Parth G | Strange Properties of Spinning Black Holes - Kerr Metric, General Relativity, Physics Explained @ParthGChannel | Uploaded 3 years ago | Updated 11 hours ago
Hey everyone, I'm back with a video about black holes! This time, we're talking about spinning (rotating) black holes, and their rather interesting characteristics.
The mathematical (and theoretical) properties of a rotating black hole are described by the Kerr metric. This metric is a solution of Einstein's Field Equations, thought to be a good description of our universe on the large scale. Just like how the Minkowski metric describes empty, flat spacetime, and the Schwarzschild metric describes the spacetime around a stationary black hole, the Kerr metric describes the spacetime around a rotating black hole.
Something worth discussing is the event horizon of the black hole we happen to be studying. This is the boundary around the hole, beyond which not even light can escape. If any object is closer to the centre of the black hole than the event horizon, then it's not coming back. A strange (but mathematically accurate) way to think about this behaviour is like time and space reversing properties. Outside the event horizon, you can only move in one direction in time (forward) but multiple directions in space. Inside the event horizon, you can only move in one direction in space (toward the centre of the black hole) but time travel may be possible there.
For a stationary black hole, the event horizon is spherical. For a rotating black hole it's an oblate spheroid - basically a sphere that's been squished at the poles of the rotating axis, and stretches further out at the equator. But rather more interestingly, the Kerr metric suggests that there should exist another event horizon inside the one we have been discussing so far. This inner horizon is slightly problematic for a couple of reasons. Firstly, we currently have no way of probing whether or not it exists, because not even light can escape the outer horizon. Secondly, the Kerr metric is technically only accurate for the spacetime outside our black hole. But if we extend the mathematics to inside the black hole, we find that it tells us an inner horizon may exist.
The Kerr metric also suggests the existence of another important surface, outside the event horizon. This surface is known as the stationary limit surface. Any object crossing this surface must move with the same sense as the rotation of the black hole. In other words, an object is inside the stationary limit surface, and the black hole is rotating anticlockwise / counterclockwise, then the object cannot rotate clockwise. Interestingly, particles that are inside the stationary limit surface but outside the event horizon, are in a region known as the ergosphere. This region is called the ergosphere because we can actually extract energy or work from the rotating black hole (ergon = work). This happens because particles in the ergosphere can "pick up" rotational energy from the black hole, having been forced to rotate with the same sense of the black hole, and then escape the black hole (since they haven't yet fallen into the event horizon), taking the energy away from the hole. The rotation of the black hole diminishes as a result. This energy extraction method is known as the Penrose Process, and I'd like to make a separate video about this at some point.
Another interesting idea we can glean from the Kerr metric is that a rotating black hole has a different kind of singularity at its centre than a stationary one. A singularity is a region of infinite density, where mass is extremely tightly packed into basically zero space. A stationary black hole has a small point singularity at its centre. But it seems like a rotating black hole has a ring singularity - a ring shaped region where mass is extremely tightly packed.
The Kerr metric states that as a black hole rotates faster and faster, the (outer) event horizon gets smaller. Eventually, the horizon ceases to exist, and we're left with a naked singularity. This is a singularity that we can theoretically observe, because there is no event horizon to prevent particles from reaching an observer elsewhere in space. However, Penrose came up with a hypothesis known as the "Cosmic Censorship Hypothesis" to suggest why we may never be able to observe a naked singularity. I'd like to save this discussion for another video too.
In this video we discuss rotating, uncharged black holes. Previously I've discussed stationary uncharged black holes. In future videos, I'd like to talk about stationary and rotating charged black holes too.
Thanks so much for watching, please subscribe and hit the bell button if you enjoyed this video. Check out my socials:
Instagram - parthvlogs
Patreon - patreon.com/parthg
Hey everyone, I'm back with a video about black holes! This time, we're talking about spinning (rotating) black holes, and their rather interesting characteristics.
The mathematical (and theoretical) properties of a rotating black hole are described by the Kerr metric. This metric is a solution of Einstein's Field Equations, thought to be a good description of our universe on the large scale. Just like how the Minkowski metric describes empty, flat spacetime, and the Schwarzschild metric describes the spacetime around a stationary black hole, the Kerr metric describes the spacetime around a rotating black hole.
Something worth discussing is the event horizon of the black hole we happen to be studying. This is the boundary around the hole, beyond which not even light can escape. If any object is closer to the centre of the black hole than the event horizon, then it's not coming back. A strange (but mathematically accurate) way to think about this behaviour is like time and space reversing properties. Outside the event horizon, you can only move in one direction in time (forward) but multiple directions in space. Inside the event horizon, you can only move in one direction in space (toward the centre of the black hole) but time travel may be possible there.
For a stationary black hole, the event horizon is spherical. For a rotating black hole it's an oblate spheroid - basically a sphere that's been squished at the poles of the rotating axis, and stretches further out at the equator. But rather more interestingly, the Kerr metric suggests that there should exist another event horizon inside the one we have been discussing so far. This inner horizon is slightly problematic for a couple of reasons. Firstly, we currently have no way of probing whether or not it exists, because not even light can escape the outer horizon. Secondly, the Kerr metric is technically only accurate for the spacetime outside our black hole. But if we extend the mathematics to inside the black hole, we find that it tells us an inner horizon may exist.
The Kerr metric also suggests the existence of another important surface, outside the event horizon. This surface is known as the stationary limit surface. Any object crossing this surface must move with the same sense as the rotation of the black hole. In other words, an object is inside the stationary limit surface, and the black hole is rotating anticlockwise / counterclockwise, then the object cannot rotate clockwise. Interestingly, particles that are inside the stationary limit surface but outside the event horizon, are in a region known as the ergosphere. This region is called the ergosphere because we can actually extract energy or work from the rotating black hole (ergon = work). This happens because particles in the ergosphere can "pick up" rotational energy from the black hole, having been forced to rotate with the same sense of the black hole, and then escape the black hole (since they haven't yet fallen into the event horizon), taking the energy away from the hole. The rotation of the black hole diminishes as a result. This energy extraction method is known as the Penrose Process, and I'd like to make a separate video about this at some point.
Another interesting idea we can glean from the Kerr metric is that a rotating black hole has a different kind of singularity at its centre than a stationary one. A singularity is a region of infinite density, where mass is extremely tightly packed into basically zero space. A stationary black hole has a small point singularity at its centre. But it seems like a rotating black hole has a ring singularity - a ring shaped region where mass is extremely tightly packed.
The Kerr metric states that as a black hole rotates faster and faster, the (outer) event horizon gets smaller. Eventually, the horizon ceases to exist, and we're left with a naked singularity. This is a singularity that we can theoretically observe, because there is no event horizon to prevent particles from reaching an observer elsewhere in space. However, Penrose came up with a hypothesis known as the "Cosmic Censorship Hypothesis" to suggest why we may never be able to observe a naked singularity. I'd like to save this discussion for another video too.
In this video we discuss rotating, uncharged black holes. Previously I've discussed stationary uncharged black holes. In future videos, I'd like to talk about stationary and rotating charged black holes too.
Thanks so much for watching, please subscribe and hit the bell button if you enjoyed this video. Check out my socials:
Instagram - parthvlogs
Patreon - patreon.com/parthg
