Starship Asterisk*

orin stepanek wrote: ↑Tue Aug 25, 2020 11:25 am
Is today's APOD Hypothesis; Theory; or Law?

neufer wrote: ↑Tue Aug 25, 2020 1:57 pm

orin stepanek wrote: ↑Tue Aug 25, 2020 11:25 am
Is today's APOD Hypothesis; Theory; or Law?

Einstein's General Theory of Relativity couldn't predict if black holes would form in the first place.
But now that we know that they, in fact, do this is what the Theory predicts that they should look like.
At least one blurry black hole image by the Event Horizon Telescope suggests that that is, in fact, the case.

earthltd wrote: ↑Tue Aug 25, 2020 3:52 pm The frame with the info is only in the thumbnail and is too small to read. It isn't in the video which I can expand.

APOD Robot wrote: ↑Tue Aug 25, 2020 4:05 am ... The featured animated video gives a visualization. ...

earthltd wrote: ↑Tue Aug 25, 2020 3:52 pm The frame with the info is only in the thumbnail and is too small to read. It isn't in the video which I can expand.

APOD Robot wrote: ↑Tue Aug 25, 2020 4:05 am Visualization: A Black Hole Accretion Disk

Explanation: What would it look like to circle a black hole? If the black hole was surrounded by a swirling disk of glowing and accreting gas, then the great gravity of the black hole would deflect light emitted by the disk to make it look very unusual. The featured animated video gives a visualization. The video starts with you, the observer, looking toward the black hole from just above the plane of the accretion disk. Surrounding the central black hole is a thin circular image of the orbiting disk that marks the position of the photon sphere -- inside of which lies the black hole's event horizon. Toward the left, parts of the large main image of the disk appear brighter as they move toward you. As the video continues, you loop over the black hole, soon looking down from the top, then passing through the disk plane on the far side, then returning to your original vantage point. The accretion disk does some interesting image inversions -- but never appears flat. Visualizations such as this are particularly relevant today as black holes are being imaged in unprecedented detail by the Event Horizon Telescope.

johnnydeep wrote: ↑Tue Aug 25, 2020 4:34 pm So, the text says the accretion disk "never appears flat", but it sure looks flat to me, at least when looking down from the top!

Also, I'm always a bit surprised that the accretion disk is flat in the first place. Is an accretion disk only possible if the black hole is rotating? And is the accretion disk always perpendicular to the axis of the black hole's rotation? I realize that it's almost a certainty that all black holes rotate (since the stars that they formed from rotate and angular momentum is preserved during shrinking, and also during accreting as matter falls in non-perpendicularly), but what would a non-rotating black hole look like while it was growing? Though perhaps it wouldn't remain non-rotating for long.

JohnD wrote: ↑Tue Aug 25, 2020 2:41 pm
Surely, Neufer, Einstein's Theory certainly predicted black holes! But it was Schwarzchild who used his theory to explore the singularity, to predict the event horizon and even its diameter, in his Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie? And in 1916, only one year after Einstein published his four papers in 1915!

Also certainly, this prediction was considered to be a mathematical curiosity for many years, but there can be no doubt that the power of Einstein's thought and Schwarzchild's insight predicted them.

https://en.wikipedia.org/wiki/Black_hole#Formation_and_evolution wrote:
<<Given the bizarre character of black holes, it was long questioned whether such objects could actually exist in nature or whether they were merely pathological solutions to Einstein's equations. Einstein himself wrongly thought black holes would not form, because he held that the angular momentum of collapsing particles would stabilize their motion at some radius. This led the general relativity community to dismiss all results to the contrary for many years. However, a minority of relativists continued to contend that black holes were physical objects, and by the end of the 1960s, they had persuaded the majority of researchers in the field that there is no obstacle to the formation of an event horizon.

