seems to be distorted due to gravitational lensing.
In gravitational lensing, when a heavy object comes in front of a star, galaxy or quasar it bends the light coming from them and thus distorts is totally. Sometimes it forms a ring and sometimes multiple images. Like in yesterday’s APOD - https://apod.nasa.gov/apod/ap170227.html
And the following picture shows other gravitational lenses taken by Hubble Space Telescope.


The video shows how the bottom of a glass can be used to see a ring of light when the source of light and the bottom of glass are aligned.

As this experiment was inside my mind, I saw another way of looking at the effect using only water in a bowl.
You can see in the image below, when the light from LED falls in the center of bowl a ring is formed even though its not a full circle.

Schwarzschild black hole is the simplest black hole. Its assumed to be non-rotating and with no charge. So what would it be like to travel inside it?

There are some mindbending simulations on this page made by Andrew J. S. Hamilton.
But there are other black holes which are not formed after death of stars, they are called supermassive black holes.
And astronomers have found these supermassive black holes at the centre of every galaxy. So how these black holes are formed? And what came first galaxy or black hole?

As theoretical physicist Michio Kaku explain in this video, the latest theory tells us that supermassive black holes formed first and then the galaxy itself formed around it. But its still difficult to tell which formed first.

Theoretical physicist Carlo Rovelli in a course at World Science U describes that a quantum theory of gravity is needed to explain the interior of black holes. 

So we have still many mysteries to unravel as in Newton's time.


Thursday, 29 December 2016


“The black holes collide in complete darkness. None of the energy exploding from the collision comes out as light. No telescope will ever see the event. That profusion of energy emanates from the coalescing holes in a purely gravitational form, as waves in the shape of spacetime, as gravitational waves.”
 -Janna Levin in “Black Hole Blues and Other Songs From Outer Space”


In 1969 Joseph Weber announced that he had detected Gravitational Waves. He used a large Aluminum bar which he thought would ring when a GW passed through it. But later he was proved wrong.
The basic principle behind LIGO was actually invented in a course of general relativity taught by professor Rainer Weiss. It was a Gedanken problem he gave to students.
Later he built a small 1.5m prototype. And he realized that instrument needed to be big.

Construction of LIGO began in 1994 and completed in 1999. The name LIGO was actually suggested by Rainer but Kip Thorne wanted it to be “beam detector”.

There are two LIGO observatories: LHO (LIGO Hanford Observatory) and LLO (LIGO Livingston).


And on September 14, 2015 the detectors caught the final four orbits of a black hole 29 times the mass of the sun in a pair with a black hole 36 times the mass of the sun.

Even though gravitational waves are not sound waves, they can be converted to sound. In the video you can hear that chirp of merger of two black holes.

Same exciting moment came again on December 26, 2015 when GWs were detected but this time it was due to merger of two smaller black holes.

The best thing about the GW astronomy would be that it will allow us to see the earliest moments of the Big Bang, because early universe was opaque to light but it was not opaque to GWs. The first light which we now detect as CMB radiation was free to travel only 300000 years after the Big Bang. But by detecting GWs we will be able to see what actually happened in the earliest moments of the Big Bang!
There are some great lectures of WorldScienceU by Rainer Weiss, Gabriela Gonzalez and Nergis Mavalvala.

Wednesday, 30 November 2016

Big Bang

Big Bang.
These words were first aired on a BBC radio show when Sir Fred Hoyle was describing the two theories of creation of the universe at that time: Dynamic evolving model and Steady state model. He used these two words to describe the Dynamic evolving model of the universe which he opposed throughout his life even when there were much observational evidence and almost every scientist accepted it.

At first Einstein was also in favor of the steady state model. He used cosmological constant so that the equations do not predict a collapsing universe.
But Alexander Friedmann used equations of general relativity to show that different values of cosmological constant give rise to different fate of universe,

1.      It expands and then contracts
2.      Continuous expansion
3.      Neither collapses nor expands

Even though Einstein found Friedmann’s calculations correct, he refused to believe in such a dynamical universe. So Friedmann’s work didn’t become popular.

Later Georges Lemaitre rediscovered all these facts without knowing Friedmann had already gone through same thought process. Using the concept of radioactive decay Lemaitre speculated that on a greater scale a similar process might have given birth to the universe. By extrapolating backwards in time the universe began in a small compact region from which it exploded outward he found all the stars squeezed into a super compact universe, which he called primeval atom.
In his words,

“The evolution of the universe can be likened to a display of fireworks that has just ended: some few wisps, ashes and smoke. Standing on a well-cooled cinder, we see the fading of the suns, and try to recall the vanished brilliance of the origins of the worlds.”

But at that time there were no observational evidence to these theories. Later when Edwin Hubble using his observational data (of red shifted galaxies) drew a graph which showed a linear relationship between the distance and velocity of galaxies, scientists concluded that if galaxies are moving away from us, in past they must have been closer to each other.

 v = Hd

Using this equation, if we know the speed of a galaxy, its distance can be calculated. And we can also evaluate the time when the galaxies were closer to each other. As the measurements became more accurate, age of the universe came out bigger and it was concluded between 10 – 20 billion years.

