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How to use the Wolfram|Alpha time dilation calculator on Black Holes?

Posted 10 years ago
POSTED BY: Jack M
9 Replies
Posted 7 years ago

Hello,

I am also trying to use the time dilation tool for a supermassive black hole, specifically, TON 618, which has approximately 66 Billion solar masses. However. I continue to get imaginary numbers. Here is the rundown:

So this gives us a horizon radius of 1.949x10^14 m, or 1.949x10^11 km

Converting to g, this gives us 23.515 g (doesn't this seem really low?)

Entering these figures, I keep getting imaginary numbers. Does I make a mistake somewhere along the line?

So this gives us a horizon radius of 1.949x10^14 m, or 1.949x10^11 km

Converting to g, this gives us 23.515 g (doesn't this seem really low?)

Entering these figures, I keep getting imaginary numbers. Does I make a mistake somewhere along the line? Thanks in advance.

POSTED BY: Joseph Wiese
Posted 10 years ago

Dear David,

Thank you for your reply. Unfortunately, I need further clarification here too. What does 0.00707089 correspond to? Is that how many seconds of my time near the black hole passes relative to my friend's at a safe distance?

I looked into your book on Amazon ($175!). Remember -- I'm a graphic artist and haven't done algebra in twenty years. I can tell you the difference between Helvetica and Helvetica Neue, or make you a darn good logo ;-)

POSTED BY: Jack M

Yes, that's how many seconds would pass on the clock that near the event horizon compared to 1 second passing on the far clock. And even less time would pass as you got closer. At r = 2 no time would pass. But to make a good book you should get the help of an interested physicist. Maybe like Lawrence Krauss at Arizona University.

And I bought that book for $37.50 at Border's Book Store sometime after 2000.

Hi Jack, the answer to you question is 63.6 years. You can get easily this value using Wolfram|Alpha:

  1. Ask Wolfram|Alpha for "black hole 10 solar masses"

    enter image description here

  2. Then go to the Wolfram|Alpha gravitational time calculator and insert the previous values for the horizon radius, the surface gravity and 90 years (time that your friend turns 100) and you will get the answer:

    enter image description here

Posted 10 years ago

Dear Jofre,

Thank you for your reply. I don't see your response on the website but I did get an email. Unfortunately, I must be doing something wrong. My input is this:

  1. time in rest frame (what or where is the rest frame?): 90 years
  2. gravitational acceleration: 1.52 x 10^12g
  3. radius: 30km

My answer is -1.423 x 10^9 i seconds. I don't know what i means, and I'm not seeing where I wait 63 years to watch my friend age 90 years. It also contradicts an astronomer who only would say I'd wait "less than a blink of an eye." I apologize for the confusion. This subject is a bit thicker than I'm used to :-)

POSTED BY: Jack M
Posted 10 years ago
POSTED BY: Jack M

A good starting point is On Continued Gravitational Contraction by J. R. Oppenheimer and H. Snyder. If I remember it correctly that is the nice paper where light cones fall graceful along the geodetic lines of the metric of the black hole into it, explaining the event horizon virtually by means of illustration ... a point that could be appealing to a graphic artist.

POSTED BY: Udo Krause
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