Spinning bodies and their effect on space/time.

[Sorcerer]

Does a spinning body have more mass than a stationary one. What frame of reference applies, does an observer on a spinning body interpret it as extra mass and an outside observer view it as spin?

 

To what extent is spacetime twisted by a spinning body? Can they warp it like the coriolis force warps convection currents?

 

If a black hole formed from a rotating accretion disk and we take the ballerina pulling in their arms analogy, the closer to the center the greater the speed of rotation. So a hypothetically large as possible disk could form a black hole that spins at a speed approaching the speed of light.

 

How does this alter the black holes effect on spacetime. Does the black hole have greater energy and therefore mass equivalence compared to a non rotating black hole made of an equal amount of matter?

 

If there were multiple micro black holes rotating at close to the speed of light, what density would be needed to account for them as dark matter.

 

How does it make any sense to say a singularity is rotating? It lacks the dimensions for a rotational axis, while being the axis for material rotating around it.

 

Is it seen as the rotational energy (E) becoming mass (m) at the singularity, since as it approaches it forms a limit to ( c ). But at the singularity c isn't a property, because there is no distance in 0 dimensions. However mass and energy are conserved and their effect observed by gravity?

 

Just as the moon earth system loses earth spin and seperates in distance. Wouldn't tidal forces from orbiting stars also slow the singularity's spin. But since it isn't spinning, isn't it just transferring it's mass to energy?

 

How does this mass energy equivalency have meaning where outside the singularity E=mc^2, but inside c isn't a value, because there is no distance and therefore no speed only E=m.

 

Could this conflict of physical laws across the dimensions, allow for the creation of mass without loss to the singularity? The singularity spin energy can't be tapped because it isn't spinning, ie it locks that energy away as perpetual.

Edited December 12, 2015 by Sorcerer

[ajb]

Mass and energy in general relativity are almost synonymous using E=mc^2. However, the notion of energy is quite subtle.

 

Look up Komar mass, Bondi mass and ADM mass.

 

The first works for stationary space-times and the other two for asymptotically flat.

 

The important thing is that energy is something to do with physics being invariant under time translations. If there is no sensible way of thinking about space + time then these is going to be trouble with defining energy of a space-time.

[MigL]

Neither a Black Hole or a ballerina 'gains' angular momentum or 'spinning' energy as they collapse or draw in their arms.

Angular momentum is conserved.

That is the cause of the increased spinning speed.

 

Although rotating Black Holes do have some interesting effects on their local space-time, such as frame 'dragging'.

[Strange]

Although rotating Black Holes do have some interesting effects on their local space-time, such as frame 'dragging'.

 

All rotating masses cause frame dragging but it is usually a very small effect.

https://en.wikipedia.org/wiki/Gravity_Probe_B

[Sorcerer]

Neither a Black Hole or a ballerina 'gains' angular momentum or 'spinning' energy as they collapse or draw in their arms.

Angular momentum is conserved.

That is the cause of the increased spinning speed.

 

 

 

If a black hole formed from a rotating accretion disk and we take the ballerina pulling in their arms analogy, the closer to the center the greater the speed of rotation. So a hypothetically large as possible disk could form a black hole that spins at a speed approaching the speed of light.

 

I guess you could have interpreted what I said as meaning it "gains" momentum. But yes I understand that the same speed over a smaller distance = more revolutions.

 

So what would the size of a disk a black hole formed from and what initial speed would it need to be rotating in order for it to end up spinning at close to the speed of light.

 

How fast is this: https://en.wikipedia.org/wiki/GRS_1915%2B105BH spinning, it says 1,150 revs but what is the size of the equator at the event horizon.

 

What does it mean for a singularity to be revolving?

 

Is frame dragging influenced by speed of rotation, ie the same mass spinning faster will drag space time further? Is that the correct relationship, from: https://en.wikipedia.org/wiki/Frame-dragging

 

What's this, it just seems like some weird Hawking radiation : https://en.wikipedia.org/wiki/Penrose_process and how is it that " the infalling piece has negative mass-energy".

 

If a spaceship were to travel from the pole of a rotating black hole (just outside the event horizon) to the equator, what path would it follow. Can any similarities be made between this and the Coriolis effect? Is space dragging here analogous to the curvature of convection cells in the atmosphere. Do any of the equations overlap?

[Strange]

How fast is this: https://en.wikipedia.org/wiki/GRS_1915%2B105BH spinning, it says 1,150 revs but what is the size of the equator at the event horizon.

