      # What Equation Determines When A Black Hole Forms?

Black holes Equation

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### #1 TheGamerPlayz

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Posted 12 March 2016 - 03:12 AM

What equation determines when a black hole forms?
In other words, how much would I need to compress a certain amount of mass for it to form a black hole.

Please put it in ways I can understand as I know only the very basics of black holes. I have found some equations, but for the life of me could not understand them.

Thank You.

Edited by TheGamerPlayz, 12 March 2016 - 03:13 AM.

### #2 CraigD

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Posted 12 March 2016 - 10:18 AM

Welcome to hypography, GamerPlayz! Please feel free to start a topic in the introductions forum to tell us something about yourself.

What equation determines when a black hole forms?
In other words, how much would I need to compress a certain amount of mass for it to form a black hole.

The simplest equation describing a black hole is the Schwarzschild radius,
$r_s = \frac{2 M G}{c^2}$.

It applies to uncharged, non-rotating black holes. Other cases are more complicated, but this equation is good for first aproximations.

If the body’s physical radius is less than its Schwarzschild radius, it is a black hole. Otherwise, it isn’t.

You can calculate it for any body. For example, for the Earth, it's about 0.00887 m, about the size of you thumb. If the Earth’s mass were somehow compressed to fit within this radius, it would be a black hole.

### #3 TheGamerPlayz

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Posted 13 March 2016 - 12:28 AM

Welcome to hypography, GamerPlayz! Please feel free to start a topic in the introductions forum to tell us something about yourself. The simplest equation describing a black hole is the Schwarzschild radius,$r_s = \frac{2 M G}{c^2}$.It applies to uncharged, non-rotating black holes. Other cases are more complicated, but this equation is good for first aproximations.If the body’s physical radius ?is less than its Schwarzschild radius, it is a black hole. Otherwise, it isn’t.You can calculate it for any body. For example, for the Earth, it's about 0.00887 m, about the size of you thumb. If the Earth’s mass were somehow compressed to fit within this radius, it would be a black hole.

OK, I understand what you said for everything but t

Welcome to hypography, GamerPlayz! Please feel free to start a topic in the introductions forum to tell us something about yourself. The simplest equation describing a black hole is the Schwarzschild radius,$r_s = \frac{2 M G}{c^2}$.It applies to uncharged, non-rotating black holes. Other cases are more complicated, but this equation is good for first aproximations.If the body’s physical radius is less than its Schwarzschild radius, it is a black hole. Otherwise, it isn’t.You can calculate it for any body. For example, for the Earth, it's about 0.00887 m, about the size of you thumb. If the Earth’s mass were somehow compressed to fit within this radius, it would be a black hole.

I see, now my question is how to find G in the schwarzchild radius. I realise that it is Gravity Constant, but what exactly is this and how do I calculate it? Sorry if I do not understand the this much

Edited by TheGamerPlayz, 13 March 2016 - 12:28 AM.

### #4 CraigD

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Posted 13 March 2016 - 03:38 AM

I see, now my question is how to find G in the schwarzchild radius. I realise that it is Gravity Constant, but what exactly is this and how do I calculate it? Sorry if I do not understand the this much

If you follow the link to Wikipedia in my previous post, you’ll find links to all the needed constants, but for our convenience, here’s everything we need, in MKS units:
G = 6.67408 x 10-11 m3 kg-1 s-2 = 0.0000000000667408 10-11 cubic meter per kilogram per second per second
c = 2.99792458 x 108 m s-1 = 299792458 m s-1
so $\frac{2G}{c^2}$ = 1.48518309 x 10-27 m kg-1

Multiply this time the mass of your body in kilograms to get its Schwarzschild radius in meters.

For example, the Sun has a mass of about 1.9891 x 1030 kg, so it’s rs = 1.48518309 x 10-27 x 1.9891 x 1030 kg = 2.95418 x 103 = 2954 m. The Sun’s radius is 696342000 m, so it’s not a black hole.

### #5 TheGamerPlayz

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Posted 13 March 2016 - 03:42 AM

If you follow the link to Wikipedia in my previous post, you’ll find links to all the needed constants, but for our convenience, here’s everything we need, in MKS units:G = 6.67408 x 10-11 m3 kg-1 s-2 = 0.0000000000667408 10-11 cubic meter per kilogram per second per secondc = 2.99792458 x 108 m s-1 = 299792458 m s-1so $\frac{2G}{c^2}$ = 1.48518309 x 10-27 m kg-1Multiply this time the mass of your body in kilograms to get its Schwarzschild radius in meters.For example, the Sun has a mass of about 1.9891 x 1030 kg, so it’s rs = 1.48518309 x 10-27 x 1.9891 x 1030 kg = 2.95418 x 103 = 2954 m. The Sun’s radius is 696342000 m, so it’s not a black hole.

Oh I see. Thanks yfor your help

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