Kerr Binary Blackhole systems

[artbeing B]

Hi everyone!

 

Yeah, I am a new guy with some burning questions that need member brainstorming.

 

I am writing a script requiring me get knowledge of a plausible way for a wormhole to form. Wormholes are so cliched in scfi writing that it is embarrassing to even mention that I want to use this dusty literary excuse to get my crew across the galaxy so they can be "lost".

 

But my research and emails with an astrophysicist have shed some light on the possibility of the WH forming in a Kerr Black Hole when the singularity is "ring" shaped. I understand that if a spaceship would enter the ergosphere of the KBH (and survive gravitational drag forces) then you could pass into the top of the inner/outer event horizons (which are toroidal in shape?) and going with the angular BH spin (maybe matching speed, although the current would do that anyway), wind in a spiral down through the singularity ring, where hopefully you imerge in another universe intact and not so much metal bits and spaghetti.

 

Assuming some of what I have said is correct. I would love some thoughts on:

 

- The flight path, what would the ship need to avoid?

 

- Is the top of the horizon shell weaker in tidal forces than the equator?

 

- Any kind of known or theorized information about the dynamics of this kind of BH (no equations please, there are many detailed BH papers full of equations, it is Greek to me!)

 

- I like the idea of a binary KBH for this scenario, The astrophysicist I emailed with alluded to the binary systems as being significant for the wormholes effect, can anybody shed light on this idea?

 

-Do the BHs of the binary need to be identical in mass and spin to be a stable system?

 

-What would be ideal specifications for this system? i.e. angular spin, solar masses of BHs, orbiting speed and radius etc.

 

 

Thanks so much in advance for your replies and answers! I look forward to the responses.

 

Take care everyone.

[Widdekind]

Relativistically-compact objects "trough" the fabric of space-time, i.e. they generate a curvature, into the fabric of space-time, that resembles a "deep grove", in what would otherwise be a flat "sheet" of (x,t) "fabric". Note, that "x" coordinate is a radial-like coordinate, that threads through the center of the spheroidal object, and out the other side, i.e. take the spheroidal object, run a radius all the way through it, from far far away on one side, through to far far away on the other side. In the absence of curvature, that one-spatial-dimension (x) could be represented as a two-space-time-dimensional (x,t) "fabric" of space-time. The mass at the center (x=0) "troughs" that fabric of space-time.

 

So, what would a rotating compact object do? Inexpertly, i offer that rotation "rolls up" the "troughed groove" that would otherwise "droop down". I.e. start with the "troughed" space-time fabric, and "grab the bottom of the groove", and "roll it up" (a little like a sleeping bag). In the following figure, time runs vaguely "lower right to upper left"; and the space-time fabric "rolls up to the right" representing the counter-clockwise rotation of the object. Again, the "x" coordinate represents a radial trajectory, from far far away, through the equator, and then center of the rotating object (latitude = 0 degrees), and then on back out the equator at the opposite side, and on out to far far the other way. Thus, the compact object would "hang like a bead" on that "x" coordinate line; but the x coordinate line is not polar, but equatorial, so that the "bead" would actually be rotating counter-clockwise (left-handedly). Extracting energy, as by the Penrose process, would involve "un-furling" the spacetime fabric (even as the rotation "furls" the "trough groove" imputed into spacetime, by mass):

 

 

Is the above an acceptable way of visualizing (in 1+1D) the curvature effects, of rotating compact objects, that "frame drag" the fabric of space-time?

 

---

 

oops -- i think that's wrong. About their equators, idealized rotating compact objects are symmetric. So, no radius, from the center on out, is distinguishable, from any other. But my drawing above, which tries to tie two radii rays together, shows a qualitative difference, in the curvature, on one side ("curls in and around") vs. the other ("curls the other way"). At best, only half of my drawing could possibly be qualitatively correct -- perhaps one of the radial rays qualitatively captures the gist of curvature, imputed into spacetime, by rotating compact objects. If i had to guess, since rotation acts like "anti-gravity" in the sense of centrifugal forces, so i would guess, that the ray incoming from the RHS in the above figure -- the ray for whom spacetime "furls the other way" -- might be more correct (less wrong). Somehow, all radial rays, from all azimuthal angles, would then "stitch together", for visualizing the fabric of spacetime, near a rotating compact object. (By way of comparison, the Flamm paraboloid for non-rotating BH is generated, by taking the solution for a single radial ray, and sweeping it around 2pi azimuthal radians, i.e. it is a surface-of-revolution; likewise, if any part of the above picture is correct, then one radial ray would have to be swept around 2pi azimuthal radians; every radial ray would be indistinguishable.)

