would not a cloud be visible? thus a black hole is hypothesized.

per The Pearlman Spiral cosmological redshift hypothesis the galaxies are only 5776 years old and we are in a loitering (somewhat static) universe so there may be no requirement for a black hole or the likes of a Gas cloud to fit the natural observations..

From the orbits around the central mass in our galaxy it can be concluded that the central mass is about 4 million solar masses (cf. Sagittarius A*).

The Schwarzschild-radius r=2GM/c^2 of 4 million solar masses is roughly 10^10m.

A star is orbiting the central mass at a closest distance of round 10^13 m, the radius of the central mass must be much less, otherwise the star would collide with it. 

The linked page shows the orbits of stars in the core. Note that S0-2 passes with 17 light-hours of the central point so it cannot be larger than that in radius. The closest alternative would have to be a globular cluster of >2 million neutron stars and no normal stars at all. That would be clearly visible but nothing can be seen.

http://www.galacticcenter.astro.ucla.edu/blackhole.html

If I'm not mistaken, this mass (4 million solar masses) in a volume of 10 Light Hour  correspond to about 1/1000 of Earth's atmosphere at the sea level.

Why a dense (~1/1000 of the earth atmosphere density) cloud of gaz is excluded ?

Such a cloud shoul emit in IR (i guess) to not collpase into a star.

I think that would greatly exceed the Jeans Mass and would collapse to one or more protostars very quickly.

http://burro.astr.cwru.edu/Academics/Astr221/LifeCycle/jeans.html

P.s. Note that the object known as G2 which was first thought to be a gas cloud passed close to Sag A*. It is visible in the telescopes used to monitor the core and much larger than the central object. It would have had a mass of just three times the Earth had it been just a cloud, although now it is thought that there may be a star inside. The size of a stable cloud of the mass of Sag A* would fill the core region.

http://www.space.com/27811-milky-way-monster-black-hole-snack.html

Dear George,

You say that such spheroidal mass of gas, with, say, 2 million solar masses whose mass span would  be larger that the Jeans' length would turn into fragments. But, if spheroidal the cloud would resemble a giant pro to-star, with very very long cooling time. Am I right ? wrong ? 

Do people have considered the possible existence of such giant pro to star ? I admit this is a very exotic idea. 

About the origin, I think about the last trace of a QSO. But what QSO model ? 

With Gilles we think about the infall of a ring-like density made, towards the center of a galaxy (due to bimetric process, coupled metric instability). The this wave moves towards the center of the galaxy.This is associated to our bimetric "Janus model". 

I think that there are measurements of radial velocities in such rings, observed. But we cannot decide if that gas moves inwards or outwards, because we cannot decide how the plane of the galaxy is oriented. Right ? 

Suppose the ring moves inwards.  As spiral arms it works like a shock wave. It would trigger the birth of new stars, which would ionize the gas by UV emission. In that gas the magnetic Reynlods number could become large and the ring would then gather together the small magnetic field lines of the galaxy ( initially 1 micro Gauss ? ). Il would enhance the field and, at the end, we would get a strong magnetic dipole. What B-value ? No idea. Is it possible to size B in QSO ? 

When that mass of gas would reache the center, we would get a hot spheroidal mass of gas in which the Lawson conditions could be reached in the bulk. So that fusion would occur in a large volume, and the subsequent emitted energy  could be possibly comparable the the radiation emitted by the whole galaxy. 

The magnetic lines would focus the emitted plasma and we would get two opposite lobes. It would work, thanks to the magnetic gradient, as a natural particles accelerator and that would produce very energetic particles ( "cosmic rays" origin ?  ). 

That's my vision of the quasar phenomenon, since 20 years. I published this idea in France in a book, in 1997, entitled "lost, half part of the universe".

Perhaps I am wrong. Todays' simulation could master such problem, I think.

By the way, I am retired (78 yrs) . Gilles and me have only PC. If guys have big computers we would be OK for collaboration.

So, if I am right QSO  would correspond to a transient phenomenon. How long would it work ? I don't know. But if the decay time of such "machine" is longer that a century we have no chance to observe the decay of a QSO. 

How would it ends ? These "giant black holes" could be the waste of a QSO, after fusion process ends. As this quasar phenomenon would be very common, all galaxies with gas would own their "giant black hole". 

Question : do we observe "giant black holes" in elliptic galaxies which own no gas. I would thing observers need gas to make velocity measurement by Doppler effect. 

Jean-Pierre Petit 

what is the formula giving the collapsing time (i guess versus T and total mass ) ?