Penrose demonstrated that once an event horizon forms, general relativity without quantum mechanics requires that a singularity will form within. Shortly afterwards, Hawking showed that many cosmological solutions that describe the Big Bang have singularities without scalar fields or other exotic matter. The Kerr solution, the no-hair theorem, and the laws of black hole thermodynamics showed that the physical properties of black holes were simple and comprehensible, making them respectable subjects for research. Conventional black holes are formed by gravitational collapse of heavy objects such as stars, but they can also in theory be formed by other processes.>>

Chris Peterson wrote: ↑Tue Aug 25, 2020 5:12 pm

johnnydeep wrote: ↑Tue Aug 25, 2020 4:34 pm So, the text says the accretion disk "never appears flat", but it sure looks flat to me, at least when looking down from the top!

What doesn't?

Chris Peterson wrote: ↑Tue Aug 25, 2020 5:12 pm An accretion disc does not depend upon a rotating black hole. Infalling matter is in orbit, and interacts with other matter such that particles exchange angular momentum and are ejected or end up in the same plane.

In general, an accretion disc does not need to align in any particular way with the body it is orbiting. For instance, there is no reason a planetary system couldn't form on a different plane than that defined by the rotational axis of the protostar it orbits. (In practice they would normally be aligned, but only because both originate in the same rotating gas cloud.) That might be different for the special case of a black hole accretion disc, given the way that a rotating black hole warps spacetime around it. Not sure about that.

johnnydeep wrote: ↑Tue Aug 25, 2020 10:08 pm

Chris Peterson wrote: ↑Tue Aug 25, 2020 5:12 pm

johnnydeep wrote: ↑Tue Aug 25, 2020 4:34 pm So, the text says the accretion disk "never appears flat", but it sure looks flat to me, at least when looking down from the top!

What doesn't?

:lol2:

Chris Peterson wrote: ↑Tue Aug 25, 2020 5:12 pm An accretion disc does not depend upon a rotating black hole. Infalling matter is in orbit, and interacts with other matter such that particles exchange angular momentum and are ejected or end up in the same plane.

In general, an accretion disc does not need to align in any particular way with the body it is orbiting. For instance, there is no reason a planetary system couldn't form on a different plane than that defined by the rotational axis of the protostar it orbits. (In practice they would normally be aligned, but only because both originate in the same rotating gas cloud.) That might be different for the special case of a black hole accretion disc, given the way that a rotating black hole warps spacetime around it. Not sure about that.

Given that in-falling matter could come from any direction, why isn't there just a cloud of stuff, instead of a disk?

johnnydeep wrote: ↑Tue Aug 25, 2020 10:08 pm
Given that in-falling matter could come from any direction, why isn't there just a cloud of stuff, instead of a disk?

https://en.wikipedia.org/wiki/Frame-dragging#Astronomical_evidence wrote:

Relativistic jet. The environment around the AGN where the relativistic plasma is collimated into jets which escape along the pole of the supermassive black hole

---

<<Frame-dragging is an effect on spacetime, predicted by Albert Einstein's general theory of relativity, that is due to non-static stationary distributions of mass–energy. A stationary field is one that is in a steady state, but the masses causing that field may be non-static -— rotating, for instance. More generally, the subject that deals with the effects caused by mass–energy currents is known as gravitomagnetism, which is analogous to the magnetism of classical electromagnetism.

The first frame-dragging effect was derived in 1918, in the framework of general relativity, by the Austrian physicists Josef Lense and Hans Thirring, and is also known as the Lense–Thirring effect. They predicted that the rotation of a massive object would distort the spacetime metric, making the orbit of a nearby test particle precess.

Relativistic jets may provide evidence for the reality of frame-dragging. Gravitomagnetic forces produced by the Lense–Thirring effect (frame dragging) within the ergosphere of rotating black holes combined with the energy extraction mechanism by Penrose have been used to explain the observed properties of relativistic jets. The gravitomagnetic model developed by Reva Kay Williams predicts the observed high energy particles (~GeV) emitted by quasars and active galactic nuclei; the extraction of X-rays, γ-rays, and relativistic e−–e+ pairs; the collimated jets about the polar axis; and the asymmetrical formation of jets (relative to the orbital plane).>>

neufer wrote: ↑Tue Aug 25, 2020 11:41 pm

johnnydeep wrote: ↑Tue Aug 25, 2020 10:08 pm
Given that in-falling matter could come from any direction, why isn't there just a cloud of stuff, instead of a disk?