Ralph Alpher and Robert Herman proposed that the oldest light in the universe which spread everywhere 300000 years after the creation can be taken as the test for big bang model.

Later Robert Wilson and Arno Penzias detected signal from space which was proved to be the echo from the big bang: the cosmic microwave background radiation (oldest light in the universe). Since steady state model does not predict this radiation, it was now clear that the universe started billions of years ago with Big Bang.

But still scientists including Fred Hoyle along with Jayant Vishnu Narlikar were working on steady state model, and developed it to a new Quasi-steady state model.

Since the CMB radiation detected is just a few thousand years older than the universe’s creations. So any density variation at that time would have given rise to the density variation later like galaxies. After many efforts and other experiments COBE (Cosmic Background Explorer Satellite) was launched on 18 Nov. 1989.
A comparison of the sensitivity of WMAP with COBE and Penzias and Wilson's telescope. Simulated data : NASA

COBE had four detectors and its main purpose was to observe the density variations in CMB radiation. Later WMAP (Wilkinson Microwave Anisotropy Probe) launched in 2001, provided more data and thus the age of the universe was calculated to be 13.8 billion years and it also became known that universe 23% Dark Matter, 73% Dark Energy, 4% Ordinary Matter.
Another space observatory was launched by ESA in 2009, Planck. Its data provided most accurate measurements of these cosmological parameters.

Sunday, 9 October 2016

How far is Andromeda

As I have written in my previous post, Edwin Powell Hubble expanded our understanding of the universe by calculating the distance of Andromeda using Cepheid Variable stars using 100 inch Hooker telescope at Mount Wilson. It was believed that it’s a nebula like many others inside our own galaxy but he calculated that its distance is 90,000 light years from earth.

 Later Walter Baade studied the RR Lyrae stars using the same telescope. RR Lyrae are also variable star similar to Cepheids but less luminous. It was shown before that like Cepheids, the variability of RR Lyrae stars can be used to measure distances. 

The movie shows RR Lyrae stars in a globular cluster. You can see their brightness changing; they look blue as they become brighter.

Walter Baade wanted to use these stars to measure the distance of Andromeda as it was done before using Cepheids. But the 100 inch telescope was not good enough to detect those stars. So he had to wait until the 200 inch (~5 meter) telescope was ready which was being built by George Hale but sadly he died two years after the project started. Later the telescope was named after him.

When the new Hale telescope became operational Baade used the telescope to search the faint variable stars in Andromeda but even after searching for a long time he was not able to find any sign of these stars.
He concluded that the only possible reason for this can be the distance of Andromeda previously measured is not correct!

At that time it was becoming evident that stars can be categorized into two broad types called populations. Older stars fall in Population2 and younger and brighter stars in Population1.

So Baade assumed that Cepheid variable stars will also have two different types. Thus he reasoned his argument that the previously measured distance of Andromeda was wrong using two points,
1.      Population1 Cepheids are brighter than Population2 Cepheids.
2.      Astronomers only saw the brighter Population1 stars in Andromeda and compared it to the dimmer population2 stars in Milky Way.

That’s what lacked in the calculations made by Hubble. And that’s why he measured the distance of Andromeda little less.
Baade calculated that Population1 stars are on average 4 times more luminous than Popluations2 stars of same period of variations. So if a star is moved twice as far away it will appear 4 times fainter. Thus Andromeda Galaxy should be twice as far away - approximately 2 million light years away!
More accurately,

How far is Andromeda? Its 2.537 million light years away.

Sunday, 25 September 2016

Formulas of area

I was wondering how you can know that your formula is correct when you are discovering it. In this post I am sharing some of my findings related to it.

The triangle can be thought of as half of rectangle, so its area should also be half,

½  ar(rectangle) = ½ (ab)

But in this sense, to discover this formula you need to know the area of a rectangle.
Heron’s formula gives the area of triangle without using it,

Where s = ½ (a+b+c)

Now let’s take another formula, the area of a cuboid which is,


This formula also involves the area of rectangle. There are three pairs of identical rectangles, so their area lb, bh, hl adds up twice to give the formula 2(lb+bh+hl).

Similarly in a cube all the sides have equal length so the area of cube is,

2(3a²) = 6a²

I tried to discover formula of triangle without using any other formula but I failed to do so. So how our ancient mathematicians discovered them and how they knew that their formulas are correct? I will try to find answers of these questions in future.

But the formulas discovered in ancient times were not always correct. Like an Egyptian formula for finding the area of a circle was to take the square of 8/9 of the circle’s diameter. It’s not correct because if we compare it with the formula we now know, then we get very less accurate value of pi.

Pi r² = (8/9)²(2r)²

Pi = 256/81 = 3.1604…