Edited October 10, 2012 by Widdekind

[MigL]

Tidal forces would still be impossible to deal with.

 

Read Kip Thorne's book ' Black Holes and Time Warps: Einstein's outrageous Legacy' for an explanation of wormholes, their problems and their uses for generating CTL ( time machines ).

Turns out the biggest problem is keeping them open as they would collapse immediately upon entry. The only way to keep them open is threading them with exotic matter ( ie possessing negative energy ). The one place this exotic material can be harvested is at the event horizon of a black hole.

A Kerr black hole is a rotating black hole and, as a result, has an inner and an outer event horizon which is thickest at the'equator and co-incidental at the poles. This area between the event horizons is an area of negative energy where large amounts of exotic matter could be harvested ( by a sufficiently advanced civilization ).

[Widdekind]

Please ponder a plane single-time "snapshot" slice (2+0D) of spacetime, bisecting the spherical compact object. Draw radial & azimuthal coordinates on the "rubber sheet"; add a relativistically-compact mass; and the sheet sags deep down. Now, spin the mass up, and the "throat" of the space-time fabric twirls around, a little like spaghetti on a fork, via "frame dragging":

According to the Kerr solution, that winding-around of the spatial fabric squeezes the throat down, by (up to) a factor of two. Also, as the originally-radial coordinate lines twirl down the throat towards the compact object, their "winding angle" flattens out. A Kerr black-hole is maximally rotating, when the twirling around of the spatial fabric is so extreme, that the winding angle approaches zero, i.e. an originally radial ray, on approaching towards the object, gets "wrapped around the axel" infinitely many times; the originally-radial ray, down in at the Kerr radius (1/2 Schwarzschild radius) becomes wrapped around the event horizon, without crossing.

If you dropped a rock onto a Kerr-like object, you would not see the object fall straight towards the surface; instead the object would veer off in the direction of spin, and become entrained into a spiraling orbit around the object.

[Widdekind]

oops x2

 

Flat space-time fabric

Imagine a flat two-spatial-dimensional plane (to be the equatorial plane, of a black-hole). Lay out concentric circles ("hoola-hoops in space"); measure their lengths once around; divide by 2pi; define L/2pi = R. Then you label each of those rings with those calculated "R" values.

 

Schwarzschild space-time fabric

Add the mass to the middle. Viewed imaginatively from a higher-dimensional "hyperspace" perspective, "flat-land" sags in the center. Physically, if you were crawling around on one of those rings (in a space-suit say), labeled "radius = R"; and if you then reached out for the next space ring, labeled (from before the positioning of the mass) with the words "radius = R + 1m"; then you would observe that an actual meter-stick could now be placed in between the two rings, with lots of space to spare. If those rings had been tethered together, along radial rays, with bungee cords; then those bungee cords would have stretched. That is all you would notice, embedded into the curved space-time fabric. From "hyperspace", you could see, that all that extra space in between the rings, and stretch of bungee tethers, was due to each of those rings, being displaced from each other, "down" through an extra hyper-dimension:

 

Kerr space-time fabric

Now, spin the black-hole up. According to the Kerr solution, now space-time stretches, not only in the radial direction ("can't reach the next ring out"), but also in the azimuthal direction. Those space-rings labeled "radius = R" would be stretched apart; if they, too, were made of flexible "bungee tethers", then they would be observed to stretch out. Anything rigid would be ripped apart. For example, for a maximally-rotating black-hole, the space-ring around the equator of its event horizon, which had been labeled "radius = R_S" before spin-up, would now stretch out by about 25%. That azimuthal distension could be visualized, as the rotating black-hole "spinning out" the space-time around it, as if by a centrifugal-like force. From "hyperspace" perspective, that centrifugal "fling out" would widen the "throat" of the curved space-time fabric by up to about 25%:

