<p><a href="https://en.wikipedia.org/wiki/Hawking_radiation#Black_hole_evaporation" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Hawking_radiation#Black_hole_evaporation</a> gives the necessary formulae.</p>
<p>And if you just want the answers then change the top line of this javascript calculator to 1 Earth mass.  <a href="https://www.vttoth.com/CMS/physics-notes/311-hawking-radiation-calculator" rel="nofollow noreferrer">https://www.vttoth.com/CMS/physics-notes/311-hawking-radiation-calculator</a>.</p>
<p>Lifetime <span class="math-container">$9.9\times 10^{57}$</span> seconds.</p>
<p>The luminosity (energy emitted per second) increases right up until the moment the black hole disappears, so there is no one answer, but it is <span class="math-container">$10^{-17}$</span> Watts when the black hole is of one Earth mass (which it would be for many times the current lifetime of the universe).</p>
<p>The Schwarzschild radius, <span class="math-container">$r= 2GM/c^2$</span>, is 8.9 mm.</p>
<p>There is no known astrophysical route to producing black holes with this mass other than as <a href="https://en.wikipedia.org/wiki/Primordial_black_hole" rel="nofollow noreferrer">primordial objects</a> created in the big bang. There is no evidence that these exist.</p>

CC BY-SA 4.0
2022-02-08T08:52:45.610Z
As a side note: The Hawking temperature of an Earth mass black hole is about 0.02 K. This is well below the temperature of the CMB. Consequently, an Earth mass black hole would absorb more energy from the CMB than it emits through Hawking radiation. Therefore in order an Earth mass black hole to evaporate, we need to wait for the universe to cool below 0.02 K. This itself will take a very long time (but one that is utterly insignificant compared to the total evaporation time).
TimRias
CC BY-SA 4.0
2022-02-07T23:01:09.293Z
2022-02-07T23:09:14.113Z
2022-02-07T23:09:14.113Z
ProfRob
<p>A raft of related questions:</p>
<ul>
<li>Is an Earth-mass black hole even possible?</li>
<li>Assuming Hawking Radiation (HR) is a fact (has it been verified yet?), would HR cause an earth-mass black hole to evaporate quickly, not so quickly, or after a long time?</li>
<li>How intense would the energy generated by the HR of such a black hole be, even without additional matter falling into it?</li>
<li>If you know a way to calculate it, what would be the diameter of the event horizon of such a black hole?</li>
</ul>

<black-hole><hawking-radiation>
How soon would an earth-mass black hole evaporate?
Cyberherbalist
# How soon would an earth-mass black hole evaporate?

(Asked by: username_0 on 2022-02-07)

A raft of related questions:

* Is an Earth-mass black hole even possible?
* Assuming Hawking Radiation (HR) is a fact (has it been verified yet?), would HR cause an earth-mass black hole to evaporate quickly, not so quickly, or after a long time?
* How intense would the energy generated by the HR of such a black hole be, even without additional matter falling into it?
* If you know a way to calculate it, what would be the diameter of the event horizon of such a black hole?

**Tags:** black-hole, hawking-radiation


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## 1 answers

### Answer by username_1 on 2022-02-07. Score: 4

<https://en.wikipedia.org/wiki/Hawking_radiation#Black_hole_evaporation> gives the necessary formulae.

And if you just want the answers then change the top line of this javascript calculator to 1 Earth mass. <https://www.vttoth.com/CMS/physics-notes/311-hawking-radiation-calculator>.

Lifetime $9.9\times 10^{57}$ seconds.

The luminosity (energy emitted per second) increases right up until the moment the black hole disappears, so there is no one answer, but it is $10^{-17}$ Watts when the black hole is of one Earth mass (which it would be for many times the current lifetime of the universe).

The Schwarzschild radius, $r= 2GM/c^2$, is 8.9 mm.

There is no known astrophysical route to producing black holes with this mass other than as [primordial objects](https://en.wikipedia.org/wiki/Primordial_black_hole) created in the big bang. There is no evidence that these exist.

> **Comments:**
> **username_2**: As a side note: The Hawking temperature of an Earth mass black hole is about 0.02 K. This is well below the temperature of the CMB. Consequently, an Earth mass black hole would absorb more energy from the CMB than it emits through Hawking radiation. Therefore in order an Earth mass black hole to evaporate, we need to wait for the universe to cool below 0.02 K. This itself will take a very long time (but one that is utterly insignificant compared to the total evaporation time).  

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