Accelerated Orbits Around Black Holes

I hope you can get over with the thinking, its quite massive!!! you know. and you'll be pulled into it. That's right no sex, no beer, no sports, no gigs-->boredom

Hi Jim,

I wrote, a bit hastily: "No amount of propulsion can get it to c in any orbit, because then the radial gravitational acceleration for anything with mass will become infinite."

It is in fact the mechanical orbital energy that diverges to infinity, not the gravity, which only diverges at the central singularity, AFAIK.

Interestingly, the 'local'^(a) gravitational acceleration at circular orbit radius r is given by: a = -(GM/r²)(1+2v²/c²). At r=3GM/c², with v=c, it means that a = -3GMc⁴/(3GM)² = -c⁴/(3GM). This is huge, but finite.

-J

(a) To be precise, one must specify that local means as measured on the spot by a momentarily static inertial observer.

Hi Jorrie;

Thanks very much for the replies. I will find your answers quite useful.

Jim

Hi Jorrie;

I was contemplating the following scenario while attending Mass last Sunday of all places. The priest saying the Mass would likely have given me a real shellacking if he was aware of my inattentiveness. I wanted to check the following ideas out we you before bothering to proceed with them any further.

Imagine the development of an extremely advanced future human or ETI civilization based on a system of roving super massive black holes, perhaps even ultra-massive ones having a mass as great as 10¹⁵ solar masses. Further consider that all of the subject black holes would be accelerated together in tandem to a translational gamma factor of about 10⁵.

Further consider that each black hole would have an orbiting civilization around it such that the orbit of the very large and extensive habitat would be maintained just above the Event Horizon of the black hole but well within the black hole photosphere of the black hole. Further consider scenarios where each orbital trajectory is orthogonal to the direction of the overall translational velocity of the many black hole based civilization. Now the minimum distance for a circular stable orbit around a black hole is r = 3GM/[C²] and the radius of a black hole photosphere is 3GM/{2[C²]}. For non-rotating black holes, the radius of the photosphere is 1.5 times that of the Event Horizon. In order for the habitation modules to obtain stable orbits around the black hole within the photosphere where the semi-major axis of the orbits would lie within the black hole photosphere, the modules would need to be accelerated or have accelerated motion. Such accelerated motion may be provided by a power source located at a radial distance greater than that for stable non-accelerated orbits around the black hole. Note that stable orbits of massive objects having a non-zero rest mass within the photosphere must be elliptical.

Now assume that the distance between two such supermassive black holes which have orbiting habitats around them is 10,000,000,000 light-years in the overall civilization frame and thus 100,000 billion light years in the background reference frame due to Lorentz length contraction.

Further assume that the special relativistic orbital velocities of the habitats around the black holes in itself provide an average special relativistic time dilation of 10⁵ with respect to a location that lies well outside of any of the black holes but which is moving translationally through space in tandem with the black hole based civilizations. For this external location, we assume that the Newtonian approximation for gravitational time dilation would be a very useful first order approximation for such external locations well within the overall system of the black hole civilization.

Further assume that the average general relativistic time dilation of the sub-photon-sphere orbiting habitat is 10⁵ with respect to a location well outside of the black hole and moving in tandem with the overall civilization.

Would not the averaged total time dilation for the orbiting habitat relative to the external safely removed location moving in tandem with the overall civilization be a product of the above special and general relativistic time dilations or equal to delta t = (10⁵)(10⁵) = 10¹⁰. Could not the two habitats send messages back and forth to each other in such a manner that the experienced time delay of the two way messages would be only one year =2 (10¹⁰)/(10¹⁰) =2 years for each of the habitats?

Even though the effect would seem to violate the cherished light speed limit for inertial reference frames, for the safely removed observer outside of the habitats, it would take 10 billion years for a one year long habitat frame message to be uploaded into the inter-black-hole space. For the external observer, the message would take 10 billion years to travel to the other black hole location but the leading end of the message sent from the first black hole habitat would almost immediately begin traveling into the inter-black-hole distance upon the start of the initial transmission. Meanwhile, the habitat receiving the transmitted message would having a time dilation that is 10¹⁰ with respect to the external inter-black-hole space observer and would experience only one year of time delay as the leading end of the transmitted message traveled the inter-black-hole distance of 10 billion light years in the overall translational civilization frame.

