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Associate

Join Date: Jun 2011
Posts: 30

### Black Hole Attraction-Based Kinetic Energy Gains

05/15/2012 1:31 PM

Hi Folks;

I had a rather simple question.

Suppose that a black hole with an invariant mass of say 10 solar masses is traveling inertially through space at a gamma factor of say 50 or at approximately 0.9998 C. Now consider the scenario where a black hole having a mass of say 0.01 solar mass is located directly in angular front of the 10 solar mass black hole but where the 0.01 solar mass black hole is essentially stationary with respect to the background interstellar medium. What would be the kinetic energy gain for the 10 solar mass black hole under the condition that the 10 solar mass black hole pulls the 0.01 mass black hole into the larger black hole's Event Horizon. Also, what is the general formula for such energy gains given a larger black hole of invariant mass Mo, traveling at a gamma factor of Go, for which a smaller black hole of mass M1, is located directly angularly infront of the larger black hole but where the smaller black hole is essentially stationary with respect to the black ground interstellar medium in which it is disposed. Note that I am assumming that the smaller black hole's initial seperation from the larger black hole while the larger black hole is traveling at the gamma factor of Go, is effectively infinity in the sense that an effective nearly maximum acceleration path is provided. I am also neglecting gravitational radiation generated by the collision since the larger black hole is several orders of magnitude greater in invariant mass than the smaller blackhole

Thanks;

Jim

Pathfinder Tags: black hole Kinetic energy special relativity
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Guru

Join Date: Apr 2010
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#1

### Re: Black Hole Attraction-Based Kinetic Energy Gains

05/15/2012 1:48 PM

1. I don't think 0.01 Solar Mass black holes are ordinarily possible. The mechanisms I'm aware of that make black holes require multiple solar masses.

2. Regardless of point 1 (let's say a 0.01 solar mass BH got created somehow), the laws of conservation of momentum and energy still apply. Take the total energy and momentum of the pair long before collision, and you'd have the same total momentum and energy after the collision. I think.

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#2

### Re: Black Hole Attraction-Based Kinetic Energy Gains

05/16/2012 12:43 AM

I'm surprised that you need to ask.

The set up to the question uses a number of technical terms (like Gamma factor) that imply you either already know a lot about the topic (and should be able to solve it from first principles) or that it's a homework question (and you should be able to solve it from first principles).

Whatever the answer I doubt it's ".. a rather simple question".

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Associate

Join Date: Jun 2011
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#3

### Re: Black Hole Attraction-Based Kinetic Energy Gains

05/16/2012 8:44 AM

Regarding solving the problem based on first priciples, for all I know, General Relativistic effects complicate the answer. And no, its not a homework question. I am just tinkering with an interstellar propulsion concept, and even though the question I asked involves impractical values for invariant mass, the correct answer will help me with the general formulation of the concept.

Off Topic (Score 5)
Associate

Join Date: Jun 2011
Posts: 30
#4

### Re: Black Hole Attraction-Based Kinetic Energy Gains

05/16/2012 9:16 AM

Hi Folks;

The first answer to my question makes sense according to momentum conservative laws. I merely wanted to make sure there was not anything else I was missing. I'll go with the first answer. If I cannot trust momentum conservation, then I have some real issues. I wanted to double check to see if there were any other mechanisms that might change the situation.

Jim

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#5

### Re: Black Hole Attraction-Based Kinetic Energy Gains

05/16/2012 11:43 AM

If that's a "simple question," please don't ask us a complex one!