Another property of Kerr space-time, is that, in the azimuthal direction (perpendicular to radial rays), light-cones (cdt vs. dl) get "squashed to the side". Traveling towards a maximally-rotating black-hole, along a radial ray, towards its equator, by the time you reach the inner Kerr-radius, both the prograde & retrograde light-trajectories (defining the azimuthal edges of the light-cone from that point in space-time) converge towards a common, prograde, orbit, around the black-hole, at light-speed. And, since all physical world-lines, of massive particles, must lie within their (forward) light-cones, so near rotating black-holes, frame-dragging whips everything into a "prograde at light-speed" orbit.

 

Putting the pieces together, if you ringed (the equator of) a maximally-rotating black-hole, at its Kerr radius, with a fiber-optic cable; then you would find that that fiber-optic cable had an absolute metric length of 2pi*R_S. And, if you tried to send light pulses, in both directions, around the space ring; then both bunches of photons would actually be whipped around prograde at light-speed. And, if you suddenly removed the mass entirely, then your "Kerr ring" would contract, down to half of its original length. Alternatively, starting from flat-space as above, the space-ring which would wind up girdling the introduced rotating black-hole's inner-most Kerr radius, would be the one, which you had previously (painstakingly) measured, and labeled with the words, "radius = 1/2 x R_S". But, due to the azimuthal stretching of space-time around a rapidly rotating black-hole, after the same was introduced & spun up, that "Kerr ring" would now have an absolute metric length equal to 2pi*R_S. The factor of half implies, that upon spinning up the black-hole, space-rings previously inside of its event horizon, would emerge outwards, as space-time was "flung outwards", and as the "throat" was stretched wider.

 

Note, that space-time does not "twirl" around a rotating black-hole, as seemingly suggested, by common visualizations, of frame-dragging (which show radial rays twirling around the central object, like a vortex spiraling down a drain). The Kerr solution is a steady-state solution; space-time is not "winding around the black-hole, more & more, like a growing twirl of spaghetti". Instead, space-time spins with the central object, like a bunch of concentric onion shells, shearing past each other, at different angular velocities ("oblate spheroids spinning within oblate spheroids"). Space-time is not being stretched, or expanded, as if it were really a "rubber sheet". Instead, layers of space-time can shear past each other, like a non-viscous fluid. Regions of space-time near to the central object spin around with the same, entrained into its rotations -- the term "frame dragging" seems appropriate; space-time spins around with the central object (but is not stretching as if from fixed anchors, like rubber bands, which would pull back against the spin).

[artbeing B]

oops x2

 

Flat space-time fabric

Imagine a flat two-spatial-dimensional plane (to be the equatorial plane, of a black-hole). Lay out concentric circles ("hoola-hoops in space"); measure their lengths once around; divide by 2pi; define L/2pi = R. Then you label each of those rings with those calculated "R" values.

 

Schwarzschild space-time fabric

Add the mass to the middle. Viewed imaginatively from a higher-dimensional "hyperspace" perspective, "flat-land" sags in the center. Physically, if you were crawling around on one of those rings (in a space-suit say), labeled "radius = R"; and if you then reached out for the next space ring, labeled (from before the positioning of the mass) with the words "radius = R + 1m"; then you would observe that an actual meter-stick could now be placed in between the two rings, with lots of space to spare. If those rings had been tethered together, along radial rays, with bungee cords; then those bungee cords would have stretched. That is all you would notice, embedded into the curved space-time fabric. From "hyperspace", you could see, that all that extra space in between the rings, and stretch of bungee tethers, was due to each of those rings, being displaced from each other, "down" through an extra hyper-dimension:

 

Kerr space-time fabric

Now, spin the black-hole up. According to the Kerr solution, now space-time stretches, not only in the radial direction ("can't reach the next ring out"), but also in the azimuthal direction. Those space-rings labeled "radius = R" would be stretched apart; if they, too, were made of flexible "bungee tethers", then they would be observed to stretch out. Anything rigid would be ripped apart. For example, for a maximally-rotating black-hole, the space-ring around the equator of its event horizon, which had been labeled "radius = R_S" before spin-up, would now stretch out by about 25%. That azimuthal distension could be visualized, as the rotating black-hole "spinning out" the space-time around it, as if by a centrifugal-like force. From "hyperspace" perspective, that centrifugal "fling out" would widen the "throat" of the curved space-time fabric by up to about 25%:

Another property of Kerr space-time, is that, in the azimuthal direction (perpendicular to radial rays), light-cones (cdt vs. dl) get "squashed to the side". Traveling towards a maximally-rotating black-hole, along a radial ray, towards its equator, by the time you reach the inner Kerr-radius, both the prograde & retrograde light-trajectories (defining the azimuthal edges of the light-cone from that point in space-time) converge towards a common, prograde, orbit, around the black-hole, at light-speed. And, since all physical world-lines, of massive particles, must lie within their (forward) light-cones, so near rotating black-holes, frame-dragging whips everything into a "prograde at light-speed" orbit.

 

Putting the pieces together, if you ringed (the equator of) a maximally-rotating black-hole, at its Kerr radius, with a fiber-optic cable; then you would find that that fiber-optic cable had an absolute metric length of 2pi*R_S. And, if you tried to send light pulses, in both directions, around the space ring; then both bunches of photons would actually be whipped around prograde at light-speed. And, if you suddenly removed the mass entirely, then your "Kerr ring" would contract, down to half of its original length. Alternatively, starting from flat-space as above, the space-ring which would wind up girdling the introduced rotating black-hole's inner-most Kerr radius, would be the one, which you had previously (painstakingly) measured, and labeled with the words, "radius = 1/2 x R_S". But, due to the azimuthal stretching of space-time around a rapidly rotating black-hole, after the same was introduced & spun up, that "Kerr ring" would now have an absolute metric length equal to 2pi*R_S. The factor of half implies, that upon spinning up the black-hole, space-rings previously inside of its event horizon, would emerge outwards, as space-time was "flung outwards", and as the "throat" was stretched wider.

 

Note, that space-time does not "twirl" around a rotating black-hole, as seemingly suggested, by common visualizations, of frame-dragging (which show radial rays twirling around the central object, like a vortex spiraling down a drain). The Kerr solution is a steady-state solution; space-time is not "winding around the black-hole, more & more, like a growing twirl of spaghetti". Instead, space-time spins with the central object, like a bunch of concentric onion shells, shearing past each other, at different angular velocities ("oblate spheroids spinning within oblate spheroids"). Space-time is not being stretched, or expanded, as if it were really a "rubber sheet". Instead, layers of space-time can shear past each other, like a non-viscous fluid. Regions of space-time near to the central object spin around with the same, entrained into its rotations -- the term "frame dragging" seems appropriate; space-time spins around with the central object (but is not stretching as if from fixed anchors, like rubber bands, which would pull back against the spin).

 

Hi Windekind:

 

Thanks so much for your replies. I must confess that I didn't understand your first couple of entries. But this last one is really good and closer to the info i need. I will need to read through it very carefully to turn it into a visual model that works for my ships flight path. I have a couple of more questions:

 

1) What orbital speed would 2 black holes be going around one another in a binary system? Would it be like running to jump on a playground spin platform (don't know what their called) to sync with one of the black holes?

 

2) Then is the approach into the singularity ring horizontal through the accretion disc and event horizons or would the path be at an angle to the equatorial region and sync with the angular speed to go through the ring? This all may sound really simplistic and not correct but I have to figure out a flight path into the black hole.

 

3) If you wouldn't mind, could you describe the flight path in that you would take? From approaching the system to going into the ring.

 

 

Thanks again for all your help!

 

Ken

[Widdekind]

i don't know the answer to your questions. i'll offer what i've worked out:

---

 

(1A) Imagine constructing a coordinate grid, of "geodesic Dyson-spheres", in flat space-time.