Jean-Pierre wrote: "You say that such spheroidal mass of gas, with, say, 2 million solar masses whose mass span would  be larger that the Jeans' length would turn into fragments. But, if spheroidal the cloud would resemble a giant pro to-star, with very very long cooling time. Am I right ? wrong ?"

As long as the gas starts being optically thin, the thermal cooling time is less than the gravitational collapse time so the collapse is isothermal, at constant temperature. If there is sufficient dust in the mix, it can become optically thick so the temperature starts to rise. The radiation becomes a black body but only from the surface of the sphere and cooling time becomes much longer than gravitational collapse and internal radiation pressure becomes significant.

Gilles wrote: "what is the formula giving the collapsing time (i guess versus T and total mass ) ?"

There are three key formulae giving the time for gravitational collapse and the cooling time for an optically thin or thick medium. I've linked a useful lecture presentation which includes the formulae and also describes fragmentation and how it releats to the IMF. That should give you enough to find more detailed descriptions.

http://www.ast.leeds.ac.uk/~jsu/star_and_planet_formation/Lecture6.pdf

This is Omega Centauri, the largest globular cluster. Its mass is 4.05 million Msun, about 94% of the mass of Sag A*. It is 150 light years across and about half as far away at 15,800 light years. This would be the result of collapse and fragmentation of a gas cloud of comparable mass. The size of such a cluster is determined mainly by the Virial Theorem after some relaxation time.

Sag A* has almost the same mass but is definitely less than 17 light hours in radius and gives off no light at all, it is not a cloud and not a globular cluster.

On the image of the globular cluster, the entire orbit of star S0-2 would have a width of one tenth of a pixel.

http://cdn.eso.org/images/screen/eso1119b.jpg

https://upload.wikimedia.org/wikipedia/en/c/cf/SO-102_Orbital_Plot.jpg

The observations do not demand it. Indeed, the presence of an object possessing an event horizon cannot be strictly inferred by any means. However, the situation is not completely hopeless from a scientific viewpoint. The lack of an event horizon can be betrayed by observational cues, and active galactic nuclei can be interpreted in this way. Also, theorists have run into all kinds of problems by simply assuming that these objects are black holes. Einstein formulated general relativity a century ago now and famously dismissed the notion of black holes decades after reflecting on the Schwarzschild solution. His warnings have been generally ignored but there are strong reasons to think he was correct, both empirical and theoretical. I outline my own thoughts on what has gone wrong in this article:

Preprint Dispelling Black Hole Pathologies Through Theory and Observation

What is certain is that the central  mass that causes stars to move in very eccentric orbits with very small closest approach to the center exceeds million solar masses.  In principle, it can be a very compact supermassive star or a cloud. But such a massive, dense object with high core temperature  is unstable - gravitationally (i.e. from Eddington limit considerations) as well as from instability due to pair productions in the core. That is the reason why one concludes that the central object is a supermassive blackhole.

Why High core temperature ? is it observed ? Do you have some references that i can read ?

I though that the instabilities (collapse) begin when temperature decrease below a given limit (depending of the global mass and spatial extension), i.e. when pressure does not equilibate the gravitationnal forces.

This article lists the most massive stars and explains the Eddington Limit. You can easily find more detailed mathematical analyses of this on-line.

https://en.wikipedia.org/wiki/List_of_most_massive_known_stars#Eddington.27s_size_limit

TDM: At very high spin rates, one gets an increase of the apparent mass.

Only due to the rotational energy which is small compared to the matter component. It also causes frame dragging which would be more evident if spin was significant.

In that equation, am I right in thinking that lambda, m and omega are determined solely by the rotation and structure of the central object while r is the distance to the smaller orbiting mass?

In that case, the apparent mass of the larger object should vary as r^-3, but the orbits of the stars near Sag A* are Keplerian implying a constant central mass. The eccentricity for star S2 is 0.876 so the variation of the radius, the ratio of apoapsis to periapsis, is 15.1. For star S14 with an eccentricity of 0.9389, it is even larger at 31.7. The apparent mass should vary by a factor of 32000 in that case so the orbit should be nothing like Keplerian.

Do you mean that, if future measurements show deviations from keplerian trajectories, it coul enforce the idea of a rotating black hole ?

And in the contrary, if there is no deviation, can we said that  it cannot be a rotating black hole ? without exception ?

TDM: So, by knowing the deviation from the "Keplerian" orbits, one should be able to determine the spin rate of Sag A*.

