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Nov 26, 2022

Penrose Singularity

Spacetime singularity is a place where all laws of physics become meaningless and the notion of reality itself changes completely, a region where gravitational force is so enormous that nothing known to science can escape the clutches of gravity and anything coming close will be crushed to an infinitely dense point. The Penrose singularity theorem helped us understand the singularity even better than before and also explained to us how spacetime gets affected due to its enormous gravitational force with the help of light. ⁠

⁠Now singularities form when a star atleast 3 solar – masses (3 times heavier than the sun) dies after it uses all its thermonuclear fuel by which nuclear fusion occurs in a star, now in a star there two opposing forces which helps keep the star stable the nuclear fusion pushes the mass of the star outward and the star’s gravity pushes all the mass of the star inwards to the center. When a star (atleast 3 solar – masses) completely runs out of thermonuclear fuel after fusing almost every fusible element and after it becomes a red giant due to fusion of heavy elements, gravity overcomes the entire outward force and due to the enormous weight of the star the core collapses and then the entire mass of the star implodes at 25% speed of light due to the tremendous gravitational force feeding even more mass to the core and the outer layers burst causing a supernova and after that what’s left now is a black hole which contains a singularity at its center. 



Light Cones


Before understanding the theorem we must first understand what light cones are, now light cones can be imagined as a cone representing an event that has happened in a moment of time on a spacetime surface in 3 dimensions. Which is used in physics to represent causality distinguishing the past, present and the future, now the observer can’t affect the past event since he cannot move or signal faster than the speed of light. The arrow of time therefore always moves towards the future. Now imagine you are in a dark room and you light a candle now when the candle is burned the flash of light then travels in all directions forming a cone shape and you can’t escape it since you will have to move faster than the speed of light to do it. Now since it travels in all directions we can say that the path is in the form of a cone which gets bigger and bigger with time. And if we decompose it image by image and stack the images, the cone gets bigger as it goes towards the future by which we can represent the arrow of time. The light cones are inclined at angle of 45 degrees, and these light cones get bigger at the speed of light and no matter what we do we are bound by it which forces us to move in one direction in time towards the future. Now these light cones are really essential in relativity because it helps us understand the structure of the universe and the cause and effect relation.


Now imagine an event happening in space like a supernova which is almost 1 light year away from the earth so it won’t affect us nor we will get any information about it until 1 year since nothing can be transmitted faster than the speed of light. So therefore the explosion won’t affect us until we enter its light cone, so the fact that one event can trigger another or causality is limited by the speed of light. We all know that there are 3 dimensions of space and 1 dimension of time and in space we are free to move in any direction but we can only move in direction in the dimension of time towards the future, but there is a catch as gravity distorts space it distorts time also, for instance take a celestial object with a lot of mass like the earth now as an object approaches earth it tends to fall towards the center of earth and therefore the direction of the light cone is also bend by the gravity towards the center and therefore near a heavy body like the sun light is bent by its gravitational pull. It’s because now the geometry of space bents the direction of light cones are bend and time becomes relative. 

123.png Why does Spacetime Swap in a Black Hole 

Now black holes are the heaviest known celestial objects in the universe and  they bend spacetime to an unimaginable extent, so much that after a certain boundary the tables turn. As observer A approaches the event horizon of a black hole the geometry of space bends more and after observer A crosses the event horizon all the light cones bent at angle of 45 degree and points directly towards the center at a 90 degree angle, therefore space and time switch places and now all the things including the light cones are destined to fall towards the singularity and now the singularity is no longer a point in space but a point in time, it’s the future of the objects which have crossed the event horizon and that’s why it is impossible to avoid it just like one can’t avoid the next day. While on the other hand observer B who is at a great from the black hole will see observer A frozen at the event horizon, never seeing him crossing the it and slowly seeing observer A fading away due to extreme time dilation. 


The End of SpaceTime


Now as the observer A gets closer and closer to the singularity his lower body will start to stretch because there will be a huge difference in the gravitational force being applied on his upper body and lower body and g – force (1g = 9.8 m/s^2 acceleration) will be tremendous, a billion trillion times more than here on earth, and his atoms will shred completely into subatomic particles.


And at the singularity all the laws of physics breakdown catastrophically and space and time come to a stop.


So far there have only been a few promising theoretical explanations about the singularity but this description about the singularity with the help of the Penrose theorem we have understood it quite better by the use of light cones to represent how time acts inside the black hole and why the singularity is unavoidable after crossing the event horizon. 

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