Thus, even though the spatial separation of the habitats is 10 billion light years in the overall civilization frame, I assume that the civilizations could send messages back and forth with an experienced time delay of two years for each habitat in the habitats' frames.

The effective two way transmission time of communications from one such habitat and another would be [2 x 10¹⁰] years for the external observer moving in tandem with the habitat but only 2 years with respect to the habitats.

Thanks!

Jim

Oops! Made a mistake! The 100,000 billion light-years background frame should be 100,000 years background frame.

Hi Jorrie;

I was contemplating the following scenario while attending Mass last Sunday of all places. The priest saying the Mass would likely have given me a real shellacking if he was aware of my inattentiveness. I wanted to check the following ideas out we you before bothering to proceed with them any further.

Imagine the development of an extremely advanced future human or ETI civilization based on a system of roving super massive black holes, perhaps even ultra-massive ones having a mass as great as 10¹⁵ solar masses. Further consider that all of the subject black holes would be accelerated together in tandem to a translational gamma factor of about 10⁵.

Further consider that each black hole would have an orbiting civilization around it such that the orbit of the very large and extensive habitat would be maintained just above the Event Horizon of the black hole but well within the black hole photosphere of the black hole. Further consider scenarios where each orbital trajectory is orthogonal to the direction of the overall translational velocity of the many black hole based civilization. Now the minimum distance for a circular stable orbit around a black hole is r = 3GM/[C²] and the radius of a black hole photosphere is 3GM/{2[C²]}. For non-rotating black holes, the radius of the photosphere is 1.5 times that of the Event Horizon. In order for the habitation modules to obtain stable orbits around the black hole within the photosphere where the semi-major axis of the orbits would lie within the black hole photosphere, the modules would need to be accelerated or have accelerated motion. Such accelerated motion may be provided by a power source located at a radial distance greater than that for stable non-accelerated orbits around the black hole. Note that stable orbits of massive objects having a non-zero rest mass within the photosphere must be elliptical.

Now assume that the distance between two such supermassive black holes which have orbiting habitats around them is 10,000,000,000 light-years in the overall civilization frame and thus 100,000 light years in the background reference frame due to Lorentz length contraction.

Further assume that the special relativistic orbital velocities of the habitats around the black holes in itself provide an average special relativistic time dilation of 10⁵ with respect to a location that lies well outside of any of the black holes but which is moving translationally through space in tandem with the black hole based civilizations. For this external location, we assume that the Newtonian approximation for gravitational time dilation would be a very useful first order approximation for such external locations well within the overall system of the black hole civilization.

Further assume that the average general relativistic time dilation of the sub-photon-sphere orbiting habitat is 10⁵ with respect to a location well outside of the black hole and moving in tandem with the overall civilization.

Would not the averaged total time dilation for the orbiting habitat relative to the external safely removed location moving in tandem with the overall civilization be a product of the above special and general relativistic time dilations or equal to delta t = (10⁵)(10⁵) = 10¹⁰. Could not the two habitats send messages back and forth to each other in such a manner that the experienced time delay of the two way messages would be only one year =2 (10¹⁰)/(10¹⁰) =2 years for each of the habitats?

Even though the effect would seem to violate the cherished light speed limit for inertial reference frames, for the safely removed observer outside of the habitats, it would take 10 billion years for a one year long habitat frame message to be uploaded into the inter-black-hole space. For the external observer, the message would take 10 billion years to travel to the other black hole location but the leading end of the message sent from the first black hole habitat would almost immediately begin traveling into the inter-black-hole distance upon the start of the initial transmission. Meanwhile, the habitat receiving the transmitted message would having a time dilation that is 10¹⁰ with respect to the external inter-black-hole space observer and would experience only one year of time delay as the leading end of the transmitted message traveled the inter-black-hole distance of 10 billion light years in the overall translational civilization frame.

