# Black Hole Time Machine (time dilation)

1. Oct 23, 2009

### sciroccokid

All,

I am familiar with the concept of orbiting a black hole with out entering its event horizon as a means of time travel. Does anyone have any research on this matter, or know of any papers which deal with this concept.

I would really like to explain this concept to a colleague and additional materials would be very helpful!

Thanks

2. Oct 23, 2009

### sciroccokid

I can't find anything on this. Maybe I don't know how to use google. . . Anyone have any resources regarding time travel via orbiting a black hole?

3. Oct 23, 2009

### Dmitry67

You need a super extreme Black Hole in order to do what you want.
We dont know if such BH exist
In the ordinary BH the area with closed timelike loops is hidden INSIDE the horizon => is useless for timetravel in our Universe

4. Oct 23, 2009

### Nabeshin

Judging from the OP's post, I don't think he was referring to closed timelike curves. I think he meant simply using the gravitational potential of a black hole to "travel into the future".

OP: If this is the case, what do you want to know? Do you want to know why this type of effect occurs, or how to calculate it, or what?

5. Oct 23, 2009

### sciroccokid

No, this would happen as a result of gravitational time dilation. Correct?

Hypothetically, there is a black hole not to far away (i.e. not the center of the galaxy) I get in my rocket ship and fly to the black hole. I enter into orbit with just the right amount of velocity that i don't get pulled in or shot out. I orbit the black hole a few times. My time in orbit would go slower due to gravitational time dilation. I turn on the ol rocket boosters, break free from orbit, come home, and less time has elapsed for me, then on earth.

6. Oct 23, 2009

### Nabeshin

That's precisely the effect I mentioned.

The closed timelike curves mentioned by dmitry would hypothetically allow a traveler to travel into the past, though. Most physicists think these curves are simply artifacts of theories though, rather than objects that actually exist...

7. Oct 23, 2009

### sciroccokid

I would like to explain this to a colleague and provide him some materials which he can refer to, other then this forum, haha. I was curious if anyone had written popular articles, or research papers on this.

8. Oct 23, 2009

### sciroccokid

So are there any articles which talk about using the orbit of a lack hole as a time machine?

9. Oct 23, 2009

### matheinste

I have little knowledge of gravitational time dilation, but, if gravitation had such a dilatory effect wouldn't it be the same if the body orbited was a black hole or not. With no gravtational effects wouldn't you still age less than someone who remained on earth even if you just travelled to where you were going and then returned to earth.

Matheinste.

10. Oct 23, 2009

### sciroccokid

Well that would be time dilation due to velocity from traveling, presuming your were traveling at greatly accelerated rate.

11. Oct 23, 2009

### Nabeshin

This effect occurs whether you orbit a black hole or not. For example, you could pilot your space ship close to the event horizon and hover there for a while. This would a dilation effect, even though there might not be any motion between observers. This is actually separate from the velocity effect!

Sciroccokid: I don't know of any research papers which discuss this (my knowledge of papers is limited in general), but I don't think many would. The primary reason is that this isn't an incredibly complicated topic. It's not the kind of thing people do research on, seeing as it's solvable with a 1st year introduction to General Relativity, and probably available as an exercise or example in any textbook.

I did a quick search and couldn't find anything from a popular publication from google, but did find this, which explains the subject (perhaps in more detail than you're interested):

12. Oct 23, 2009

### sciroccokid

Agreed. Thanks.

13. Oct 23, 2009

### pervect

Staff Emeritus
I'm not quite sure what your question is, but "Black holes and time warps: Einstein's outrageous legacy" by Kip Thorne is a good popular book about black holes, wormholes, and time travel, and has a description of orbiting a black hole.

14. Oct 24, 2009

### stevebd1

The following is an approximation of the time dilation for an object in stable orbit around a static black hole.

In order to maintain a stable orbit-

$$a_c=a_g$$

where ac is centripetal acceleration of the orbiting object (m2) and ag is gravitational acceleration of the main body (m1), both in units of m/s2

For centripetal acceleration-

$$a_c=\frac{v_t^2\ m_2}{r}$$

where vt is the tangential velocity of the orbiting object and r is the radius of orbit

For gravitational acceleration (in GR)-

$$a_g=\frac{Gm_1m_2}{r^2 }\frac{1}{\sqrt{g_{tt}}}$$

where $g_{tt}=1-2M/r$ and $M=Gm_1/c^2$

if ac=ag then-

$$\frac{v_t^2\ m_2}{r}=\frac{Gm_1m_2}{r^2}\frac{1}{\sqrt{g_{tt}}}$$

solve for vt for a stable orbit-

$$v_t=\sqrt{\frac{Gm_1}{r\sqrt{g_{tt}}}$$

Total time dilation of orbiting object

time dilation due to gravity-

$$t'_g=t\sqrt{g_{tt}}$$

time dilation due to velocity-

$$t'_v=t\sqrt{1-\frac{v^2}{c^2}}$$

According to a number of sources on the forum, in order to obtain the total time dilation (t'T), the consequence of time dilation due to gravity and velocity should be multiplied so-

$$t'_T=t'_g \cdot t'_v$$

substituting the equation for vt into t'v-

$$t'_v=t\sqrt{1-\frac{Gm_1}{r\sqrt{g_{tt}}\ c^2}$$

substitute $M=Gm_1/c^2$ and solve for t'T, the total time dilation for an object in stable orbit around a static black hole is-

$$t'_T=t\sqrt{g_{tt}} \cdot \sqrt{1-\frac{M}{r\sqrt{g_{tt}}}$$

So the time dilation of an object with a stable orbit at 6M around a SM BH with a mass of 3.7e+6 sol would be t'T= 0.7284 and the tangental velocity would be vt=0.4518c

Last edited: Oct 24, 2009