https://en.wikipedia.org/wiki/Frame-dragging#Astronomical_evidence wrote:

Relativistic jet. The environment around the AGN where the relativistic plasma is collimated into jets which escape along the pole of the supermassive black hole

---

<<Frame-dragging is an effect on spacetime, predicted by Albert Einstein's general theory of relativity, that is due to non-static stationary distributions of mass–energy. A stationary field is one that is in a steady state, but the masses causing that field may be non-static -— rotating, for instance. More generally, the subject that deals with the effects caused by mass–energy currents is known as gravitomagnetism, which is analogous to the magnetism of classical electromagnetism.

The first frame-dragging effect was derived in 1918, in the framework of general relativity, by the Austrian physicists Josef Lense and Hans Thirring, and is also known as the Lense–Thirring effect. They predicted that the rotation of a massive object would distort the spacetime metric, making the orbit of a nearby test particle precess.

Relativistic jets may provide evidence for the reality of frame-dragging. Gravitomagnetic forces produced by the Lense–Thirring effect (frame dragging) within the ergosphere of rotating black holes combined with the energy extraction mechanism by Penrose have been used to explain the observed properties of relativistic jets. The gravitomagnetic model developed by Reva Kay Williams predicts the observed high energy particles (~GeV) emitted by quasars and active galactic nuclei; the extraction of X-rays, γ-rays, and relativistic e−–e+ pairs; the collimated jets about the polar axis; and the asymmetrical formation of jets (relative to the orbital plane).>>

Chris Peterson wrote: ↑Tue Aug 25, 2020 11:48 pm
Yes... but you don't need frame dragging to explain the collapse of infalling matter to a disc.

• King Lear : Act II, scene IV

• Are in the poorest thing superfluous:
  Allow not nature more than nature needs,

Relativistic jets may provide evidence for the reality of frame-dragging. Gravitomagnetic forces produced by the Lense–Thirring effect (frame dragging) within the ergosphere of rotating black holes combined with the energy extraction mechanism by Penrose have been used to explain the observed properties of relativistic jets.

BDanielMayfield wrote: ↑Wed Aug 26, 2020 4:08 am

Relativistic jets may provide evidence for the reality of frame-dragging. Gravitomagnetic forces produced by the Lense–Thirring effect (frame dragging) within the ergosphere of rotating black holes combined with the energy extraction mechanism by Penrose have been used to explain the observed properties of relativistic jets.

Er, what's an ergosphere? How far out do they extend?

https://en.wikipedia.org/wiki/Ergosphere wrote:

In the ergosphere (shown here in light gray), the component gtt is negative, i.e., acts like a purely spatial metric component. Consequently, timelike or lightlike worldlines within this region must co-rotate with the inner mass. Cartesian Kerr–Schild coordinates, equatorial perspective.

---

<<The ergosphere is a region located outside a rotating black hole's outer event horizon. Its name was proposed by Remo Ruffini and John Archibald Wheeler during the Les Houches lectures in 1971 and is derived from the Greek word ἔργον (ergon), which means "work". It received this name because it is theoretically possible to extract energy and mass from this region. The ergosphere touches the event horizon at the poles of a rotating black hole and extends to a greater radius at the equator. A black hole with modest angular momentum has an ergosphere with a shape approximated by an oblate spheroid, while faster spins produce a more pumpkin-shaped ergosphere. The equatorial (maximal) radius of an ergosphere is the Schwarzschild radius, the radius of a non-rotating black hole. The polar (minimal) radius is also the polar (minimal) radius of the event horizon which can be as little as half the Schwarzschild radius for a maximally rotating black hole.

The size of the ergosphere, the distance between the ergosurface and the event horizon, is not necessarily proportional to the radius of the event horizon, but rather to the black hole's gravity and its angular momentum. A point at the poles does not move, and thus has no angular momentum, while at the equator a point would have its greatest angular momentum. This variation of angular momentum that extends from the poles to the equator is what gives the ergosphere its oblate shape. As the mass of the black hole or its rotation speed increases, the size of the ergosphere increases as well.

