Parth G | Meet the Man Who Solved General Relativity in a Month. @ParthGChannel | Uploaded 1 year ago | Updated 14 hours ago
The Einstein Field Equations can be used to predict the existence of gravitational waves!
In the theory of General Relativity, the Einstein Field Equations is a tensor equation that governs the theory completely. It links together the distribution of stuff (e.g. mass, energy, momentum, and pressure) found in any region of spacetime that we want to consider, and the warping of the spacetime in that region as a result.
Basically, mass tells spacetime how to warp, and the warping of spacetime tells objects within it how to move. This is a simplification, but check out my more detailed video on the Einstein Field Equations for a more detailed description: youtu.be/FJnTItLVIqQ
The interesting thing we'll look at in this video is how to solve the Einstein Field Equations. A solution to these equations links together a realistic warping of spacetime with the distribution of stuff inside it that causes the warping. More accurately, a solution is in the form a metric tensor which describes the bending of spacetime and the geometries within it.
The first solution we look at is the Schwarzschild solution. It studies the shape of spacetime around a spherical object with mass. The mass and size of the sphere can be varied, and the solution still works. This solution was first discovered by Karl Schwarzschild only about a month after Einstein published his paper on General Relativity. It was also discovered by Johannes Droste not long after, with a more elegant method.
The Schwarzschild solution studies a non-rotating, uncharged sphere, so can be used to describe the spacetime around celestial bodies like the Earth and the Sun. Of course both these bodies are not perfect spheres and they are slowly rotating, but on a cosmological scale they are very approximately perfect, non-rotating, uncharged spheres.
The Schwarzschild solution also describes the spacetime around black holes. These are dense objects, where a lot of mass is packed into a very small region of space. The spacetime solution works outside the black hole, up until the event horizon. The solution also predicts what happens inside the black hole, but we have no way of knowing this since not even light can escape (to bring us information) once past the event horizon. Other solutions of the equation deal with rotating or charged black holes - check out my video on the Kerr solution here: youtu.be/kIbP2Sg8y18
The next solution we look at is the flat spacetime solution for an empty region of spacetime. This is a very important, but trivial, solution. It just says that spacetime is NOT warped when there is no mass to warp it - just as we'd expect in a steady-state case. But this is not the only solution that studies an empty region of spacetime.
Gravitational waves are another possible solution to the equation. They are a rippling of the spacetime fabric, transferring energy from the source, and they do not need mass to exist in the region through which they travel (though they are usually formed by interactions of massive objects).
Thanks for watching, please do check out my links:
MERCH - https://parth-gs-merch-stand.creator-spring.com/
INSTAGRAM - @parthvlogs
PATREON - patreon.com/parthg
MUSIC CHANNEL - Parth G's Shenanigans
Here are some affiliate links for things I use!
Quantum Physics Book I Enjoy: https://amzn.to/3sxLlgL
My Camera: https://amzn.to/2SjZzWq
ND Filter: https://amzn.to/3qoGwHk
Timestamps:
0:00 - Einstein's Field Equations in General Relativity
2:26 - What Does It Mean to Solve Einstein's Field Equations?
3:29 - The Schwarzschild Solution (Black Holes!)
6:20 - The Flat Spacetime Solution
6:59 - Gravitational Waves!
The Einstein Field Equations can be used to predict the existence of gravitational waves!
In the theory of General Relativity, the Einstein Field Equations is a tensor equation that governs the theory completely. It links together the distribution of stuff (e.g. mass, energy, momentum, and pressure) found in any region of spacetime that we want to consider, and the warping of the spacetime in that region as a result.
Basically, mass tells spacetime how to warp, and the warping of spacetime tells objects within it how to move. This is a simplification, but check out my more detailed video on the Einstein Field Equations for a more detailed description: youtu.be/FJnTItLVIqQ
The interesting thing we'll look at in this video is how to solve the Einstein Field Equations. A solution to these equations links together a realistic warping of spacetime with the distribution of stuff inside it that causes the warping. More accurately, a solution is in the form a metric tensor which describes the bending of spacetime and the geometries within it.
The first solution we look at is the Schwarzschild solution. It studies the shape of spacetime around a spherical object with mass. The mass and size of the sphere can be varied, and the solution still works. This solution was first discovered by Karl Schwarzschild only about a month after Einstein published his paper on General Relativity. It was also discovered by Johannes Droste not long after, with a more elegant method.
The Schwarzschild solution studies a non-rotating, uncharged sphere, so can be used to describe the spacetime around celestial bodies like the Earth and the Sun. Of course both these bodies are not perfect spheres and they are slowly rotating, but on a cosmological scale they are very approximately perfect, non-rotating, uncharged spheres.
The Schwarzschild solution also describes the spacetime around black holes. These are dense objects, where a lot of mass is packed into a very small region of space. The spacetime solution works outside the black hole, up until the event horizon. The solution also predicts what happens inside the black hole, but we have no way of knowing this since not even light can escape (to bring us information) once past the event horizon. Other solutions of the equation deal with rotating or charged black holes - check out my video on the Kerr solution here: youtu.be/kIbP2Sg8y18
The next solution we look at is the flat spacetime solution for an empty region of spacetime. This is a very important, but trivial, solution. It just says that spacetime is NOT warped when there is no mass to warp it - just as we'd expect in a steady-state case. But this is not the only solution that studies an empty region of spacetime.
Gravitational waves are another possible solution to the equation. They are a rippling of the spacetime fabric, transferring energy from the source, and they do not need mass to exist in the region through which they travel (though they are usually formed by interactions of massive objects).
Thanks for watching, please do check out my links:
MERCH - https://parth-gs-merch-stand.creator-spring.com/
INSTAGRAM - @parthvlogs
PATREON - patreon.com/parthg
MUSIC CHANNEL - Parth G's Shenanigans
Here are some affiliate links for things I use!
Quantum Physics Book I Enjoy: https://amzn.to/3sxLlgL
My Camera: https://amzn.to/2SjZzWq
ND Filter: https://amzn.to/3qoGwHk
Timestamps:
0:00 - Einstein's Field Equations in General Relativity
2:26 - What Does It Mean to Solve Einstein's Field Equations?
3:29 - The Schwarzschild Solution (Black Holes!)
6:20 - The Flat Spacetime Solution
6:59 - Gravitational Waves!
