## Många kritiska till SVT:s propagandafilm

På facebook är det många som är kritiska till SVT:s nya propagandafilm ”Höna av en fjäder” där man varnar för Trump, Putin och Boris Johnsson och förklarar att deras egna ”nyheter” är ”saklig journalistik”. Skärmdumpar från facebook nedan:          Propagandafilmen finns att tillgå på youtube:

Även på youtube är människor kritiska. Det här är de kommentarerna som finns under filmen på youtube 19:30 2019-10-07:                        Det finns väl en risk att några av dessa kommentarer kommer vara raderade när man går in och tittar vid ett senare tillfälle.

## Some orbits using 2019 expression

Here are some orbits made using my ”new expression” for 2019 that is a bit different then my old expression in my paper. As stated before, the new expression is: As before, the green circle represents the Schwarzschild radius and the red circle the radius of the ”innermost stable circular orbit”, located at three times the Schwarzschild radius. All the simulations are based on starting off with the value of the orbital speed and radial distance of the planet Mercury at aphelion. Relativistic effects are then scaled up by increasing the initial velocity with a ”scale factor” and decreasing the initial radial distance with ”scale factor squared”. Classically we would just get the same shape of the orbit no matter what the scale factor. Above we see an orbit using a scale factor of 1357. The point of closes approach is located at 7.1643 Schwarzschild radiuses. Above we see an orbit using a scale factor of 1460. The point of closes approach is at 5.8764 Schwarzschild radiuses. Above we see an orbit using scale factor 1571. The point of closest approach is at 4.6413 Schwarzschild radiuses. Above we see an orbit using scale factor 1665.1. The point of closest approach is at 3.4495 Schwarzschild radiuses. Above we see an orbit using a scale factor of 1678.767. Closest approach is 3.042 Schwarzshild radiuses. Above we see an orbit with scale factor 1679.085365. The point of closest approach is at 2.978 Schwarzschild radiuses. Above we see an orbit with scale factor 1679.0859. The simulation breaks down at the Schwarzschild radius. Maybe I should try using a very small time step and see if things get better.

## Tejeda – Rosswog orbits

Five or six years ago I stumbled upon an article on Arxiv written by Stephan Rosswog and Emilio Tejeda. From the look of the orbit they presented, it seemed like they had come up with something similiar to me, generalized Newtonian accelerations to account for GR effects, and maybe they had done a better job. For most of they article they use polar coordinates in which a comparizon with the Schwarzschild solution is easier, since the Schwarzschild solution is usually expressed in polar coordinates. To find what their expression for the acceleration looks like in our ”beloved cartesian coordinates” we have to look at the last page, appendix A, in their article and do a little re-writing. If I am not doing any mistakes it becomes: By inspection we see that the acceleration is zero at the Schwarzschild radius for an object with no motion, but that you have an attractive gravitational acceleration for a non-moving object both for radiuses larger and smaller than the Schwarzschild radius.

(To be continued)

(Image not related to the above) (This image is not related to the above either) ## Relativisitic generalisation of the Newtonian gravitational acceleration

In my old paper i stuffed: into: and out popped: .

In the paper it is seen that this gives the expected results as far as the case of a circular orbit, no velocity at all, the anomalous perihelion shift and the Schwarzschild radius. From this site it seems like we also get the right value for the radius of the ”innermost stable circular orbit”.

In the paper we saw that the ”post-Newtonian expansion” at the 1PN level (that expression is for instance used by JPL-Horizons when calculating ephemerides) gives strange results for the case of a circular orbit and the case of no velocity at all. From this site we see that in the strong field limit we get very strange results in the form of ”bouncing”. This is because NASA/JPL approximates GR by using a repulsive ”inverse r cube” term.

I managed to get to peer review at the paper ”General Relativity and Gravitation” back in 2012 but instead of appreciating that my expression seems to give results closer to what is expected from the Schwarzschild solution then what the post-Newtonian expansion does I got the response:

”​The post-Newtonian expansion is well known to correctly describe all observable quantities for orbits in the Solar System and in the binary pulsar systems, for instance. The author should be demonstrating that his model reproduces post-Newtonian observables, not that it gives different results”

he also wrote:

”If the author were to write a paper with a rigorous derivation of a model that correctly reproduced post-Newtonian observables then this would stand a much greater chance of publication.”

I tried to get published in around seven different jornals before I gave up.

