Question about Black Holes and Speed

[Paragon_X]

Hello everyone this is my first post. I just recently started getting interested in physics but just from a very theoretical view and in very simple ways

My problem goes like this:
As far as i am concerned according to Relativity Theory nothing can go faster than light. So then we have the gravity which accelerates objects. So if a Black Hole has unlimited gravity then an object entering its event horizon wouldn't have unlimited acceleration which would evolve into unlimited speed?

thanks in advance!

 

[bcrowell]

So if a Black Hole has unlimited gravity then an object entering its event horizon wouldn't have unlimited acceleration which would evolve into unlimited speed?

It's not true in relativity that unlimited acceleration leads to unlimited speed.

One way to see this is through relativistic velocity addition. If you accelerate in a spaceship by 0.1000c, then by 0.1000c relative to your immediately preceding speed of 0.1000c, then by another 0.1000c relative to that, you don't get 0.3000c, you get 0.2922c. If you continue like this, you never get to c, even though your accelerometer has some high reading for an unlimited length of time.

In your black hole example, the accelerometer attached to the object falling into the black hole will actually read zero at all times.

 

[tiny-tim]

Welcome to PF!

Hello Paragon_X! Welcome to PF!

… have unlimited acceleration which would evolve into unlimited speed?

From good ol' https://www.physicsforums.com/library.php?do=view_item&itemid=26" …

so unlimited acceleration does lead to unlimited momentum

but momentum is "relativistic mass" times velocity,

and unlimited momentum gives unlimited "relativistic mass", but limited velocity.

 

[pervect]

One can see from the relativistic rocket equations http://www.xs4all.nl/~johanw/PhysFAQ/Relativity/SR/rocket.html that one can accelerate indefinitely without exceeding the speed of light.

For an object falling into a black hole, you can measure the velocity as it passes by a static observer stationary with respect to the black hole, and you'll always get a number less than c. In the limiting case, the number will approach c as the object nears the event horizon, but it will never quite reach 'c'.

To be specific, if the object free-falls from zero velocity at infinity, the velocity will be c*sqrt(r/r_s), where r / r_s is the ratio of the Schwarzschild r coordinate of the observer and the Schwarzschild radius.

You cannot have a stationary observer exactly at the event horizon, though you can get one arbitrarily close. Thus you'll never measure a velocity greater than or equal to 'c' as an object falls into a black hole from any other physical observer, though you can approach 'c' arbitrarily closely.

 

[Paragon_X]

Thank you all ! i know get it !