Thus, even though the spatial separation of the habitats is 10 billion light years in the overall civilization frame, I assume that the civilizations could send messages back and forth with an experienced time delay of two years for each habitat in the habitats' frames.

The effective two way transmission time of communications from one such habitat and another would be [2 x 10¹⁰] years for the external observer moving in tandem with the habitat but only 2 years with respect to the habitats.

Thanks!

Jim

Hi Jim, your scenario is too complex for a quick answer, but just a technical point. You wrote: "Note that stable orbits of massive objects having a non-zero rest mass within the photosphere must be elliptical."

I do not agree. A massive, unpowered particle venturing closer than r=4GM/c² will always fall into the Schwarzschild hole. As the periapsis approaches that radius from the higher side (decreasing the orbital energy), the orbit makes a number of almost circular revolutions and then zooms out to apoapsis again. This all while the periapsis precesses around the coordinate system center, yielding the interesting orbit that I wrote about here. At r=4GM/c² the circular orbit speed equals the escape velocity.

I will look at the rest of your scenario as time allows.

-J

Wouldn't such an advanced civilization likely be communicating via quantum entanglement method, cutting communication time to zero?

Wouldn't you need to get entangled particles to the place that you wanted to communicate with?

I don't know, the're advanced.....Do you think they still use cell phones?

Hi Jim, you wrote: "Would not the averaged total time dilation for the orbiting habitat relative to the external safely removed location moving in tandem with the overall civilization be a product of the above special and general relativistic time dilations or equal to delta t = (10⁵)(10⁵) = 10¹⁰."

Yes, the product 10¹⁰ relative to a distant comoving observer is approximately correct - gravitational and orbital velocity time dilation together. However, the movement of your holes 'through space' has no value relative to themselves, so I see no purpose in that.

"Could not the two habitats send messages back and forth to each other in such a manner that the experienced time delay of the two way messages would be only one year =2 (10¹⁰)/(10¹⁰) =2 years for each of the habitats?"

If I understand you correctly, you have 2 monster black holes, half an observable universe (10 billion light years) apart and send a two-way signal between their closely-orbiting 'habitats' as you defined them (10¹⁰ time dilation). Now you hope that the two-way time delay will be only 2 years in habitat time?

If it was not for the expansion of the universe, I guess that this could have worked! It is essentially the Shapiro time delay of light in reverse. The universe would have appeared to be quite a small place for those hypothetical habitat-dwellers.

-J

Accelerated Orbits Around Black Holes

Yes, this is true. Why do you think the standard morphology of galaxies is spiral?

I post this minor note to keep the discussion firmly grounded in the theoretical, without possibility of escaping into engineering contemplations, like habitats.

Any obiect of a real size experiences differential gravity (tides) of such monstrous magnitude, that no material known, or yet imagined can withstand it. By definition, the black hole swallows anything stripped to its basic particles.

The radiation of a feeding black hole between its accretion disk and the event horizon can be crudely compared to that of a supernova. Any such in our sector of the Milky Way is perfectly capable of sterilizing good old Earth, at least the land parts near and dear to me.

Hi leveles;

A black hole of sufficient size would even permit the Earth to enter its photosphere and even pass through the event Horizon with less tidal stressing than that caused by the Sun Earth system. The degree of tidal stressing for a given object is reduced as the radius and therefore the mass of the black hole increaes for objects crossing through the Event Horizon.

However, once inside the Event Horizon, one is utterly doomed no matter how small or large a swallowing black hole. For all we know, the infalling mass-energy is simply crushed out of existence.

A black hole with a mass of about 100,000 suns would have a radius of 290,000 kilometers and might permit a small probe made of diamond or other high end bulk modulus known material to safely pass throught the hole's event horizon but only to be crushed out of existence upon reaching the central singularity which would be point like according to General Relativity for the case of a non-rotating black hole or perhaps alterntively a smeared out lump of whatever if certain quantum gravity formulations hold valid.

It depends on where and how the black hole was constructed. Perhaps the black hole can be constructed in the depths of intergalactic space far away from dense ordinary baryonic matter concentrations.