As a black hole rotates, it twists spacetime in the direction of the rotation at a speed that decreases with distance from the event horizon. This process is known as the Lense–Thirring effect or frame-dragging. Because of this dragging effect, an object within the ergosphere cannot appear stationary with respect to an outside observer at a great distance unless that object were to move at faster than the speed of light (an impossibility) with respect to the local spacetime. The speed necessary for such an object to appear stationary decreases at points further out from the event horizon, until at some distance the required speed is that of the speed of light.

A suspended plumb, held stationary outside the ergosphere, will experience an infinite/diverging radial pull as it approaches the static limit. At some point it will start to fall, resulting in a gravitomagnetically induced spinward motion.

---

The set of all such points defines the ergosphere surface, called ergosurface. The outer surface of the ergosphere is called the static surface or static limit. This is because world lines change from being time-like outside the static limit to being space-like inside it. It is the speed of light that arbitrarily defines the ergosphere surface. Such a surface would appear as an oblate that is coincident with the event horizon at the pole of rotation, but at a greater distance from the event horizon at the equator. Outside this surface, space is still dragged, but at a lesser rate.

Since the ergosphere is outside the event horizon, it is still possible for objects that enter that region with sufficient velocity to escape from the gravitational pull of the black hole. An object can gain energy by entering the black hole's rotation and then escaping from it, thus taking some of the black hole's energy with it (making the maneuver similar to the exploitation of the Oberth effect around "normal" space objects).

This process of removing energy from a rotating black hole was proposed by the mathematician Roger Penrose in 1969 and is called the Penrose process. The maximal amount of energy gain possible for a single particle via this process is 20.7% in terms of its mass equivalence,[7] and if this process is repeated by the same mass, the theoretical maximal energy gain approaches 29% of its original mass-energy equivalent. As this energy is removed, the black hole loses angular momentum, the limit of zero rotation is approached as spacetime dragging is reduced. In the limit, the ergosphere no longer exists. This process is considered a possible explanation for a source of energy of such energetic phenomena as gamma ray bursts. Results from computer models show that the Penrose process is capable of producing the high-energy particles that are observed being emitted from quasars and other active galactic nuclei.>>

Chris Peterson wrote: ↑Tue Aug 25, 2020 10:16 pm

johnnydeep wrote: ↑Tue Aug 25, 2020 10:08 pm

Chris Peterson wrote: ↑Tue Aug 25, 2020 5:12 pm
What doesn't?

Chris Peterson wrote: ↑Tue Aug 25, 2020 5:12 pm An accretion disc does not depend upon a rotating black hole. Infalling matter is in orbit, and interacts with other matter such that particles exchange angular momentum and are ejected or end up in the same plane.

In general, an accretion disc does not need to align in any particular way with the body it is orbiting. For instance, there is no reason a planetary system couldn't form on a different plane than that defined by the rotational axis of the protostar it orbits. (In practice they would normally be aligned, but only because both originate in the same rotating gas cloud.) That might be different for the special case of a black hole accretion disc, given the way that a rotating black hole warps spacetime around it. Not sure about that.

Given that in-falling matter could come from any direction, why isn't there just a cloud of stuff, instead of a disk?

Only if it is tenuous enough to not interact hydrodynamically. That's how globular clusters and Oort clouds remain spherical. But if you get strong interactions, spherical clouds with particles at random inclinations always collapse into discs. Like spiral galaxies and accretion discs.

Cool! And based on that, I gather that the Kuiper Belt is concentrated enough to interact hydrodynamically - acting like a liquid? - and therefor become disk-like. I need to take a physics course...

Yes... but you don't need frame dragging to explain the collapse of infalling matter to a disc.

neufer wrote: ↑Wed Aug 26, 2020 12:23 pm

BDanielMayfield wrote: ↑Wed Aug 26, 2020 4:08 am

Relativistic jets may provide evidence for the reality of frame-dragging. Gravitomagnetic forces produced by the Lense–Thirring effect (frame dragging) within the ergosphere of rotating black holes combined with the energy extraction mechanism by Penrose have been used to explain the observed properties of relativistic jets.

