I was doing pictures. It was possible to extend the numerical solution for the place that people call the Schwarzschild radius. Now you can describe how g_ {00} behaves,
Strong enlargement of the picture.
The point at which the calculation ends (x=0.947, y(x)=1.5 x 10-322)
Preprint Точное уравнение гравитационного поля на основе эйнштейновск...
I might be able to help with point 3 of your question:
"3 The solution apparently exists everywhere, except for the origin"
I use as my reference the excellent book by P.A.M. Dirac titled General Theory of Relativity. In chapter 18 he discusses the Schwarzschild solution for r >2m which is the familiar equation in polar coordinates.
In chapter 19 Black holes he considers values of r < 2m and states that it is necessary to use a nonstatic system of coordinates. He derives a different equation for r < 2m. He also shows how to get rid of the singularity at r = 2m.
As regards r = 0 this is a singularity introduced as a result of the choice of the polar coordinate system and there would be no singularity at that point if we chose cartesian coordinates.
There is a narrative about the formation of black holes which goes like this:
" A star collapses under gravity and forms a neutron star. If the original star is sufficiently massive the collapse continues to a singularity and this results in a black hole."
There is an alternative narrative which I prefer:
A star collapses to a neutron star and above a certain size an event horizon will form around the neutron star. This will occur if the neutron star is greater than 3.4 solar masses. (You can calculate this value by taking the density of a neutron particle and determining using the Schwarzschild radius calculation the value at which the radius of the star coincides with the Schwarzschild radius. This matches with all observations of neutron stars and black holes i.e. all black holes are greater than 3.4 solar masses and all observed neutron stars are smaller than 3.4 solar masses.) With this description we can include black holes forming directly from neutron stars which formed from the accretion of dark matter e.g. the supermassive black holes at the centre of a galaxy.
The modelling of collapsing stars has used the concept of a pressureless dust (Ref: Nobel prize lecture by Sir Roger Penrose) as an assumption and if there is no pressure resisting the collapse, the model will of course result in a singularity. In reality you cannot crush matter out of existence so there will come a point when the density of the collapsing star is equal to the density of a neutron and the star cannot collapse further.
So there is no physical requirement for a singularity at r = 0 and no mathematical requirement for a singularity at r = 0 if we ignore coordinate based singularities.
Data Black Holes
Richard
Richard Lewis
The point is that we are not talking about solving the Einstein equation. This is another equation in which the energy-momentum tensor of the gravitational field is introduced as a source. f_μν.
G_μν=κ(T_μν+f_μν).
This is what Einstein proposed from the very beginning (1913), but could not do.
Preprint Exact equation of gravity field based on Einstein's separati...
Best regards, Valery
Einstein proposed a model according to which a black hole never forms because the fall time is infinite. In fact, everything is simpler and meaningless decisions do not take place in reality.
Valery Borisovich Morozov ,
Thank you for letting me know about this new RG discussion thread question, which looks very interesting!
I found the following article while I was surfing the Internet, although you are probably already knowledgeable about its contents, but some of the information is new to me. I appreciate your patience and understanding.
SCIENCE
"Scientists See the Backside of a Black Hole for the First Time, Prove Albert Einstein's Theory of General Relativity Correct"
"The backside of a black hole has to be a wonder of the world, err, universe."
📷 By Wesley LeBlanc* Updated: 30 Jul 2021 4:44 am
Posted: 29 Jul 2021 3:02 pm
"Scientists have finally seen the backside of a black hole and in doing so, they've proved that a 1915 theory posited by Albert Einstein was correct. Einstein's 1915 Theory of General Relativity predicted that the gravitational pull of black holes is so large that black holes warp the fabric of space, according to _The Telegraph_. His theory posited that this extremely massive gravitational pull was so massive that it twists magnetic fields and bends lightwaves near black holes. Scientists Have Revealed the First Photo of a Black Hole0:42 Autoplay setting: On
As reported by _The Telegraph_, a new _Nature_ report proves Einstein's theory correct ."Fifty years ago, when astrophysicists started speculating about how the magnetic field might behave close to a black hole, they had no idea that one day we might have the techniques to observe this directly and see Einstein's general theory of relativity in action," Stanford University professor and research report co-author, Roger Blandford, said. Einstein's theory stated that because of how black holes warp the space fabric around them, it should be possible to see light waves ejected out of a black hole's backside as the twisted magnetic fields act as a mirror for the black hole. This theory was accepted by experts, according to _The Telegraph_, but it was never technically proven as it was always deemed an unobservable phenomenon.