 

It says that the mass is probably between 10 and 18 times that of the sun, so the radius is between 30 and 54km. (I'll let you work out the speed!)

 

What does it mean for a singularity to be revolving?

 

Note that in a rotating black hole, the singularity is a ring, not a point.

 

What's this, it just seems like some weird Hawking radiation : https://en.wikipedia.org/wiki/Penrose_process and how is it that " the infalling piece has negative mass-energy.

 

I think that, like Hawking's similar description of Hawking radiation, it is an analogy to the mathematical description of what is happening. And possibly not a very accurate one.

[MigL]

Please note, Sorcerer, that the event horizon doesn't rotate as it is a mathematical construct.

 

The Penrose process ( didn't know it was due to Penrose ) is actually a process for extracting energy from a rotating BH.

[Sorcerer]

Please note, Sorcerer, that the event horizon doesn't rotate as it is a mathematical construct.

 

 

Good point, so when wiki says:

"It is also a microquasar, and it appears that the black hole may rotate at 1,150 times per second.^[6]"

 

What part of it are they meaning? Wouldn't an object in synchronous orbit just above the event horizon be a good point to measure from, can such an orbit be achieved?

 

and Strange points out:

 

 

Note that in a rotating black hole, the singularity is a ring, not a point.

What is the diameter of the ring? Because that would determine how fast it is "spinning", right?

 

I use "spinning", because it's actually moving in a closed curve trajectory and that's not really spinning. But to be fair I guess that's like how only the central axis of the earth "spins" and everything else moves around it in a closed curve.

 

 

The Penrose process ( didn't know it was due to Penrose ) is actually a process for extracting energy from a rotating BH.

 

Shouldn't there be other ways? The moon is moving away from the earth and the earths rotation is slowing down. I'm still confused as to how: "the infalling piece has negative mass-energy". It seems unnecessary to me.

 

I have another topic on bremsstrahlung radiation (which would probably apply more to charged BH's). Similarly, shouldn't an object passing through the gravitation field and accelerating or decelerating, but not crossing the event horizon reduce mass, like how voyager was sling shot? Since mass-energy is related to momentum through E=mc^2, what would determine a preference for mass over rotation?

Which leads to another question, if there is no preference what stops all the mass evaporating leaving "nothing" rotating. So long as there was enough warping of gravity by rotation to maintain an event horizon. We can tell there's mass-energy, by gravity, and we can tell there's rotation by frame dragging. Isn't that hidden information posing a problem, surely the must be something to rotate, to drag the frame.

Edited January 5, 2016 by Sorcerer

[Strange]

What is the diameter of the ring? Because that would determine how fast it is "spinning", right?

 

I have no idea what the diameter of the ring is - or even if that question makes sense. It may be measured in seconds rather than metres.

http://www.daviddarling.info/encyclopedia/K/Kerr_black_hole.html

[Sorcerer]

 

I have no idea what the diameter of the ring is - or even if that question makes sense. It may be measured in seconds rather than metres.

http://www.daviddarling.info/encyclopedia/K/Kerr_black_hole.html

Being a point and considering other point particles normally act as waves, wouldn't hertz, or wavelength be more appropriate. A 1d wave around an axis of a 4d time-space?

And that leads me to ask, why the need for a ring? Point particles can have angular momentum, or "spin", why not a Black Hole, why does the maths give a ring shape? (why is probably the wrong question, is there something particular about the solution, that when altered, would produce an answer which allowed for a point?)

Could we test whether it was a ring or a point by measuring the extent of the ergosphere, a ring would produce an elipse and a point a sphere. It is possible to do that from outside the ergosphere, eg from earth with a telescope?

Edited January 5, 2016 by Sorcerer

[Strange]

Being a point and considering other point particles normally act as waves, wouldn't hertz, or wavelength be more appropriate. A 1d wave around an axis of a 4d time-space?

 

It is not a point, it is a ring. And the reason I think the radius may be measured in seconds is because isnide a black hole one of the spatial dimensions and the time dimension get swapped.

 

And that leads me to ask, why the need for a ring? Point particles can have angular momentum, or "spin", why not a Black Hole, why does the maths give a ring shape?

 

I guess the only way one could understand "why" would be to be intimately familiar with the maths. Which is waay over my head.

 

Could we test whether it was a ring or a point by measuring the extent of the ergosphere, a ring would produce an elipse and a point a sphere. It is possible to do that from outside the ergosphere, eg from earth with a telescope?

