# Is there a formula for scaling explosive detonation velocity? (Supernova level) [closed]

For context, I’m planning a novel with as much ridiculous magic as ridiculous science so, yes I know, it’s impossible but bear with me.

There is a supermassive black hole that weighs 1 trillion solar masses and to “kill” it, the cast decides to lure it to a magic-made 1 trillion solar mass star and then collide a 1 trillion solar mass star made of antimatter into the regular matter star and hope that the explosive force is enough to blow it apart.

Let me drop my numbers (if you want to check my work or poke holes in the math and expose my psuedophyics please go ahead :P) :

according to: https://youtu.be/3ZWqQciAQlU?t=139

1 kg of matter + 1 kg of antimatter = the energy of Hiroshima bomb x 3000

1 kg of matter + 1 kg of antimatter = 63 terajoules or (6.3 x 10^13 joules x 3000)

1 kg of matter + 1 kg of antimatter = 1.89 x 10^17 joules of energy

1M☉ = 2x10^30 kg so a 1 trillion M☉ star weighs 2x10^42 kg!

So I was trying to find how much energy would be released if 2x10^42 kg of matter smacked 2x10^42 kg of antimatter and did some cross-multiplication.

1kg of matter + 1 kg of antimatter OVER 1.89 x 10^17 joules of energy is EQUAL to 2x10^42 kg of matter + 2x10^42 kg of antimatter OVER x.

x=a whopping 3.78x10^59 joules

I divided this number by the energy output of a supernova (10^44 J)

To put it in perspective, for a 1 Trillion M☉ sun made of regular matter smacking a 1 Trillion M☉ sun made of antimatter, the explosion will be 3.78 QUADRILLION times more energetic than a supernova. Y I K E S!!!

Back to the question at hand.

I found out that a supernova’s explosive velocity is 10% the speed of light and its shockwave is 3% the speed of light. I’m wondering if that rate stays the same for an explosion of above-stated magnitude or if the velocity increases.

Is there like a formula or chart or something to scale this?

And I know to get to the speed of light require an infinite amount of energy, but considering that a supernova explodes at 10%, what would be the velocity for an explosion 3.78 quadrillion times more energetic? And what would happen if that explosion is faster than the speed of light with all that ridiculous energy output? Would that be enough to “kill” the 1 trillion solar mass black hole since light would be able to escape (considering how freaking luminous the explosion would be)?

Also, would the explosion put out enough force to disrupt the massive gravitational pull of the 1 trillion solar mass black hole?

• There cannot be an explosion (as such) faster than the speed of light (unless you decide there can be in your world). We have a "one question , one best answer" framework here. You have asked several questions - each needs it's own thread perhaps. What would make you think that current science (you used the tag science-based) would support the destruction of a black hole by light? Voted to close as unclear what you are asking. I'm also concerned that your question lacks the requisite research. – Tantalus' touch. May 11 '19 at 21:39
• Makes me wonder what would happen if you just fired the antimatter at the black hole directly - like a firehose of antiprotons. I suppose that since even the gamma rays produced can’t escape, it’d still be a black hole but you’d eventually have mass without matter? – Dubukay May 12 '19 at 3:33
• @Dubukay the gamma rays have mass too - not very much, but still m = E/c^2. What you need is negative energy particles - Hawking particles - being somehow created near the event horizon and dropped in. That will make the black hole shrink. The problem being that, the smaller it gets, the faster it will shrink, and the more Hawking radiation it will produce. At the very end, you'll get a sizeable photon source and a proportional explosion. If you then stabilized the black hole by feeding it ordinary mass, while keeping it far enough from the runaway blast, it could work as an energy source. – LSerni May 12 '19 at 9:00

Energy per kg = $$m \cdot c^2$$; c = 299 792 458 $$\frac ms$$

So 2 kg (1 kg antimatter, 1kg matter) = $$1.79 \cdot 10^{17}$$ not 1.89 x 10^17 following values are false due to this value.

A trillion is not 10^12 it's 10^15 so your mass value should be 2x10^45 not 2x10^42.

Is there a formula or chart or something to scale this?

• Chart? No
• Formula? Not specifically for this but maybe usable?:

$$v = c \cdot\frac {(\frac {mi}{mf})^2 -1}{(\frac {mi}{mf})^2 +1}$$

mi = initial mass, mf final mass You need some rest mass for this to work otherwise you simply get lightspeed

What would be the speed of that explosion?

I have no Idea very close to lightspeed probably.

What would happen if the explosion would be faster than light?

• First: Would not happen.
• Second: no one knows (who we know at least)

Would it be enough energy to "kill" the blackhole?

Depends:

• If exploded outside the black hole the blackhole will simply absorb some of the explosion and grow in mass. Blackhole doesn't die

• If exploded inside it theoretically could spread the mass inside of it so far apart that the black hole would turn into burning stars. Because the force inside of the blackhole keeping the mass together is pretty weak:

$$F = \frac {m1 \cdot m2}{r^2} \cdot G$$; G = Gravitational constant

with our values we get 0.015 Newton or 0.015 $$\frac ms^2$$ which is less than the gravitational force of our Earth. So Theoretically it is possible for the explosion to separate the mass of the blackhole so far apart that it “uncolapses”. How anyone would be able to control the explosion when inside a blackhole is completely beyond me. As is the fact if the traditional gravitation Formula even works in the slightest when working with blackholes.

Conclusion

If you can explode these stars inside a blackhole and Newtons formula works when concerned with blackholes then it may be possible for your Idea to work.

• Un-collapsing a black hole, novel idea to me at least. +1 – Tantalus' touch. May 11 '19 at 22:55
• @Hoyle'sghost No real idea more interpretation of the solutions but no doubt unique – Soan May 11 '19 at 23:08
• "As is the fact if the traditional gravitation Formula even works in the slightest when working with blackholes." Unfortunately, the traditional gravitation formula can't be used here because it is an approximation only valid for low gravity regimes, which a black hole isn't. You'd have to use GR to get a valid answer and I'm pretty certain that the result would still be that an explosion within the black hole couldn't possibly get rid of it, no matter how big (I'm not an expert in GR though, so take that with a grain of salt). – el duderino May 11 '19 at 23:42
• Which 'trillion' are you using? I was under the impression that it went: thousand (10e3), million (10e6), billion (10e9), trillion (10e12), quadrillion (10e15)... – Samwise May 12 '19 at 0:21
• Since light can escape Earth, and you calculate an even lower gravitational force than Earth, I suspect something is wrong in your math – L.Dutch - Reinstate Monica May 12 '19 at 4:56