Yes, that is exactly my point. By obtaining that information, you could use the upper limit on deviation from Keplerian motion combined with your equation to find an upper limit on the rotation. The r^-3 connection means it would be quite a sensitive measurement. The result would need to be a very small spin rate and the spin-related fraction must therefore be very small. The observation is that the orbit is overwhelmingly determined by the non-rotating mass contribution and therefore your calculation would give almost the same prediction as conventional theory, 4.31 million Msun.

I wasn't suggesting you could use that as a test of your theory (that would need an independent measure of the rotation) but if you want to do a test in that form, remember the Sun rotates in roughly 25 days. You should be able to calculate different apparent GM values for the Sun based on the orbits of Venus and Neptune (both low eccentricity). The r^-3 part should give a measurable difference in apparent mass. The attached link gives details of the Sun's rotation.

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

The black hole was conjured by a violation of the rules of pure mathematics, and so it has no physical or mathematical validity.

The Painlevé-Gullstrand ‘Extension’ - A Black Hole Fallacy, American Journal of Modern Physic, 5, Issue 1-1 , February 2016, Pages:33-39,

http://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.s.2016050101.15.pdf

TDM: The authors of "The Shortest Known Period Star Orbiting our Galaxy’s Supermassive Black Hole" wrote: "While deviations from a pure Keplerian orbit will likely be detected in the future, this cannot be expected with the current data set, and we therefore assumed a point-mass potential and Newtonian gravity."

I think they are referring to the possible detection of precession but your ideas can be tested by the variation of radius with time, the difference in acceleration between apoapsis and periapsis would be much higher in your theory if the central object were rotating, i.e. it would violate Kepler's Laws. They have observations at numerous points round the full orbit so that should be adequate for your purpose.

TDM: The Sun's rotation is too slow for the detection of a significant influence regarding the planet's motion (even Mercury's).

What are the numbers for Venus and Neptune?

TDM: But the Gravity Probe-B experiment, in which gyroscopes in satellites were deviating due to the Earth's rotation, has proven that the effect exists.

Sure, and it was done with the LAGEOS satellites too, but those are also consistent with GR so they don't discriminate.

TDM: At the start, the theory was not mine but Oliver Heaviside's (1983), ...

I know but you're the one promoting it now and "your" is quicker to type ;-)

TDM: The authors of the paper I mentioned didn't find a rosace after many years of observation. That clearly is in violation with GR.

No, what they wrote was: "While deviations from a pure Keplerian orbit will likely be detected in the future, this cannot be expected with the current data set,"

They said the current data set is not sufficiently accurate to perform a test for precession yet but if the monitoring is continued, it will be possible in the future, that is not a violation of any prediction.

Bear in mind also that the majority of the precession of Mercury is due to the influence of the other planets. Similarly the motion of each star in the core will also be influenced by the other nearby stars. Extracting the non-Newtonian component will not be an easy task.

However, the accuracy of measurement of the radial distance from the central object is certainly adequate for you to set an upper limit on the rotation. These are different measurements, and as you say the r^-3 characteristic works to your benefit.

TDM: But the Thirring-Lense effect of general relativity is only confirmed to 20% precision. That means: GR is 20% wrong.

No it doesn't, it means that that is the confidence only, the actual value measured might be exactly in accordance with prediction.

TDM: I have successfully tested the theory ...

That is good but what you need to do decide the matter is to show either that GR fails where your alternative succeeds or vice versa. I've suggested a way to approach that, it's your choice whether you do the calculations.

In their paper ‘The Discovery of the shortest period star in the Galactic Center: S0-102, Science, 5 October 2012: Vol. 338, pp. 84 – 87,

http://www.sciencemag.org/content/338/6103/84.full.pdf?keytype=ref&siteid=sci&ijkey=vIte1RjZpLlKc

A. Ghez (UCLA) et al allege a ‘supermassive black hole’ at Sgr A*:

“Here we report the detection of another star, S0-102, in orbit around the supermassive black hole at the center of our Galaxy”

“The gravitational potential in this region of the Galaxy is dominated by the black hole, and to a good approximation the stars follow Keplerian orbits.”

They go on to assert,

“A test of Einstein’s theory of general relativity is the next goal in galactic center research, now that the existence of a black hole is well established.”

Notwithstanding, the presence of a black hole at Sgr A* is certainly false, as explained in this recent paper:

The Painlevé-Gullstrand ‘Extension’ - A Black Hole Fallacy, American Journal of Modern Physics, 5, Issue 1-1, February 2016, Pages: 33-39,

http://vixra.org/pdf/1512.0089v1.pdf

TDM: @George: at least, we agree that Kepler's laws are violated here ..

No we don't. I'll repeat what the authors wrote again: "While deviations from a pure Keplerian orbit will likely be detected in the future, this cannot be expected with the current data set,"

TDM: .. and that the data is not precise enough.

