Exploring the Temperature inside a Black Hole: A Giant Alien's Quirky Inquiry

Imagine a scenario where a giant alien holds a giant thermometer, intending to probe the heart of a black hole. This thought experiment, while charming, leads to a fascinating exploration of the limitations and peculiarities of black hole physics. Let's dig into the details, including the Hawking temperature, the cosmic background radiation, and the intriguing questions that arise.

First, it's crucial to understand that the idea of a giant alien with a giant thermometer is purely fictional. In reality, the laws of physics severely limit what we can do within the event horizon of a black hole. However, this thought experiment opens the door to discussing some of the most intriguing aspects of black hole thermodynamics.

The Hawking Temperature and Black Hole Physics

The Hawking temperature, named after physicist Stephen Hawking, is the temperature of a black hole based on the unification of quantum mechanics and general relativity. For a black hole with the mass of the Sun, the Hawking temperature is incredibly low, approximately 0.00000006 Kelvin. This is so minute that it's almost negligible for practical purposes.

Calculating the Temperature of a Smaller Black Hole

Recently, the question was raised about a black hole with the size of the moon and its temperature. The Hawking temperature for a black hole with the mass of the moon would be:

The sun is said to be 27 million times the mass of the moon. The Hawking temperature of a solar mass black hole is 0.00000006 K. Therefore, the Hawking temperature of a black hole with the mass of the moon would be 0.00000006 K multiplied by 27 million, resulting in approximately 1.62 K.

However, this temperature is still significantly lower than the cosmic background radiation, which is about 2.7 Kelvin. This begs the question: if the temperature of a black hole is below 2.7 Kelvin, would it ever be able to radiate any significant energy? In fact, the principles of black hole thermodynamics suggest that under these conditions, the black hole would absorb radiation rather than emit it.

The Critical Temperature and Black Hole Stability

The critical temperature for a black hole to radiate energy instead of absorbing it is the cosmic background radiation, which is about 2.7 Kelvin. Any black hole with a temperature below this threshold will be in a state of equilibrium, where it neither emits nor absorbs radiation. This means that a black hole with a moon-mass would require a mass approximately 60 times that of the moon to reach the critical temperature of 1.62 Kelvin. Any black hole with a mass above this threshold would be transient, ultimately evaporating due to Hawking radiation.

The Practical Limitations

Even if we were to speculate about a giant alien wielding a giant thermometer, the practical limitations of this scenario would be immense. It's impossible to extract any information from the inside of a black hole using traditional instruments. Additionally, even if the alien could somehow measure the temperature and extract the thermometer, the data would be irretrievable due to the extreme gravitational forces and the event horizon.

Conclusion

In conclusion, the thought experiment of a giant alien with a giant thermometer is a delightful way to explore the fascinating and often counterintuitive world of black hole physics. While the scenario is purely fictional, it helps illustrate the limitations and peculiarities of black holes. The Hawking temperature, the cosmic background radiation, and the critical temperature are all important concepts in our understanding of black hole thermodynamics.