 

No. One of the fundamental rules of a black hole is that you cannot observe anything about the internals (that is why it is called an event horizon). It has mass, angular momentum and (possibly) charge. That's it.

[Sorcerer]

 

It is not a point, it is a ring. And the reason I think the radius may be measured in seconds is because isnide a black hole one of the spatial dimensions and the time dimension get swapped.

 

Well, a point moving in 4D about a 3D axis is a ring. It may not be a point on the central axis under this solution, but that doesn't mean it isn't, we can test it.

 

 

 

No. One of the fundamental rules of a black hole is that you cannot observe anything about the internals (that is why it is called an event horizon). It has mass, angular momentum and (possibly) charge. That's it.

The ergosphere is OUTSIDE the event horizon, it is the area in which frame dragging occurs. I am only intuiting that it is an elipsoid because of the ring, there is greater extension in the plane perpendicular to the axis of rotation. By the same thinking, if it was a point on the axis, the ergosphere would be spherical.

 

I guess it probably extends into the BH too, but I'm having trouble visualising it in the middle of the ring. Also the double event horizon thing gets my head a bit buzzing too.

IF we did test it, and IF the ergosphere was another shape or ideally a sphere, could we use the result to reverse engineer from the solution, to the equation? Would this be useful in finding a GUT?

Edited January 5, 2016 by Sorcerer

[Strange]

The ergosphere is OUTSIDE the event horizon, it is the area in which frame dragging occurs. I am only intuiting that it is an elipsoid because of the ring, there is greater extension in the plane perpendicular to the axis of rotation. By the same thinking, if it was a point on the axis, the ergosphere would be spherical.

 

The ring singularity and the ergosphere are both the result of the same thing (the black hole's angular momentum) so I don't think it makes sense to think that one is caused by the other. (Especially as the singularity probably doesn't really exist.)

[Sorcerer]

 

The ring singularity and the ergosphere are both the result of the same thing (the black hole's angular momentum) so I don't think it makes sense to think that one is caused by the other. (Especially as the singularity probably doesn't really exist.)

I see how an object would bulge at the equator, much like the earth, due to centrifical effects. But a point cannot bulge, and a ring doesn't seem like an analogous shape. An effect like frame-dragging shouldn't bulge, because of centrifical effects (unless the fabric of space can be acted on like matter), but the geometry of the ergosphere would be dependent on the distribution of mass. As a ring, mass is distributed unevenly from one axis to the other, it seemingly is quite logical to see the ergospheres shape as a direct dependent result.

[Strange]

I see how an object would bulge at the equator, much like the earth, due to centrifical effects. But a point cannot bulge, and a ring doesn't seem like an analogous shape.

 

You are trying to apply intuition and common sense to general relativity. This will nearly always give you the wrong result.

[Sorcerer]

 

You are trying to apply intuition and common sense to general relativity. This will nearly always give you the wrong result.

The geometric distribution of mass directly relates to the geometric distribution of the effects of gravity. But looking at it, the event horizons are spherical, so I probably am missing something.

[imatfaal]

The geometric distribution of mass directly relates to the geometric distribution of the effects of gravity. But looking at it, the event horizons are spherical, so I probably am missing something.

 

What you really need to look at is the distribution of mass-energy etc. in the stress-energy tensor whilst utilising a Kerr Metric - this is a metric which forms this basis for the solution to the Einstein Field Equations (rotating and not charged black hole) . If you find a copy of the Kerr Metric (in usual notation) then the Angular momentum is instrinsic to every term in the metric. Now you might be able to visualize how multiplying or dividing a term by the angular momentum alters the overall value - but I can promise you that I cannot. So you really have to stick with the maths - which is pretty fiendish. Remember that much of the later work on black hole singularities was brought together by Hawking and Penrose - probably the two greatest British mathematicians of their generation.

[Strange]

And the Kerr metric wasn't worked out for 50 years (that might just be because no one looked at it, or it might be an indication of how difficult it is).

[imatfaal]

And the Kerr metric wasn't worked out for 50 years (that might just be because no one looked at it, or it might be an indication of how difficult it is).

 

As the Kerr is best approximation of most of the real black holes from the 4 black hole solutions to the EFEs then I would have thought that people were trying as soon as poor Karl Schwartzchild finished his work

[Sorcerer]

Well ok, on further reading the shape of the ergosphere is given simply by the difference in angular momentum between the poles and the equator. At the poles the distance of travel is 0 and hence the BH angular momentum is 0, the point is not spinning it is stationary and the ergosphere extends 0 distance, the ergosurface perpendicular with the axis of rotation.