Yes, that is correct. At present the data isn't good enough to measure any precesssion (which is expected).

TDM: "set an upper limit on the rotation". What do you mean? The rotation of Sag A* is what it is. In theory, it can be zero or or be very high, maybe up to the speed of light at the equator.

Right, but your variable mass term depends on that rotation speed. For Kepler's Laws, the radial acceleration varies as the inverse square of the distance, for your formula that is higher (presumably r^-5 if the apparent mass varies as r^-3) so by comparing the radial acceleration at the two extremes of the orbit, you can calculate an upper limit to the rotation speed. As you say, "it is what it is" but the method I've outlined would let you measure what it is.

TDM: Your reasoning is wrong: 'confidence' is a matter of measurement. The measurement cannot at the same time be within a confidence of 1% and within one of 20%.

Here are the actual results (link attached):

"Analysis of the data from all four gyroscopes results in a geodetic drift rate of -6,601.8±18.3 mas/yr and a frame-dragging drift rate of -37:2±7.2 mas/yr, to be compared with the GR predictions of -6,606.1 mas/yr and -39.2 mas/yr, respectively."

For geodetic drift rate, the accuracy is 18.3/6601.8 = ±0.277%. The GR prediction is 6606.1 so that is within (6606.1-6601.8) = 4.3 or 0.065% and 0.065% / 0.277% = 0.23.

For the frame-dragging drift rate, the accuracy is 7.2/37.2 = ±19.4%. The GR prediction is 39.2 so that is within (39.2-37.2) = 2.0 or 5.4% and 5.4%/19.4%= 0.28.

In both cases, the discrepancy is less than 0.3 of the measurement spread so both results are good confirmations of GR.

TDM: I can't find any cosmic issue that is in contradiction with gravitomagnetism.

I'm still waiting to see your calculations for Venus and Neptune. The reason that you haven't found any contradiction seems to be that you only look for tests that pass, that's called "confirmation bias".

https://einstein.stanford.edu/highlights/status1.html

TDM: The results you show have been obtained by appying the equations of gravitomagnetism, not GR. See annexed picture. There you see the used equations. They have nothing to do with GR calculus.

The two equations shown are derived directly from GR, one by de Sitter and the other by Lense and Thirring in 1918. Schiff combined these in 1960.

TDM: However, GR-followers use it as if it were part of GR. Big deal! But it isn't.

They are derived results from GR. As has already been mentioned earlier in the thread, the term "gravitomagnetism" is used for some GR effects which can cause confusion with Heaviside's earlier but different theory. However, the equation shown is derived from GR.

TDM: Sag A* ; Venus and Neptune

TDM: The paper is a mental exercise and has been written in order to show that there can be an apparent mass that is many times larger than the physical mass, because of a fast spin.

That's the point though, if fast spin makes the apparent mass larger, then no dependence of the apparent mass with radius implies low spin for Sag A*.

For Venus and Neptune however, we know the spin rate of the Sun in considerable detial so there's no reason why you shouldn't calculate the effect of that on the apparent mass of the Sun at the radii of the planets' orbits.

Herein the physics of black holes

https://www.youtube.com/watch?v=8I9LQfWY6pA

GD: "They are derived results from GR."

TDM: No they are not. What has been done by Kerr is adding a new term for rotation to the Schwarzschild metric, a pure invention.

Nonsense, the derivation of the Kerr Metric in GR is well documented, however, that's not what we are talking about. The topic is gravitoelectromagnetism as described for example by Mashoon or Sean Carroll in his book "Spacetime and Geometry: An Introduction to General Relativity". I don't have that personally but from other sources I believe eqn 7.25 on page 281 is relevant.

If you want to promote an alternative to GR, it would seem to be important that you understand what is derived from GR so that you can work out if and how yours differs, that would give you some testability, at least in principle, unless they turn out to be identical. You can't do that if you are unaware of the GR result.

Thierry De Mees: The title of this thread is very clear; it concerns black holes, and so your remarks about black holes, and in particular the Kerr black hole, are pertinent.  You are absolutely right that Kerr's addition of angular momentum is a pure invention. Kerr's pure invention is an addition to a pure invention.

