# Thread: gravitational field of an accelerated mass

1. In advance i would like to apologise for my poor english and the fact i am just a layman in physics, so i hope i get the terminology right.

The reason for this post is that i wondered how the gravitational field of a single linear accelerated mass is deformed (i know this is an impossible thought experiment because to do this you always need a reaction mass for nullifying the total momentum).
I reasoned that the field in the direction of the acceleration should be increased, and decreased in the other direction.

The reasoning is quite simple:

The dtau/dt can be calculated with the Schwarzschild formula:

dtau= dtfar * sqrt( 1 - 2 * G * m / (r * cē) )

Now, obviously, in the acceleration direction of the gravitational field source, the dtau would be bigger than in the opposite direction, when calculated from a small spatial interfall. This means that the gravitational field strength calculated as:

g = cē* dētau/dx

would be changed as mentioned when the source of a gravitational field is accelerated.

Again: i did not include the reaction mass for nullifying the momentum on purpose: the change in the gravitational field would be canceled.

Does anybode know if this reasoning is correct?
Does anybode know the math for the exact solution?

2. Originally Posted by physpruts
Does anybode know the math for the exact solution?
Good question. I know the exact solution for a uniformly moving spherically symmetric massive object :

Aichelburg

But I wasn't immediately able to find a solution for the accelerated case. I am not even sure whether an exact solution exists for that - if it does, it will be very complicated.

3. Originally Posted by physpruts
(i know this is an impossible thought experiment because to do this you always need a reaction mass for nullifying the total momentum).
...
Again: i did not include the reaction mass for nullifying the momentum on purpose: the change in the gravitational field would be canceled.
Herein lies the problem with regards to a general relativistically correct answer. General relativity can't handle impossible scenarios because general relativity is a fully consistent theory.

4. Originally Posted by KJW
Herein lies the problem with regards to a general relativistically correct answer. General relativity can't handle impossible scenarios because general relativity is a fully consistent theory.
Do you know an exact solution for the physically correct case, i.e. an accelerated massive particle or spherically symmetric object including the reaction mass ? I was only able to find the metric for the uniform motion case ( see link in last post ).

5. Originally Posted by KJW
Herein lies the problem with regards to a general relativistically correct answer. General relativity can't handle impossible scenarios because general relativity is a fully consistent theory.
That sounds quite logic. You're probably right.
However, when the action and reaction mass are sufficient seperated and the distance to 1 mass is much smaller than to the other, i would expect that the local result is somewhat like my single mass though experiment.

6. I did make a small program to calculate the gravitational field of one accelerated mass (using dētau/dx). It nicely showed the expected result: a gravitational field slightly directed in the opposite direction of the accelerated mass (though very small compared to the gravitation of the mass itself).
It looks a lot like an electro magnetic induction effect.

Herein lies the problem with regards to a general relativistically correct answer. General relativity can't handle impossible scenarios because general relativity is a fully consistent theory.
It occured to me: is this the reason that functuations in a gravitational field only radiate with quadrupole moment?

7. Originally Posted by Markus Hanke
Do you know an exact solution for the physically correct case, i.e. an accelerated massive particle or spherically symmetric object including the reaction mass ? I was only able to find the metric for the uniform motion case ( see link in last post ).
I'm not aware of any. I suppose part of the problem is the question of how the mass is accelerated. For example, is it a charge in an electromagnetic field, or is it a rocket propelled by its own material?

A Schwarzschild blackhole in inertial motion is quite straightforward because it can be obtained by transforming to an -coordinate system then performing a Lorentz transformation. But an accelerated object is not a coordinate transformation of an inertial object and probably requires its own Einstein equation.

8. Originally Posted by physpruts
It occured to me: is this the reason that functuations in a gravitational field only radiate with quadrupole moment?
I can't answer that because I disagree with the common view that a rotating rigid dumbbell emits gravitational radiation. My view is that a rotating rigid object cannot emit gravitational radiation regardless of its shape. Thus, I call into question the criteria for the emission of gravitational radiation.

9. Originally Posted by KJW
I can't answer that because I disagree with the common view that a rotating rigid dumbbell emits gravitational radiation. My view is that a rotating rigid object cannot emit gravitational radiation regardless of its shape. Thus, I call into question the criteria for the emission of gravitational radiation.
If i interprete Gravitational wave - Wikipedia, the free encyclopedia correct, a rotating symetric dumbell does indeed not radiate gravitational waves, but when it is asymetric it does.

10. Originally Posted by physpruts
If i interprete Gravitational wave - Wikipedia, the free encyclopedia correct, a rotating symetric dumbell does indeed not radiate gravitational waves, but when it is asymetric it does.
My view disagrees with Wikipedia. While intuition says that a rotating rigid irregularly shaped object should radiate, I reject that rotation causes radiation in objects that wouldn't radiate if they weren't rotating (assuming the objects are rigid), noting that mere variation of the gravitational field at some location over time is not sufficient for there to be gravitational radiation. Unfortunately, I can't prove that my view is correct, though personally I don't doubt it.

11. Originally Posted by KJW
I'm not aware of any. I suppose part of the problem is the question of how the mass is accelerated. For example, is it a charge in an electromagnetic field, or is it a rocket propelled by its own material?
The "charge in the electromagnetic field" is exact the example that led to this topic in the first place.
For example: take a charged body A and an uncharged body B seperated by some distance d.
Now make from B an electric dipole charged in the direction of the electric field. The body will gain momentum due to de divergence in the electric field of A. However, the momentum of body A will not change for d/c seconds after making a dipole of B, so for d/c seconds momentum is not preserved.

So, i assumed that in this case, to preserve momentum, it would require that the gravitational field of B (g_B) deforms when accelerating (instantly, hence the single accelerated mass question) and thus carries away the missing momentum. When A starts accelerating, the deformed gravitational field of A (g_A) would interfere with g_B and nullify the carried momentum.

Or is there a more simple solution?

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