(1B) Transport a black-hole to the origin

(1C) Spin the black-hole up to maximal rotation rate

 

 

(2B) The non-spinning black-hole would not contort the "Dyson spheres"; however, the radial distances between them, as measured by actual physical rulers, would increase, due to the "stretching of space-time 'out' in a hyper-dimensional direction" (the "sagging of the rubber sheet")

(2C) Once spun up, the Kerr black-hole would stretch the "Dyson spheres", both around the polar & azimuthal directions; the azimuthal stretch would exceed the polar stretch, by up to 20%. Thus, the "Dyson spheres" would be stretched out, in all directions, into oblate spheroids. Those azimuthal stretchings could be visualized, as the spinning black-hole centrifugally flinging space-time away from itself, so "widening the throat in the rubber sheet". (Note: space-time does not actually have the consistency of rubber; space-time does not twist or twirl around spinning black-holes; rather space-time co-rotates, like a tornado, or vortex, in a fluid, which can flow past itself, with space-time near to the black-hole frame-dragging more, and co-rotating faster.) The polar stretchings result from the azimuthal, as depicted below:

According to the Kerr metric, there is no stretching, along (coordinate) lines of longitude, at the equator; all of the stretching, along (coordinate) lines of longitude, occurs over the poles. Thus, at the equator, longitudinal "ribs" of the "Dyson (coordinate) spheres" would remain intact; extensional deformation would only occur (increasingly) towards the poles. And, according to the (approximation) formula for the circumference of an ellipse, the stretching around the latitudinal (azimuthal) direction is so much more, than the stretching over the longitudinal (polar) direction, that whilst the effective equatorial radius increases, the effective polar radius decreases (even though the total integrated circumference, around coordinate lines of longitude over the poles, does increase).

 

numerical method

i employed the Kerr metric, actual physical metric distances, around the spinning black-hole, both over-and-around its poles (dt=dr=dphi=0, theta=0_to_2pi), and around its equator (dt=dr=dtheta=0, phi=0_to_2pi, theta=pi), can be calculated (dl = |ds²|). In all cases, the actual physical circumference-distances measured exceed 2pi*r by some "stretch factor". i employed Wolfram|Alpha: Computational Knowledge Engine to crunch the numbers. Knowing the azimuthal stretch factor, which i assumed was simply the effective equatorial radius stretch factor (r_eq); and the integrated polar/longitudinal circumference (p_pol); i inverted the formula for the circumference of an ellipse (p=f(r_eq,r_pol)), to estimate the effective polar radius (r_pol). According to the approximation formula, near the black-hole, within a couple of R_S, the polar radius is "squashed"; hypothetical "Dyson coordinate spheres" would be flung way out, equatorially, but "stretch down" at poles.

[EquisDeXD]

Hi everyone!

 

Yeah, I am a new guy with some burning questions that need member brainstorming.

 

I am writing a script requiring me get knowledge of a plausible way for a wormhole to form. Wormholes are so cliched in scfi writing that it is embarrassing to even mention that I want to use this dusty literary excuse to get my crew across the galaxy so they can be "lost".

 

But my research and emails with an astrophysicist have shed some light on the possibility of the WH forming in a Kerr Black Hole when the singularity is "ring" shaped. I understand that if a spaceship would enter the ergosphere of the KBH (and survive gravitational drag forces) then you could pass into the top of the inner/outer event horizons (which are toroidal in shape?) and going with the angular BH spin (maybe matching speed, although the current would do that anyway), wind in a spiral down through the singularity ring, where hopefully you imerge in another universe intact and not so much metal bits and spaghetti.

 

Assuming some of what I have said is correct. I would love some thoughts on:

 

- The flight path, what would the ship need to avoid?

 

- Is the top of the horizon shell weaker in tidal forces than the equator?

 

- Any kind of known or theorized information about the dynamics of this kind of BH (no equations please, there are many detailed BH papers full of equations, it is Greek to me!)

 

- I like the idea of a binary KBH for this scenario, The astrophysicist I emailed with alluded to the binary systems as being significant for the wormholes effect, can anybody shed light on this idea?

 

-Do the BHs of the binary need to be identical in mass and spin to be a stable system?

 

-What would be ideal specifications for this system? i.e. angular spin, solar masses of BHs, orbiting speed and radius etc.

 

 

Thanks so much in advance for your replies and answers! I look forward to the responses.

 

Take care everyone.

 

Even if an infinitely dense object could take the shape of a ring, how could you get past it? Wouldn't the gravity be too strong to get away from it? You'd be stuck inside it anyway.

Edited October 12, 2012 by EquisDeXD