The black hole would most likely take a cosmic time period to construct that is unless some how zero point field energy could be reified to yield the requesite local mass concentrations.

The possibilities for galaxy scale and larger construction projects does have theoretical intellegability. A good website to consult for such extreme scenarios is the Tau Zero Centauri Dreams website which is the news forum for the Tau Zero Foundation, founded by Marc Millis, the head of the discontinued NASA Breakthrough Propulsion Program.

Regarding accretion disks and special and general relativistic blue-shifted radiation, perhaps there is a means yet to be developed even in theory to use some sort of negative refraction index materials to negatively refract the incident cosmic rays by some sort of cloaking mecnhanisms. Metamaterials that negatively refract visible light and which strongly cloak small visible objects for certain angles of EM radiation incident on the object have already been demonstrated.

Matter wave cloaks should be possible in theory. The required metamaterials may need to be fabricated out of somehow stabilized neutronium, quarkoniums, higgsiniums, monopoliums, or perhaps out of the raw undifferentiated space-time-mass-energy that existed at the very instant of our universes birth.

In consideration of how far we have progressed in 200 years, I make no defacto claims and will refuse to do so that such black hole systems will never be fielded in some distant cosmic era.

Jim

Studying the fragments of the end. You could only hope that "there will be rebirth" yet it is evident there is none.

Hi Jorrie;

Thanks for the reply.

There is always the possibility that in the end our universe will be marginally open. Many big bang models require a marginally open universe or one precisely balanced between being open and being closed. Even in consideration of Dark Energy based universal expansion rate increases that seem to be occuring, the rate of expansion may level off or eventually slow to a crawl.

Provided that the universe is closed but where the universe will not undergo collapse for another ensemble of years, the universal expansion may eventually slow to a crawl and maintain that decreasing rate of expansion for an ensemble of years.

There are still far too many uncertainties in cosmological models at present to suggest that the rate of universal expansion is going to eventually runaway.

Jim

Hi Jim, you wrote: "Even in consideration of Dark Energy based universal expansion rate increases that seem to be occuring, the rate of expansion may level off or eventually slow to a crawl."

I think you are a bit optimistic to think that the current cosmic expansion may level off, but why do you want that sort of cosmic distance? I think the Andromeda galaxy could be a feasible target.

Your very advanced civilization should not have too many problems clearing up the space around the central black holes (ours and Andromeda's) and then establish your powered habitats in orbit around them.

If they can achieve 10¹⁰ time dilation, the 2.5 million light year separation will shrink to some 2.5 light hours. Nice for communication... :)

-J

Hi Jorrie;

Thanks for the above response.

It may even be the case that the current rate of universal expansion may runaway to produce another inflationary phase change. I can imagine the panic that would set in if NASA, or the DOD announced an impending runaway inflation. Might make for an excellent SCI-FI movie.

However, if such a 10 EXP 10 light year wide blackholes civilization can be produced, even in consideration of increasing space time expansion rates, it is conceivable that the black hole habitats located near the back of the distributed civilization could be accelerated with respect to the leading edge of the civilization thus enabling the distance between the blackholes to maintained at more or less a constant level. This may even be possible where the time derivative of the rate of increase in expansion is large.

Regarding such a perpetual increase in the rate of universal expansion, it may or may not level off, but the possibility that it will has many theoretical adherents. The fact that our universe is so finely tuned between run away inflation and rapid collapse seems to indicate that nature prefers our universe to be marginally open in the temporal limits of infinity.

Provided that the overall ratio of the energy density of our universe to an exactly marginally open one would be exactly one, it would seem to suggest that the current rate of increase in the rate of universal expansion will eventually level off.

It may even be possible that our universe even if marginally open will have growth spurts where the rate of increase in expansion fluctuates.

Regardless, I can see your point about being overly optimistic. It would be a real bummer if say in 100 billion years, our universe undergoes a big rip and another phase change. Most currently buring red dwarfs will still be providing light to planets within their habitable zones, and so civilizations around those planets might be in for a real rough ride.

Jim

Dude, how are you related with Jessie James? uhmm, just asking.