What is the rate at which a black hole's gravity weakens as one gets further away?

[arknd]

If I know my physics correctly, the singularity at the center of a black hole has infinite mass. How can something that is infinite ever decrease in gravity? Wouldn't the pull of gravity from the black hole always be faster than the speed of light from any point in the universe?

[elfmotat]

It doesn't have infinite mass. Some black holes have masses only a few times that of our Sun, though we have detected others that can be up to billions of times the mass of the Sun.

 

Once a spherical object of mass M is crushed down to a ball with radius [math]r_c=\frac{9GM}{4c^2}[/math], it has no choice but to collapse into a black hole because resisting collapse would require infinite internal pressure. Once collapse is finished, the remaining black hole will have an event horizon at radius [math]r_s=\frac{2GM}{c^2}[/math]. Once anything falls inside the event horizon, it can never escape (because to do so would require infinite energy). After it falls in, it continues to fall toward the singularity. What happens at the singularity is unknown with current physics.

 

To answer the question in the title, the acceleration required to "hover" outside of a black hole (i.e. the acceleration that your rocket-ship needs to produce) is given by:

 

[math]a=\frac{GM}{r^2 \sqrt{1-r_s/r}}[/math]

 

As you can see from the equation and from a plot of the equation below, as you approach the event horizon the acceleration required to hover outside of the BH approaches infinity.

 

 

Edited January 29, 2013 by elfmotat

[arknd]

Your reply just spurred another question from me. If two black holes were to converge, would the black hole with less mass get drawn to the center of the larger one? Because, if entering an event horizon requires infinite energy or mass to escape, and two event horizons are slightly overlapping one another, would they stay locked together or would the smaller one collapse even further and reach the singularity at the center of the larger black hole?

[Arch2008]

http://www.universetoday.com/13002/what-happens-when-supermassive-black-holes-collide/

 

Apparently not always.

[arknd]

Interesting. Do you think that nature has made it impossible for black holes to overlap to avoid the consequences of it by making them spin off of each other? Or do we just not have the ability to figure out what happens when they overlap

[Airbrush]

"What is the rate at which a black hole's gravity weakens as one gets further away?"

 

Gravity weakens at a rate directly proportional to the distance between the objects.

 

"If I know my physics correctly, the singularity at the center of a black hole has infinite mass."

 

Infinite density, not infinite mass.

 

"If two black holes were to converge, would the black hole with less mass get drawn to the center of the larger one? Because, if entering an event horizon requires infinite energy or mass to escape, and two event horizons are slightly overlapping one another, would they stay locked together or would the smaller one collapse even further and reach the singularity at the center of the larger black hole?"

 

The two would behave exactly the way any two massive objects (stars, planets, moons) would behave when they approach each other. Usually this results in them spiraling inwards until they merge, which must be an incredibly immense release of energy, however that energy is not "released" but mostly contained inside the new more massive black hole. I wonder if mere spin would be enough to stop two supermassive black holes (SBH) from eventually merging? Could masses that great avoid each other? But interesting concept nevertheless.

 

"According to simulations made by G.A. Shields from the University of Texas, Austin, and E.W. Bonning, from Yale University, the result is often a powerful recoil. Instead of [sBH] coming together nicely, the forces are so extreme that one black holes is kicked away at a tremendous velocity.

 

The maximum kick happens with the two black holes are spinning in opposite directions, but they’re on the same orbital plane – imagine two spinning tops coming together. In a fraction of a second, one black hole is given enough of a kick to send it right out of the newly merged galaxy, never to return...."

 

That would be a hypervelocity SBH. Has anyone heard of that?

 

"Do you think that nature has made it impossible for black holes to overlap to avoid the consequences of it by making them spin off of each other? Or do we just not have the ability to figure out what happens when they overlap."

 

Not at all. SBHs probably merge most often when galaxies collide, with perhaps rare cases when both have extreme spins in opposite directions. If most SBHs did not merge when galaxies collide, then wouldn't there be evidence of wondering hypervelocity SBH?

Edited February 1, 2013 by Airbrush

[imatfaal]

"What is the rate at which a black hole's gravity weakens as one gets further away?"

 

Gravity weakens at a rate directly proportional to the distance between the objects.

The force is inversely proportional to the square of the distance

 

"If I know my physics correctly, the singularity at the center of a black hole has infinite mass."

 

Infinite density, not infinite mass.

We don't really know either way - our knowledge and our maths breaks down to any decent extent at the event horizon

 

 

"If two black holes were to converge, would the black hole with less mass get drawn to the center of the larger one? Because, if entering an event horizon requires infinite energy or mass to escape, and two event horizons are slightly overlapping one another, would they stay locked together or would the smaller one collapse even further and reach the singularity at the center of the larger black hole?"

 

The two would behave exactly the way any two massive objects (stars, planets, moons) would behave when they approach each other. Usually this results in them spiraling inwards until they merge, which must be an incredibly immense release of energy, however that energy is not "released" but mostly contained inside the new more massive black hole. I wonder if mere spin would be enough to stop two supermassive black holes (SBH) from eventually merging? Could masses that great avoid each other? But interesting concept nevertheless.

Planets stars and moons have a comforting and human-life-enhancing tendency not to spiral into each other. You need some way of dissipating energy a momentum - for such massive and quick moving objects in orbit you will get grav waves, but in most cases they will just orbit the centre of mass.

"According to simulations made by G.A. Shields from the University of Texas, Austin, and E.W. Bonning, from Yale University, the result is often a powerful recoil. Instead of [sBH] coming together nicely, the forces are so extreme that one black holes is kicked away at a tremendous velocity.

 

The maximum kick happens with the two black holes are spinning in opposite directions, but they’re on the same orbital plane – imagine two spinning tops coming together. In a fraction of a second, one black hole is given enough of a kick to send it right out of the newly merged galaxy, never to return...."

 

That would be a hypervelocity SBH. Has anyone heard of that?

 

"Do you think that nature has made it impossible for black holes to overlap to avoid the consequences of it by making them spin off of each other? Or do we just not have the ability to figure out what happens when they overlap."

 

Not at all. SBHs probably merge most often when galaxies collide, with perhaps rare cases when both have extreme spins in opposite directions. If most SBHs did not merge when galaxies collide, then wouldn't there be evidence of wondering hypervelocity SBH?

[Airbrush]

"The force is inversely proportional to the square of the distance."

 

Thank you for the correct answer to this question and the other information too.