Mass addition due to gravitational acceleration

[Anthony24]

I read an article about super massive black holes that are millions a billion times larger than our sun. In reading this article i began thinking about gravitational acceleration and what the effects would be on incoming objects. I ran through a bunch of equations and found that the mass gain would be over 100 million kg per kg at 98% the speed of light. My questions are: Does time dilation change the energy in a system K.E=.5mv^2 (as this would change mass addition), and does E=mc^2 still apply to gravitational acceleration since it is just the bending of space time?

 

[Dale]

Hi Anthony24, welcome to PF!

Energy is notoriously difficult to handle in GR, but in certain scenarios it does make sense: see http://www.phys.ncku.edu.tw/mirrors/physicsfaq/Relativity/GR/energy_gr.html

In the case of a supermassive black hole as something falls in it loses PE and gains KE so the total energy of the system is unchanged.

 

[Anthony24]

Wow thank you so much for that, i had not put together to relation between potential energy and kinetic energy in the system. That answers my question perfectly and nullifies some pages of math work :( oh well, thanks a bunch!

 

[Anthony24]

Okay if this is true then where does potential energy end and begin? It stands to reason that we also have the potential to be pulled toward any object in the universe. Would that not mean we have an infinite amount of potential energy? Please forgive my lack of familiarity with this concept.

 

[Dale]

The PE does not end or begin at a certain location, but because of the way that the math works it turns out to be finite anyway. It is therefore possible for an object to have more kinetic energy than potential energy, the speed corresponding to the kinetic energy which would be exactly equal to the potential energy is called escape velocity.