NASA Black Hole Gallery📷📷12 IMAGES📷📷📷📷As time has progressed, though, the mystery around black holes has grown more clear thanks to modern telescopes and the like. That's how _Nature_ report author Dan Wilkins, a Stanford University astrophysicist, and Blandford, were finally able to prove Einstein's theory correct, more than 100 years later. The team used a special high-power X-ray telescope to look at and study a black hole 800 million light-years away at the center of a galaxy far, far away and what they discovered was that the light, in the form of X-rays, was being ejected out of the black hole's backside. _The Telegraph_ notes that black holes are born when massive stars explode into a supernova and collapse in on themselves. This creates a space material so dense and so black that it essentially swallows up everything around it, hence why they're called black holes. Following that line of thinking, it should be theoretically impossible to see light on the other side of a black hole, but we now know that's not the case thanks to Wilkins, Blandford, and their team. The team was studying how black holes rip atoms and electrons apart, according to _The Telegraph_, and the X-rays created as a result. When they observed the data they had collected, they discovered that the black hole they were studying was shooting X-rays directly at earth. That's totally normal. What wasn't normal was that the team also saw X-rays being shot out in the exact opposite direction as reflections, thanks to the black hole's twisted magnetic field. This proves that Einstein's theory is correct. Black holes warp space fabric so much that their magnetic fields are able to mirror light waves shot out of a black hole's far side — without that mirror effect, scientists wouldn't be able to actually observe those far-side light waves, despite knowing them to be there. 📷📷17 IMAGES📷📷📷📷 If only Einstein knew that his theory would be proven correct just 66 years after his death.
For more about black holes, read this story about how humans can safely fall into a black hole in one very particular way, and then check out this new photo of a black hole and its surrounding magnetic fields. Read about how a black hole in the Milky Way seemingly changed the color of nearby stars after that.close dialog.
LET US DO THE WORK FOR YOU.Get Daily Deals delivered directly to your inboxevery morning Sign Me Up No, thanks
*Wesley LeBlanc is a freelance news writer, guide maker, and science guru for IGN. You can follow him on Twitter @LeBlancWes.
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SOURCE LINK: https://www.ign.com/articles/black-hole-albert-einstein-general-relativity-observation
Dear Nancy,
When people offer hypotheses, they unwittingly distort theories and reality. This is inevitable if you simplify everything by resorting to pictures. In fact, Einstein understood that black holes cannot be real objects. Because Einstein's equation does not answer the question of what a black hole is. From the point of view of mathematics, the equation does not have solutions in the region of a black hole.
The reason for this is the inaccuracy of the Einstein equation. Einstein was unable to provide both the accuracy of the equation and its covariance. He sacrificed precision for the sake of covariance.
The exact equation has solutions that exist everywhere. True, in strong fields there are areas where time almost stops. But there are no areas where time stops and space disappears. This is a real space described by a real metric, hypotheses are not needed here.
Best regards, Valery
Singularities in general relativity are not the only problem. Einstein's equation solutions do not conserve matter + field energy. energy and momentum are conserved only in closed systems. There is no local conservation in general relativity.
The new equation solves this problem.
In 1913, Einstein substantiated the relativistic theory of gravity and derived the gravity field equation in its general form. Based on these principles, the gravity field energy-momentum tensor was introduced into the gravity field equation. Upon that, successfully, the covariance of the equation was preserved. In rather weak fields, the new gravity field equation transforms into the well-known Einstein equation. The numerical solution of the equation is given here. The numerical solution is shown for g_{00}. This parameter is strictly positive. In the area of strong fields, it falls quickly to almost zero values. The area of extremely small values, g_{00}, corresponds to the interval 0 < r < 3.4r_g.
The problem is not trying to develop a theory. Not with inertness of thinking. And in the fanatical conviction of the majority that Einstein's equation is an absolute masterpiece and cannot be improved.
At the same time, people are ignorant about the history of the creation of the equation. Of course, RG is a product of the titanic labor of a genius. But Einstein's equation is a kind of compromise, a point at which empirical data on the rotation of the perihelion of Mercury were set.
The last point was made by introducing the scalar T (or the related R) into the equation. Sometimes this action is presented as a means by which the Einstein equation became covariant. There is no confirmation of this stupidity in serious publications and, most importantly, in the works of Einstein. The covariance of the equations appeared a little earlier (before calculating the perihelion), by throwing out a covariant element from it, which Einstein invented instead of the energy-momentum tensor of the gravitational field and introduced into the right side of the equation. For he believed, then and later, that the energy of the gravitational field is, like any energy, the source of the field. Einstein deliberately made the equation inaccurate!