Anyhow, moving forward to 2019, the energy of a test-body moving in a spherically symmetric gravitational field can, according to GR, be written as: This can be re-written as: If we write: we could write ”E=m(r,v)(c(r))^2”, so we sort of have a ”general relativistic relativistic mass”. Now, this is ad hoc but can maybe be be motivated by some symmetry assumption, we need to throw in an extra factor to get the orbits right. (The symmetry assumption would be that the mass of the central mass must increase (in the sense that we are dealing with here) by the same amount as the mass of the orbiting object, because they are both getting closer to each other. Sort of the same argument can be made as regards of why the speed of light slows down extra much in the radial direction.) We write: and throw this into: For the case of pure non-radial motion we get:  If we take a superposition of these two orthogonal solutions we get: (Maybe it should be proven that you can take the superposition of the two solutions to get the general solution)

This final expression that is an attempt to generalize the Newtonian gravitational acceleration to get to the accelerations expected from the Schwarzschild solution has several features in common with what is expected from the Schwarzschild solution:

• Acceleration whenever v=0. For the case of no velocity the extra terms vanishes and we retain the Newtonian acceleration, as is expected.
• Acceleration for pure non-radial motion. We see that the extra terms vanishes for pure non-radial motion, which means that we get the classical velocity for a body in circular orbit, just as expected.
• Weak field perihelion shift. Although not proven here, in the weak field limit we get precisely the anomalous perihelion shift we expect. (I do not know if there is a strong field perihelion shift to test the expression against)
• The Schwarzschild radius.  As seen from simulations, (these are made using the expression in my old paper ), the expression reproduces the Schwarzschild radius.
• The radius of the innermost stable circular orbit. As seen from these simulations, made by using the expression in my old paper, we get a spinning around in a circle behaviour just inside the ISCO-radius before the particle falls into the black hole, which is the expected behaviour. It is hard to say if the results in the simulations are exactly right.
• Acceleration of pure radial infall. According to this answer on astronomy.stackexchange the expected  acceleration for pure radial infall is exactly what we got (se two expressions up in this post).

Given that we have all of these effects more or less precisely as expected from the Schwarzschild solution we must at least be very close to have generalized the classical Newtonian gravitational acceleration to give results that exactly coincides with what is expected from the Schwarzschild solution.

I have started a few threads on the stackexchange network related to this issue:
What is the coordinate acceleration for pure radial motion?
Why are JPL using this expression to simulate Schwarzschild orbits?
3PN and higher order post-Newtonian Schwarzschild approximation
Is there a general relativistic mass in general relativity?

If you find out that the last expression above somehow give orbits that differs from what is expected from the Schwarzschild solution, please tell me. Also, if you have any idea of what kind of testing I can do to check the orbits against what is expected from the Schwarzschild solution, please let me know.

## Funny negative inverse cube strong field orbits

As discussed before, at the first post-Newtonian level, relativistic effects are approximated by adding two velocity-dependent term and one repulsive inverse cube term. The expression looks like: In the simulations below are shown how strong field orbits using this expression. In all the simulations I start the simulation at the same point but with less and less initial velocity/angular momenta. We see that the negative inverse cube term cause the orbiting body to ”bounce”. The negative inverse cube term causes gravitation to be repulsive at short distances than ”4GM/c2”, that is two times the Schwarzschild radius. As ususal the green circle in the plots denotes the Schwarzschild radius and the red circle is at the radius of the innermost stable circular orbit, which is located at three times the Schwarzschild radius. In this first plot we start the simulation with so much angular momenta that we can barely notice the ”bouncing effect”. With a little less initial angular momenta the bouncing is clearly visible. With even less initial angular momenta you get this ”beautiful flower”. With less angular momenta we just get ”sharper spikes”. With less angular momenta we get spikier spikes. Even spikier spikes.

We see that approximating General Relativity under spherical symmetri by adding an inverse cubic term get really strange results. The post-Newtonian expansion is available at the 3PN-level. At the 3PN level an attractive inverse quadruple r term and a repulsive inverse quintuple r^5 term are introduced. ## Strong field orbits from 1PN post-Newtonian expression

At the first, ”1PN”, post-Newtonian level the relativistic accleration of a test-body in a spherically symmetric gravitational field can be written as: As we see there is one component that actually is of the type ”negative inverse cube”. There is also one component that varies with velocity but points in the radial direction (away from the central mass) and one component that varies with the component of the velocity that points along the radial direction. This component is directed along the line of motion. There are terms developed also at the 3PN level, those can be seen here. Below are some calculated orbits of the strong field behaviour of the 1PN accelerations. As usual the green circle represents the Schwarzschild radius and the red circle is the radius of the innermost stable circular orbit. The simulations are based on starting with Mercury at aphelion and then scaling up the initial velocity with a ”scale factor” and decrease the initial radial distance with a factor of ”scale factor squared”. Classically, no matter what scale factor you use, you get a non revolving ellips with the same shape as that of the orbit of Mercury. At a scale factor of 400, the orbits looks like a precessing ellips. Orbits with a scale factor of 800. Orbits with a scale factor of 1200. At a scale factor of 1722 the orbit becomes roughly spherical. We see that at a scale factor of 2400 we start the simulation at ”perihelion” rather then at ”aphelion”. The negative inverse qube term of the 1PN expression make the orbiting planet ”fly away” from the central mass more and more as we start the simulation closer to the central mass. Closer to the center than four Schwarzschild radiuses it can be seen that gravitation is repulsive, even for someone with zero velocity. At a scale factor of 2700 we get the orbit as above. At a scale factor of 2740 we get orbits as above. At a scale factor of 2760 we get orbits as above.

