## Henrik Agerhell's gravitation research

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CarlBrannen
Posts: 381
Joined: Mon May 24, 2010 11:34 pm

### Henrik Agerhell's gravitation research

I thought this would be a good place to discuss Henrik Agerhell's gravitation research. It's described on his blog:
http://henrik77.wordpress.com/2011/04/1 ... arzschild/

but here we can use tex by selecting the tex code, for example, \psi, and pressing the tex button above to get: $$\psi$$.

In short, what he's doing is looking at how close he can get to the Schwarzschild equations of motion by starting with Newton's equations of motion and changing the mass, or speed of light, or mass of the gravitating body. This is a lot of ways of stirring the pot; some of them may give insight. Let's see if I can lure him over here.

negru
Posts: 307
Joined: Wed Oct 13, 2010 3:49 pm

### Re: Henrik Agerhell's gravitation research

So how do you motivate eq 7?

henrikagerhell
Posts: 2
Joined: Thu May 12, 2011 8:18 am

### Re: Henrik Agerhell's gravitation research

Hello.

The first part of equation 7 is just the Lorentz factor. I did include a derivation of this from combining classical mechanics with the mass-energy equivalence formula in my paper but I guess it can be derived in a number of ways. The latter part of equation 7 is from combing the classical expression for potential energy with the the mass-energy equivalence formula $$E=mc^2$$\$.

Also there is a typing error in equation 9. The part that says $$(1-\frac{GM}{rc^2})$$ should instead be $$(1-\frac{2GM}{rc^2})$$, which is nice and more inline with what is expected from the Schwarzschild solution.

CarlBrannen
Posts: 381
Joined: Mon May 24, 2010 11:34 pm

### Re: Henrik Agerhell's gravitation research

To me, the most remarkable equation is (5):

$$\frac{d\vec{v}}/{dt} = -\frac{GM}{r^2}(\hat{r}\cdot\hat{v})(1-v^2/c^2)\hat{v} +\frac{GM}{r^2}(\hat{r}\times\hat{v})\times\hat{v}$$

I verified this by looking through the booklet, "Another Road to Schwarzschild", which Henrik kindly sent me:
http://booksondemand.e-butik.se/?artnr=1129

When I tried to verify the above by following the logic given at the blog post:
http://henrik77.wordpress.com/2011/04/1 ... arzschild/
I found myself trying to disprove it. But when I put in various situations it worked and the paper explains it well.

What I find surprising about this way of writing the acceleration is that it is written entirely in terms of the unit vectors $$\hat{v}$$ and $$\hat{r}$$, the radius $$r$$, and the gamma factor related term $$(1-v^2/r^2)$$.

The strange thing about this term is that it appears to be very dependent on the direction of the velocity, but when one puts $$\vec{v}=0$$, one finds that the result does not depend on the direction of velocity.

And I'm intrigued by this as this is the kind of thing I'd expect from a unification of gravity with the elementary particles.

That is, the elementary particles are defined in terms of left and right handed portions. These act very much different from each other. For example, only the left handed electron participates in the weak force. But the left and right handed portions correspond to particles moving with speed c. So a stationary electron has to be described as a combination of left and right handed portions moving at speed c in opposite directions. Thus the effect of gravity on such an object should depend on the direction in which it is pointed. But on the other hand, we know from observation that the gravitational force does not depend on direction of spin orientation.

So I'm going to see if I can rewrite the exact equations of motion for motion in the Schwarzschild metric into a form similar to the above. I'll start with the equations I published for the Schwarzschild metric in Gullstrand-Painleve metric, i.e. equation (10) of:
http://arxiv.org/abs/0907.0660

negru
Posts: 307
Joined: Wed Oct 13, 2010 3:49 pm

### Re: Henrik Agerhell's gravitation research

I don't get what's so special about eq 5. It's just taking into account the relativistic effects on the mass, and plugging them into the law of attraction. I don't see anything fundamentally new here. I'm not sure it's correct either. Merging gravity with SR gives GR.

henrikagerhell
Posts: 2
Joined: Thu May 12, 2011 8:18 am

### Re: Henrik Agerhell's gravitation research

negru wrote:I don't get what's so special about eq 5. It's just taking into account the relativistic effects on the mass, and plugging them into the law of attraction. I don't see anything fundamentally new here. I'm not sure it's correct either. Merging gravity with SR gives GR.
Well, basically you are right. By inserting a mass that varies with velocity as in SR into the Newtonian expression for gravitational acceleration you get eq. 5. By also letting the mass vary with position within a gravitational field, which might seem strange, you get an expression for gravitational acceleration that causes a planet to move just like the Schwarzschild solution predicts, right down to the Schwarzschild radius.

However, that is not how GR is generally done. GR is done by assuming a world governed by four-dimensional Riemann geometry, which is much more complicated than this approach.

I now have an uppdated version of my essay online:
http://vixra.org/abs/1303.0004