This was noticed by Landau and Lifshitz, see v.2 § 95. Einstein's equations. True, they misjudged the smallness of the amendment. In fact, the absolute value of the energy of the gravitational field is a large value in relation to the square of the force of gravity (see § 106. Equations of motion of a system of bodies in the second approximation. Problem 1).
At this time, classical general relativity is developing. It successfully gets rid of serious flaws. Preprint Exact equation of gravity field based on Einstein's separati...
Preprint Gravitational Field Equation and the Structure of Black Holes
The Schwarzschild solution for r < 2m is most important and you can see the analysis in the book General Relativity by P.A.M. Dirac. This is very important because the universe has an event horizon which was located at around 8.77 billion light years at a time 13.8 billion years ago. So we live inside a region which is within an event horizon and r < 2m. This might seem surprising but you can do the maths and work out that it would only take around 28 billion galaxies at a time 13.8 billion years ago to create such an event horizon.
The point is that the Schwarzschild solution works for very low matter densities where the Schwarzschild radius is very large.
Presentation A calculation method for the distance of an object at the ti...
Data Black Holes
Richard
I have no doubts about Schwarzschild's decision. The problem is in the Einstein equation. In 1915, Einstein simplified the equation by removing the gravitational energy term on the right-hand side. He was forced to do this because he could not express the energy-momentum of the gravitational field as a tensor. I did it. The result is a covariant equation of the gravitational field that satisfies all of Einstein's principles.
Preprint Gravitational Field Equation and the Structure of Black Holes
There are no singularities in the solution.
From the point of view of solving the new equation, the gravitational field of neutron stars and "black holes" differs only in size.
Preprint Gravitational Field Equation and the Structure of Black Holes
If Einstein in 1915 drew attention to the fact that the disappearance of a part of the Ricci tensor can be associated with the disappearance of the gravitational field in the inertial coordinate system, he would undoubtedly arrive at the same equation. Instead, he used it to "simplify" the equation.
There are no reliable tests for the presence of black holes. The graph shows the differences of the gravitational potential from the Schwarzschild potential in the nearest area of heavy compact objects. But the qualitatively new potential is no different from Schwarzschild's in the external area. I did not set tasks related to astrophysical hypotheses. The reader should be satisfied with the asymptotic equality at infinity of the resulting equation to the Einstein equation. The potentials of these two solutions differ markedly at distances less than 50r_g, while the components of the binary pulsar PSR B1913 + 16 are at a distance greater than 185000r_g from each other. In such stellar systems, it is difficult to distinguish between the laws of gravitation of the new general relativity equation and the Schwarzschild solution.
Heavy Object Collision Data
Preprint GWTC-3: Compact Binary Coalescences Observed by LIGO and Vir...
Preprint Constraints on the cosmic expansion history from GWTC-3
Preprint The population of merging compact binaries inferred using gr...
Preprint Search for Gravitational Waves Associated with Gamma-Ray Bur...
the size of the gravitational anomaly is about three times larger than the "black hole"
The new gravitational field equation has a reasonable solution for the g00 point source of the field. It is positive for r> o. Although it has extremely small values in the range 0
The place of the "black hole" will be taken by a flat area with a small potential φ>-c2
Preprint Gravitational Field Equation and the Structure of Black Holes
Preprint Уравнение гравитационного поля и структура черных дыр
Preprint Brief description of the new gravitational field equation/ К...
The correct value of the tensor of the energy of the momentum of the gravitational field is obtained.
A new version
Preprint Brief description of the new gravitational field equation/ К...
and in detail
Preprint Gravitational Field Equation and the Structure of Black Holes
Strong-Field Gravity Tests with the Double Pulsar
M. Kramer et al.
Article Strong-Field Gravity Tests with the Double Pulsar
https://studio.youtube.com/video/KeRitVtQ29I/analytics/tab-overview/period-default
Article Brief description of the new gravitational field equation Кр...
Article Exact equation of the gravitational field based on the Einst...
Einstein's equation with the energy-momentum tensor of the gravitational field
It was possible to include the energy-momentum tensor of the gravitational field into the Einstein equation. This is required by the Einstein principle, according to which any energy is a source of the gravitational field, including the energy of the gravitational field, and which Einstein was forced to abandon when deriving the Einstein equation. The new gravitational field equation is covariant and asymptotically equal to the Einstein equation. The numerical solution for g_{00} of a point source noticeably differs from the Schwarzschild solution only for extremely small distances, on the order of several tens of the Schwarzschild radius. In this case, the value g_{00} quickly approaches zero without reaching it.
Preprint Уравнение Эйнштейна с тензором энергии-импульса гравитационного поля
Preprint Einstein's equation with the energy-momentum tensor of the g...