# Could a causal mass decrease cause antigravity, i.e. repulsive gravity?

Suppose some mass $M$ is located at rest in some point of space. It creates gravitational potential well, which attracts test bodies towards $M$:

Now suppose that the mass of a body drastically decreases several times to $m << M$, for example if the mass is radiated away as gravitational waves as in the recent black hole merger detected by LIGO. This causes the potential well become shallower. But this can happen at up to the speed of light, so there should an outgoing wave running on the potential plot:

Now regard the area on the wave:

$- \nabla \phi$ is directed outward here. i.e. body feels anti-gravity, i.e. repulsive gravity!

Does this effect occurs in reality, for example when two black holes merge? The mass of these holes is decreased due to gravitational wave emission.

I would say that this is the same as gravitational waves pressure, but this looks as different nature. GW are quadrupolar, while here we see monopolar pure newtonian plot.

So, will there be some additional gravitational repulsion in reality?

• In your scenario the mass is somehow destroyed (decreased) by magic. Thus I think the question "does this occur in reality?" kind of answers itself. Anyway, what you describe as antigravity is in reality just the lack of gravity. E.G. a planet orbiting a star is not pushed away but rather flies away in a straight line if the star were to magically disappear. Aug 11 '16 at 10:14
• The question regards recent observations of LIGO. No magic was there, but object lost 3 solar masses (event GW150914)
– Dims
Aug 11 '16 at 10:17
• Aug 11 '16 at 11:03
• I think there's a good question in here, and I've attempted to edit it to make it more precise. @Dims if you don't like my edit please feel free to roll it back. Aug 11 '16 at 12:13
• You really don't get gravitational repulsion. You simply get less gravitational attraction
– Jim
Aug 11 '16 at 12:40

No. In newtonian gravity we can predict what would happen if mass was magicked out of existence. However, in general relativity this gets ill-defined, so we have to stick to what's physically possible: flinging out the mass as mass or energy. For this example we have 75% of the mass sent out all at once at t=0 as gravitational waves or photons (at light speed). Furthermore, we assume that the gravity is weak enough so that there isn't strong space-time distortion (escape velocities are << c).

Your diagram is slightly wrong. The shell of radiation is not associated with a jump in potential, it is associated with a jump in force. We can easily integrate this to get the potential:

There is never a repulsion zone. At each point, the gravity force suddenly and permanently reduces to 25% of it's original value as the shell of radiation passes. After this happens the potential gradually increases, converging to the t=Inf curve but the slope of the curve (the force) is constant.

Edit:

Potential is a property that is inferred by integrating from the given location to infinity, assuming that the shell could somehow be stopped. It's slope at each point and time gives the force on a particle hovering at that point, but the overall energy at a point inside the shell and the fact that it increases toward the t=Inf curve is meaningless because there is no way for a particle to outrun the shell. A spaceship inside the shell would ignore the shell and use the t=Inf potential curve for flight calculations.

• You calculated back from force to potential? I.e. you presumed that there was no repulsion, right?
– Dims
Aug 11 '16 at 20:39
• Even more. Your plots violate causality principle: for example, when raising from purple to green, events look space-like, i.e. superluminal.
– Dims
Aug 11 '16 at 20:44
• @Dims Yes I calculated the potential but there was no presumption of not having repulsion. The raising of potential inside of the shell does not violate causality because it does not change anything about the space inside the shell. Potential is not a property of a point but a property of how much energy it takes to get to infinity. Aug 11 '16 at 20:54
• you have entire plot raising in entire space. This means, that each point of space has increasing potential, which increases without a reason. It doesn't matter how one calculate a value, the result should obey the principle of causality. I.e. if potential grows from $-2.5$ to $-1.8$ in point $x = 0.5$ it should have a reason for this in nearby points. But this is not the case in your plot. For example, your purple plot in region of point $x = 0.5$ is just normal potential plot. Why would it grow?
– Dims
Aug 12 '16 at 9:54
• Newtonian potential is directly related with $g_{00}$, by the following relation $g_{00} = 1 + 2\phi / c^2$. So, $\phi$ is a local property of the space-time. It can't just change without a reason.
– Dims
Aug 12 '16 at 9:57