PHY 101: Vector Integration

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What is Integration? Integration can be thought of as a continuous analogue of sum (\(\sum_{ }^{ }\)). We integrate or simply add infinitesimal small quantities together to form a continuous chain. Integration can be of 3 kinds rather I would call it 3 ways of integration. Linear, Area and Volume way. To show what each of them looks like here is a visual representation: $$\begin{aligned}& Linear \hspace{1mm}integration:\int_{ }^{ }f(x)dx\\ \\ &Area\hspace{1mm}or\hspace{1mm} surface\hspace{1mm} integration: \iint_S f(x,y)dxdy \\ \\ & Volume \hspace{1mm} integration: \iiint_V f(x,y,z)dxdydz \end{aligned}$$ You might have already noticed that the number of integration symbols (\(\int_{ }^{ }\)) increases with the increase in the number of variables. Hence, most books adopt the notation of calling these single, double and triple integrations. We at physics are creatures of simplicity and thus have kept it easy to remember. Let us talk about each in some detail! Single or Linear...

Blackholes: Universe's Unstoppable Cosmic Vacuum Cleaner

We all have heard of this word at least once in our lifetime. Very interesting comes its meaning.

Before 1967, the scientist called this fascinating cosmic entity “Frozen Stars”. John Wheeler then coined the word Blackhole which we now use to define this cosmic vacuum cleaner.


Why do we call it a black hole?

Do not let this name confuse you for one instance. You might take the literal meaning and say it’s black and a hole. Not True! A black hole is a region in space-time, where the entire mass is located at a locus of infinite density. It might be a little technical so let’s break things down.


Image of a Black Hole
credits: https://www.sciencenews.org/article/runaway-black-hole-galaxy-hubble

According to Einstein’s Theory of Relativity, an object having mass bends the space around it. The more the mass, the more the wrapping of space. Imagine a fabric of cloth stretched from all four corners. This is space, now put a ball of 5 Kg on the cloth, and assume this to be the planet in space. You will see that the ball created a valley in the straight cloth. That is the curvature of space by that ball. Therefore objects in space, bend the immediate area around them depending on their mass. Using this argument we say, what if all the mass was not spread over a surface but was concentrated at a single point, like a singularity. One point, huge mass ergo…infinite density. This leads to a very sharp steep curve/valley/bend in space-time, which we call a blackhole.


Sometimes, stars which are very massive in size go supernovae but cannot shed off enough mass to enter the dwarf star stage, rather they collapse under their own gravity at a single point, forming a black hole.


Are they really black?

Scientists believed that since the gravitational pull of these black holes is so immense that even light can't escape it, it will be impossible to detect one. This was obviously before the great minds worked on these equations and answered these questions for us. In truth, the light can escape the black hole if and only if it passes around the event horizon, if light falls off the edge of the Event horizon, often referred to as the “Point of No Return”, light cannot escape the gravitational pull of the singularity. So yes in one way black holes are black, but then the mass which does not fall inside the black hole is stuck around the orbit of the black hole due to gravity. So no they are not black, they emit heat as in radiation the mass stuck rotates fast, generates energy and becomes as hot as a star, and whenever they feed on other cosmic matter they give off gravitational waves.


How fast does a black hole rotate?

The smaller the size the smaller chances you might have to escape the pull of gravity. Often seen the bigger the black holes the slower they rotate, Although you might become crisp in the accretion disk, i.e. the leftover star contents.


But do you know we see black holes more often than we realise? Haven’t you ever wondered what is at the centre of our Milky Way galaxy? It’s a supermassive black hole, called SAG A*, the first image of the black hole was also found at the centre of a nearby Galaxy M87.


Rotation of Black Hole energy
credits: https://cerncourier.com/a/evidence-for-spinning-black-holes-in-our-galaxy


Time Dilates around the black hole

Ever wondered what it would be like to time travel into the future? YES! It's possible, to just hang out at the edge of the black hole because the space around you bends due to high gravity so does the time, another fascinating result of the General Theory of Relativity. The Greater the gravity, the slower the time flows. So maybe 15 minutes passed for you, but for others, it could be 10 years (just an approximation; there is no calculation to back this result up). However, it would be wise not to do that because if you fall inside (over the event horizon) you will turn into spaghetti, and your atoms and molecules will start to break apart under the immense forces of gravity leaving you in noodles. Not great!


Conclusion:

Black holes are indeed the most interesting cosmic wonders of the universe, who would have thought the death of a star could lead to something this beautiful, and dangerous but so full of matter (Joke!). They fascinate the public and scientists alike and push our understanding of matter and how it reacts with the space around us to the next level.

Before we part our ways here is the picture of the SAG A*, the black hole at the centre of our galaxy. To know more about how it was taken follow this URL https://eventhorizontelescope.org/blog/astronomers-reveal-first-image-black-hole-heart-our-galaxy


Black Hole at the center of milky way
credits: https://eventhorizontelescope.org/

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