It is not difficult to prove that the black hole is not predicted by any theory at all. The theoretical Michell-Laplace dark body, other than possessing a finite mass, does not share any other properties of the alleged black hole, and so it is not a black hole. The black hole, in all its four types (size is not a type) is obtained from General Relativity by violations of the rules of pure mathematics, and so the theory of black holes is entirely false. For example, the theory of black holes requires that the square of a real number must take on values less than zero. But that is impossible. Here is a recent detailed exposition of this simple fact:

The Painlevé-Gullstrand ‘Extension’ - A Black Hole Fallacy, American Journal of Modern Physics, 5, Issue 1-1 , February 2016, Pages:33-39,

http://vixra.org/pdf/1512.0089v1.pdf

Here is a recent simplified exposition of the foregoing simple fact:

A Few Things You Need to Know to Tell if a Mathematical Physicist is Talking Nonsense: the Black Hole - a Case Study, 29 July, 2015

http://vixra.org/pdf/1508.0007v1.pdf

Gravity waves have been found with 2 polarizations, i think we have to accept that, in so far as the  LIGO results have been published.

However, there are other theories  that suggest this result without the paradoxes of GTR

Einstein did not predict the existence of black holes, in fact he denied their existence in a paper published in 1936, Simply because that would imply the existence of singularities, with infinite density and zero time passage at the event horizon.

The force of gravity in General relativity  (GTR) is thought to come form the curvature of space-time.

Unfortunately the maths of GTR implies infinite curvature and zero time passage at the black hole event horizon  and the black hole becomes a singularity- and yet the black hole has a radius.

The Misner Wheeler Thorne interpretation partially resolved this in  that the singularity rests inside the event horizon.

But yet another paradox arises if time stops at the event horizon (frozen star) no matter would fall in hence  black hole could not accumulate matter, and all the in-falling matter would be situated at or near the event horizon.

The solution is to alter the maths of GR.

Additionally GR falls down in a number of areas, so any new maths should also resolve these problems

Yes GR works in the weak fields of the the solar system, and Intermediate

fields of neutron stars. 

1). It produces infinite density singularities in the very strong fields

such as in black holes.

2).It does not necessarily explain dark matter in galaxy cores where we

know super-massive black holes exist and the galactic dark matter

therein,

3). It does not explain dark mater present in galactic halo's,and galactic

clusters such as the bullet cluster,

4).It does not explain the presence of cosmological dark matter as a whole.

5). It has not yet been fully corroborated by the studies of neutron stars

and in black holes.

6). It does not easily explain the presence of dark energy and cannot be

translated in quantum gravity.

7). It predicts that time stops at the event horizon

Here I enclose a number of publications which explain all of these

phenomena, whilst agreeing with the results of GR where it has been

thoroughly tested.

1).First to obviate the infinite density singularities.

1a)

https://www.researchgate.net/publication/32897680_An_advanced_dynamic_adaptation_of_Newtonian_equations_of_gravity?ev=prf_pub

1b)

https://www.researchgate.net/publication/269689554_The_formulation_of_Dynamic_Newtonian_advanced_gravity_DNAg?ev=prf_pub

2).Secondly we explain the presence of dark matter at the centre of the

galaxy.

2a)

https://www.researchgate.net/publication/228858219_Advances_in_Black_Hole_Gravitational_Physics_and_Cold_Dark_Matter_Modelling._The_Gravity_of_Dark_Matter

3) Thirdly it is possible to explain the presence of dark matter in the

galactic halo.

3a)

https://www.researchgate.net/publication/269689929_Advances_in_Black_Hole_Physics_and_Dark_Matter_Modelling_of_the_Galactic_Halo?ev=prf_pub

4). It is able to explain the presence of cosmological dark matter

https://www.researchgate.net/publication/32897680_An_advanced_dynamic_adaptation_of_Newtonian_equations_of_gravity

5). It is corroborated in neutron stars (including Data from radiation

damping ) and is corroborated by black hole studies.

5a)

https://www.researchgate.net/publication/32888463_An_advanced_modification_of_dynamicgravitation

5b).

https://www.researchgate.net/publication/269667939_Corroboration_of_Dynamic_Black_Hole_Gravitational_Physics_from_Observations_of_Cygnus_X-1

6) it explains dark energy and translates into quantum gravity

https://www.researchgate.net/publication/32899306_String_quintessence_and_the_formulation_of_advanced_quantum_gravity

7). It does not offer infinite time dilation at the event horizon

https://www.researchgate.net/publication/287213872_Finite_Gravitational_Time_Dilation_In_Black_Holes_Using_Dynamic_Newtonian_Advanced_Gravity_DNAg

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Can the non-existence of gravitational waves refute General Relativity? - ResearchGate. Available from: https://www.researchgate.net/post/Can_the_non-existence_of_gravitational_waves_refute_General_Relativity2#56bf0b5e64e9b2858f8b4598 [accessed Feb 13, 2016].

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