# Black Holes and Infinity

1. May 26, 2005

### Draya22

Another question from someone who doesn't know much about physics. If black holes don't let light out, then it has to stop somewhere, right? There has to be a point where the light is not moving at c. It's been proven that gravity can "bend" light waves, so why could it not stop them? Also, if nothing moves faster than light, and light is stopped, does that mean, that at that point, time is also stopped? Or, is time sped up because when you get closer to the speed of light, time slows down, but if the speed of light is slowed, does time speed up? would you be staring infinity in the face when you look at a black hole?

2. May 27, 2005

### Art

In a black hole gravity causes space to have infinite curvature so light doesn't stop it simply continues along a straight path through infinitely curved space

3. May 30, 2005

### jdlech

Here's where I get confused. Define "infinitely curved space".

Let's take a 2 dimentional example. Start with a straight line on a piece of paper and you are a dot on the line. Bend the paper until it curled upon itself like a tube. Now the line makes a circle and we have a singularity. You are now travelling a straight line that curles up on itself. Continue curling the paper and it makes an ever tightening circle. But you will not see the curvature since the line is still straight on the paper.
I understand that part.
What I don't understand is the infinite part. The line curles up into a single point. It is no longer a line but a dot. There can be no travel because travel requires two points; origin and destination. All origin and destinations of infinitely curved space has become the same point. Therfore, travel must be impossible as all things must occupy the same space at all times. Subjectively, one should see himself occupying the entire universe forever after.
Anything else is not infinitely curved.

So if you already occupy all of space, how can you travel?
Or is there some flaw in my logic?

4. May 30, 2005

Staff Emeritus
Take a cusp, like the point of a cone. Right at the tip of the cone the curvature is "infinite".

5. Jun 12, 2005

### Sempiternity

"Infinite" as far as GR is concerned. A theory of everything will give more insight into whether or not it's really infinite.

6. Jun 16, 2005

### kurushio95

I thought there was some theory somewhere that the strength of gravity affects the passage of time? Wouldn't that give Draya's question foundation?

7. Jun 16, 2005

Staff Emeritus

Einstein's General Relativity predicts that time passes more slowly deep in a gravitational field than in the upper reaches of one. This is actually an effect that has to be allowed for in processing the signals of GPS sattelites at the ground.

An odd thing happens to time in the solution of Einstein's equations for the case of a black hole. At the event horizon, the interface between the BH and the rest of the universe, radial distance and time swap roles. Inside the horizon time runs "to infinity" down to the center, the singularity, of the black hole.

8. Jul 14, 2005

### Yaaks

But,,Time dilation w.r.t Earths gravity is Negligible ....sooo, Wht diff. does it make for the GPS sat.. ?

9. Jul 15, 2005

### George Jones

Staff Emeritus
If gravitational time dilation is not taken into account, a time error between the ground and the satellites accumulates at the rate of 39 millionths of a second per day. Distance is determined by timing signals that pass between the ground and the satellites. A rough estimate on the error in position that this causes can be obtained by calculating the distance that a signal moving at the speed of light travels in 39 millionths of a second. The answer might surprise you.

Regards,
George

10. Jul 19, 2005

### RandallB

Can you explain, maybe with some form of analogy, what it means to have "radial distance and time swap roles"?

Does that mean the radius inside the horizon is no longer measured by distance on the inside but instead by every lengthening time that the distance measured in the new values of time to the center would be "infinity"??

Thatâ€™s weird enough but then what would distance, that from the outside to us looks like the diameter of radius of the BH, be measuring inside the horizon?

Sounds like this may take some matrix math or something a bit beyond most of us.

RB