Will Accelerating a Massive Object Create a Black Hole?

[michael879]

energy and mass both exert gravitational force right? so the question "will a very fast object become a black hole" isn't answered by saying that the rest mass doesn't change right? I remember asking this question before and being told that it wouldn't since the rest mass stays the same when you speed up. But if you accelerated a "massive" object to a high enough velocity couldn't you make a black hole?

 

[Hurkyl]

Energy does curve space. But so does momentum and momentum flow. So there is a vast difference between a "stationary" very massive object and a "very fast" light object, due to the momentum component.

 

[michael879]

are you saying momentum "un-bends" spacetime? cause otherwise it seems like it would just cause more gravity.

 

[pervect]

As I said the last time this came up, an object is a black hole only if it traps light.

If light can escape from a stationary object, it can and does escape from the same object when it is moving. Thus if an object is not a black hole in its rest frame, it is not a black hole in any frame.

Also note that there is no such thing as absolute velocity. That alone should tell you that objects don't become black holes when they move quickly.

After all, relative to some observers, you yourself are moving at .9999 c - but you are not a black hole.

Since you've seen the thread before, I assume you've already seen the standard references that show that moving objects don't become black holes. But I will repeat them if anyone else is interested and can't find them, though they should be easy to find (check the sci.physics.faq).

The gravitational field of a moving object is an interesting question without a correct clearcut simple answer.

Probably one of the simplest ways to tackle the problem that is still technically correct is to look at the tidal forces of a moving object rather than the "gravitational field".

Imagine a moving observer and a non-moving observer both at the same location in space-time measuring the tidal force aka the gravity gradient with a gravity gradiometer, i.e a Forward mass detector

http://en.wikipedia.org/wiki/Robert_L._Forward#Forward_Mass_Detector

For two observers at the same point, the one in relative motion will measure an increased tidal force / gravity gradient, BUT only if he is moving perpendicularly to the mass. If he moves towards or away from the mass, he will get the same reading as a stationary observer.

Another way of describing this - the measurble effects of gravity, the tidal forces, are not spherically symmetrical for a moving object. They are concentrated in the transverse direction. This is rather similar to the way that the electric field of a moving charge appears, though in the case of the electric field we can measure the field directly, we don't have to worry about measuring the gradient instead.

 

[CarlB]

After all, relative to some observers, you yourself are moving at .9999 c - but you are not a black hole.

Funny, I've personally never met observers moving faster than about
0.0000015 c.

Carl

 

[michael879]

Funny, I've personally never met observers moving faster than about
0.0000015 c.

Carl

doesnt mean there arent any on other planets .

pervect, ok so I guess by the definition of a black hole this can't happen but as the object's speed approached c (compared to our frame) wouldn't it begin to "suck in" everything around it (except for light)?

 

[pervect]

The short answer is "to some extent". For instance, take a look at the abstract for http://dx.doi.org/10.1119/1.14280

The long answer basically explains why its difficult to quantify this. Suppose you are stationary in space, near a large object. You can then measure the gravity of that object by measuring your acceleration with an accelerometer, the acceleration you need to "hold station" a constant distance away.

If you have a massive object whizzing by, though, it becomes very difficult to determine how to "hold station". It's easy to move in free-fall, but that's not what's wanted here. So, perhaps you try to look at distant stars, to triangulate your location, but you do so you find that gravity is warping the path of light in a manner that varies with time as the massive object whizzes by. So, the triangulation idea won't work either, unless you model how the light is being bent, but the whole idea is to measure the effect directly.

Another way of explaining the issue: it turns out the answer to "what is the field" depends on the specific details of the coordinate system you choose.

The easiest (and in long run the best) thing to do is to not attempt to make a direct measurement of the "gravitational field". This avoids all the measurement and coordinate dependence issues. The paper I quoted measures, instead, the velocity that someone picks up from the large mass while it whizzes by. This is an easy measuremnt to make, because it occurs in flat space-time. You measure the velocity before, and the velocity after, and that determines some sort of effective mass number. Howver, with this approach you get only a number, and not anything that describes how the field appears in space.

Another thing you can do, as I suggested, is to use a gravity gardiometer also called a forward mass detector to measure the gravity gradient. See the previous post for a reference to the details of how this device works. It measures not gravity, but how fast it changes, i.e. tidal forces. For a stationary object, and Newtonian gravity, the gravity gradient will be 2m/r^3 in a direction pointing towards the object (as opposed to m/r^2 for the gravitational force itself). So we can see that the gravity gradient gives us a mesurement of mass.

TThe second approach, using a gravity gradiometer, gives you a slightly better description of what the field "looks like" -as I said previously, the field is concentrated in the transverse direction, much like the electric field of a moving charge.

If you are not familiar with the electric field of a moving charge, take a look at http://www.phys.ufl.edu/~rfield/PHY2061/images/relativity_15.pdf.

I've got a post somewhere that gives the results of what the tidal force (gravity gradient) of a moving mass is, mathematically, if you really want the details. This is something that I had to work out for myself, BTW - the textbooks cover some special cases, which can be used to spot-check the results, but so far I haven't found one that works out the general problem.