 

But as we move from the pole to the equator, the distance of travel over the same time interval, and hence the angular momentum increases, where it comes to be at a maximum at the equator. This forms the oblate sphereoid shape. The shape is not due to the distribution of mass at the center of the black hole, although the ring shape could be shaped as such because ofo a similar reason. The ring being the 1D equivalent of the oblate sphereoid, a singularity, or point spinning on its axis, is its axis and its equator. Therefore, during formation, the moment immediately before it collapses to a singularity, it will distribute its mass in a ring perpendicular to and centering on its axis. Otherwise as it approaches a point the speed at which it rotates approaches the speed of light.

 

From Wiki:

 

 

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 angular momentum. A point at the poles does not move, and thus has no angular momentum, while at the equator the distance covered by a point in the black hole within a given time is greater than any other point at the black hole, giving the point at the equator the greatest angular momentum. This difference of angular momentum that extends from the poles to the equator and is reflected over the equator is what gives the ergosphere its oblated shape. If the gravity or the rotation speed increases, the size of the ergosphere increases as well. Conversely, if the rotation speed decreases, the size of ergosphere decreases, too.

 

What confuses me here is the statement: "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 angular momentum."

 

I'm guessing the event horizon is determined by the total mass/energy and a (1), small black hole spinning fast, with equal mass energy, to a (2), large black hole spinning slow, would produce equal sized event horizons. While instead the ergosphere would be more angular momentum dominated, (given it's shape is governed by the distribution of angular momentum), so comparisons between 1 and 2, 1 would have a larger ergosphere than 2. Is this correct?

Also, is this how the angular momentum of a black hole is calculated? Is it from the ratio of the event horizon to the ergosphere? Or is it estimated in other ways?

Edited January 8, 2016 by Sorcerer

[MigL]

I'm just going from memory here as its been quite a while since I even attempted to understand the Kerr solution...

 

A rotating BH will have two event horizons, one inside the other, just like a charged BH ( Nordstrom solution ).

Theoretically it should be possible for a BH to gain enough angular momentum such that the inner horizon moves outside the outer horizon and we are left with a 'naked' singularity.

I don't think it could actually be realised though.

[Sorcerer]

I'm just going from memory here as its been quite a while since I even attempted to understand the Kerr solution...

 

A rotating BH will have two event horizons, one inside the other, just like a charged BH ( Nordstrom solution ).

Theoretically it should be possible for a BH to gain enough angular momentum such that the inner horizon moves outside the outer horizon and we are left with a 'naked' singularity.

I don't think it could actually be realised though.

Why don't both horizons move? I thought that horizons are proportional to mass. If one horizon grows surely so should the other.

 

I was looking at the double horizon thing and wondered about it, is it just showing and area of stable eternal orbit inside the first event horizon but before the second, where objects can stay and not join the singularity, but also cannot ever escape back past the first horizon?

 

Assuming your example of event horizons "crossing" is possible. Wouldn't the inner horizon just squeeze, or slowly annex this stable middle region, forcing the matter there out of stable orbit, having to join the singularity eventually?

 

Immediately before the horizons "cross" there would be a point where the event horizons are both of equal size, it would be impossible to tell them apart, they would be a singular horizon. If the 2nd one moved outside the 1st, it would be indistinguishable from the two simply seperating back the way they were. Space and time reversal, if that's one major factor, would be the same as it was. Rather than horizons crossing it would simply be horizons merging and separating again.

 

(I actually never understood that dimension switching thing, does space get 1 dimension and time get 3? And what the hell does that mean anyway, seems more like the math is explaining something which isn't really able to be described in words. Travelling in space is always travelling in time, how does it change anything? Being forced to travel forwards in space is meaningless since the time dimension which has become space-like ensures those previous coordinates, which are "behind" you, are in the past anyway, you could move backwards and be on the same coordinates but in the future..... it really doesn't seem of any special consequence. We can't move backwards in time here outside the event horizon and that's the same as being unable to move backwards in space, we're always moving into a region of space which is in our future. I could break a game of pool and rack them back up, the balls go backwards to where they were in space relative to the table, but they're at another point in time.)

 

It'd be nice if you could answer some of my questions from the previous posts MigL, so far there's more questions than answers.