Our conclusion from this exercise is that the orbits do not really look much as what is expected from general relativity. This result can be compared with the results using a different expression for relativistic gravitational acceleration here.

## Strong field anomalous precession of perihelion

I ran a few simulations using expression (11) in my old paper and are here presenting some of the more ”symmetric results”. See also this post. Scale factor here means that we start with the values for Mercury at aphelion but scale up the relativistic effect by increasing the planets velocity ”scale factor” times and decreasing its initial radial distance by ”scale factor” squared. As usual the green circle is the Schwarzschild radius and the red circle is the innermost stable circular radius that is located at a radial distance of three Schwarzschild radiuses. I do not actually know right now how much perihelion shift there should be in the strong field cases below according to the analytic Schwarzschild solution. The expression that is used for the acceleration to numerically integrate the orbits looks like:  Above we see orbits using a scale factor of 1357. We see that the precession between concecutive aphelions in this case is pi/2 radians. Above we se orbits using scale factor 1460. We see that the precession between succesive aphelions is 2pi/3. Above we see orbits using a scale factor of 1571. Above we see that at a scale factor of 1668 the orbiter completes two revolutions before returning to aphelion. Above we see that at a scale factor of 1682.167 the orbiter completes three revolutions before returning to aphelion. Above we see that at a scale factor of 1682.452 the orbiter completes four revolutions before returning to aphelion.

## Innermost stable circular orbit

In the Matlab-plots below the ”Schwarzshild radius” is marked by the green circle and the red circle, which has a radial distance of three times the Schwarzschild radius is marked in red. I ran this simulation by starting with the values for Mercury at aphelion, velocity = 38600 meter per second, distance from the sun = 69820000000 meter. Then I scale up the relativistic effects by increasing the initial speed of Mercury by a certain factor and dividing the inital radial distance by the same factor squared. i call this factor ”scale factor” below. As we can se, when the relativistic effects are scaled up, we get closer and closer to the red circle. In the limiting case just before ”Mercury” falls in to the Schwarzschild radius, in the plot just before the last plot below, it spins around at a minimal radial distance of 2.973 Schwarzschild radiuses before ”escaping”. In the last picture the object falls down to the Schwarzschild radius and stops.

All the simulations below are done with the expression (expression (11)) in my old paper from 2013:  Above we see orbits using a scale factor of 1668. The point of closest approach, ”perihelion” is located at 3.445 Schwarzschild radiuses. Above we see orbits using a scale factor of 1682.167. The point of closest approach is located at 3.023 Schwarzschild radiuses. Above we see orbits using a scale factor of 1682.452. The point of closest approach is located at 2.98 Schwarzschild radiuses. Above we see orbits using a scale factor of 1682.45754. The point of closest approach is located at 2.973 Schwarzschild radiuses. At a scale factor of 1682.45768 we crash down to the Schwarzschild radius. All the simulations are as stated earlier made by numerical integration of expression (11) in my paper. In my old paper I wrote expression (11) as: This is the same expression as the first expression written above in this post, although written slightly differently ## Some relativistic orbits

These are some old orbits I computed when I was trying to get published regarding my project of relativistic gravitational acceleration. My old paper is found here:

Note that the expression i used in the paper is slightly different from the one I now think is more correct.

orbit168245754gr-eps-converted-to

orbit168245755gr-eps-converted-to    Local copy1303.0004v1_kopia of my old paper which is a bit messy and uses an expression I now think is not one hundred percent correct.

See for instance this post.

## Vad är syftet med Försvarsmakten?

Har vi i Sverige idag ett folkstamsförsvar eller ett värderingsförsvar?

Soldatinstruktion Allmän del 1930 I min bokhylla har jag ett litet häfte på 92 sidor i 1930 års upplaga som heter ”Soldatinstruktion. Allmän del”, ”Vårt Fädernesland och dess försvar”. Hela texten i boken finns att tillgå på nätet

Slår man upp första sidan efter innehållsförteckningen, sida fem, så lyder den första underrubriken ”Vår Folkstam” och brödtexten inleds med följande stycke:

”Inom det område, vilket nu bildar Sveriges rike, har sedan urminnes tider bott samma nordiska folkstam.”

Redan här antyds alltså att syftet med den svenska Försvarsmakten skulle vara folkstamskonservativt, att skydda, värna, vårda och försvara den nordiska folkstammen mot utlänningar.  