Er, what's an ergosphere? How far out do they extend?

https://en.wikipedia.org/wiki/Ergosphere wrote:

In the ergosphere (shown here in light gray), the component gtt is negative, i.e., acts like a purely spatial metric component. Consequently, timelike or lightlike worldlines within this region must co-rotate with the inner mass. Cartesian Kerr–Schild coordinates, equatorial perspective.

---

<<The ergosphere is a region located outside a rotating black hole's outer event horizon. Its name was proposed by Remo Ruffini and John Archibald Wheeler during the Les Houches lectures in 1971 and is derived from the Greek word ἔργον (ergon), which means "work". It received this name because it is theoretically possible to extract energy and mass from this region. The ergosphere touches the event horizon at the poles of a rotating black hole and extends to a greater radius at the equator. A black hole with modest angular momentum has an ergosphere with a shape approximated by an oblate spheroid, while faster spins produce a more pumpkin-shaped ergosphere. The equatorial (maximal) radius of an ergosphere is the Schwarzschild radius, the radius of a non-rotating black hole. The polar (minimal) radius is also the polar (minimal) radius of the event horizon which can be as little as half the Schwarzschild radius for a maximally rotating black hole.

The size of the ergosphere, the distance between the ergosurface and the event horizon, is not necessarily proportional to the radius of the event horizon, but rather to the black hole's gravity and its angular momentum. A point at the poles does not move, and thus has no angular momentum, while at the equator a point would have its greatest angular momentum. This variation of angular momentum that extends from the poles to the equator is what gives the ergosphere its oblate shape. As the mass of the black hole or its rotation speed increases, the size of the ergosphere increases as well.

As a black hole rotates, it twists spacetime in the direction of the rotation at a speed that decreases with distance from the event horizon. This process is known as the Lense–Thirring effect or frame-dragging. Because of this dragging effect, an object within the ergosphere cannot appear stationary with respect to an outside observer at a great distance unless that object were to move at faster than the speed of light (an impossibility) with respect to the local spacetime. The speed necessary for such an object to appear stationary decreases at points further out from the event horizon, until at some distance the required speed is that of the speed of light.

A suspended plumb, held stationary outside the ergosphere, will experience an infinite/diverging radial pull as it approaches the static limit. At some point it will start to fall, resulting in a gravitomagnetically induced spinward motion.

---

The set of all such points defines the ergosphere surface, called ergosurface. The outer surface of the ergosphere is called the static surface or static limit. This is because world lines change from being time-like outside the static limit to being space-like inside it. It is the speed of light that arbitrarily defines the ergosphere surface. Such a surface would appear as an oblate that is coincident with the event horizon at the pole of rotation, but at a greater distance from the event horizon at the equator. Outside this surface, space is still dragged, but at a lesser rate.

Since the ergosphere is outside the event horizon, it is still possible for objects that enter that region with sufficient velocity to escape from the gravitational pull of the black hole. An object can gain energy by entering the black hole's rotation and then escaping from it, thus taking some of the black hole's energy with it (making the maneuver similar to the exploitation of the Oberth effect around "normal" space objects).

This process of removing energy from a rotating black hole was proposed by the mathematician Roger Penrose in 1969 and is called the Penrose process. The maximal amount of energy gain possible for a single particle via this process is 20.7% in terms of its mass equivalence,[7] and if this process is repeated by the same mass, the theoretical maximal energy gain approaches 29% of its original mass-energy equivalent. As this energy is removed, the black hole loses angular momentum, the limit of zero rotation is approached as spacetime dragging is reduced. In the limit, the ergosphere no longer exists. This process is considered a possible explanation for a source of energy of such energetic phenomena as gamma ray bursts. Results from computer models show that the Penrose process is capable of producing the high-energy particles that are observed being emitted from quasars and other active galactic nuclei.>>

johnnydeep wrote: ↑Wed Aug 26, 2020 2:28 pm
Thanks neufer, and especially for your always very well-formatted posts, even if sometimes I have to try real hard to follow your occasionally non-sequitur train of thought