Edited January 8, 2016 by Sorcerer

[Sorcerer]

http://www.einstein-online.info/spotlights/changing_places

So this confused the hell out of me:

"This is exceedingly weird. From the outside, the region of a black hole looks like the surface of a sphere (in our model with two space dimensions and one time dimension, like the circumference of a circle). But inside that sphere, which has only a finite surface area, you can "hide" objects that are infinitely large - infinitely extended in space. How does this work? Again, it works because time and space trade places. Our simple scenario corresponds to an eternal black hole - a black hole that has always existed and will continue to exist indefinitely in the future. From the outside, the black hole is infinitely extended in time, but has only a finite size in space. Inside, the tables are turned: Time is only of finite extent (it starts at the horizon and ends abruptly at the singularity-axis), but instead one space direction, the axis direction, is now infinitely long."

 

 

First I don't understand how the black hole has a finite size in space.

 

1. The black hole is the sum of all it's parts over an infinite time. If we had a 2 meter diameter sphere which was eternal its size would be 4/3 pi^3 summed to infinity. It would be an infinitely large tube in both time and space. To say it's finite in space, just doesn't make any sense, each moment of time is a new moment of space, space is cumulative.

 

2. If the axis direction inside the even horizon is infinite, but the time direction finite, anything travelling to the center would be travelling at an infinite velocity. v= d/t, since d is infinite dividing it by any finite number will produce an infinite result. The speed of light is the limit for speed, infinite speed is greater than the speed of light. It shouldn't be possible. However if the black hole is infinitely large (as in 1), then infinity divides neatly into infinity....... giving a velocity of 1 using the largest possible unit, meaning travelling at the speed of light.

 

Second, I don't understand why eternal black holes can't have a beginning in time. A timeline is infinite in both directions, if we label an origin, there is still an infinite amount of time in the future. The black hole still existed before the event horizon formed, it's just that it was outside of it. And the universe may (I think must) have also had a beginning in time.

 

Third, why begin with the least likely type, this doesn't make sense and can't be real. Why waste time.

Edited January 8, 2016 by Sorcerer

[Strange]

1. Is that how you calculate the volume of the earth, for example? Multiply its size by the life time? I don't think so.

 

As for why the "least likely"; simply because it is the simplest. Finding solutions to the Einstein field equations is very difficult. So making simplifying assumptions like making it eternal, spherical, non-rotating, etc makes the problem tractable. And is a good approximation for many cases.

[Sorcerer]

1. Is that how you calculate the volume of the earth, for example? Multiply its size by the life time? I don't think so.

 

As for why the "least likely"; simply because it is the simplest. Finding solutions to the Einstein field equations is very difficult. So making simplifying assumptions like making it eternal, spherical, non-rotating, etc makes the problem tractable. And is a good approximation for many cases.

The size of the earth for what? The earth has its 3D size and you might want that, for a measurement of a particular moment in time. But what if you wanted to know how much space the earth occupied in a year? The earth occupied the entire orbit around the sun. It occupied all those points in space time. So in order to ask how big something is, you must also define over what time you are measuring it.

 

Separating space and time and then reversing the components, but first giving one an eternal infinite label and then having weirdness pop up when trying to describe it, isn't a indicator of a weird reality, it's an indicator of a weird set of conditions. If you give an object infinite time and then only consider length or size of an object under a small fraction of it, you must also then ignore the rest of the time. And thus you must ignore the rest of the space dimension when considering only a finite ammount of time inside the horizon. You can't have both.

 

In the moment you look at the BH and consider the length of the axis, it is only as long as that moment. Space is the same. Space is cut into intervals by arbitrary coordinates, 3 of space and 1 of time. You cannot measure any length without taking a small amount of time to do so, another observer may get another result, because either his length or his time disagreed. They're not separate.

As for why the "least likely"; simply because it is the simplest. Finding solutions to the Einstein field equations is very difficult. So making simplifying assumptions like making it eternal, spherical, non-rotating, etc makes the problem tractable. And is a good approximation for many cases.

 

Hopefully one day our computing / AI will be good enough that we won't have to dumb things down. This is most likely why we're having so much trouble finding a GUT. If we simplify 2 halves of a whole and exclude the places they interlink, we'll never fit them together. It's like cutting a third of the peg off a puzzle piece and filling in half of it's opposites hole, they'll never line up.

Edited January 9, 2016 by Sorcerer