Entropy of a black hole after evaporation

In summary, the conversation discusses the topic of black hole entropy and its evaporation. The participants mention the use of various theories and types of black holes to calculate the entropy difference between the beginning and end of evaporation. However, there are challenges with the semiclassical calculation and the breakdown of current theories for black holes smaller than a Planck mass. One participant suggests using Bekenstein's formula and calculating the entropy for thermal radiation to better understand the process. Additionally, there is a mention of a theory that relates the universe's ground state energy/frequency to the Planck mass, which could potentially provide insights into black hole entropy.
  • #1
trimok
8
0
Black holes have an entropy, but they evaporate. At the end of the evaporation, the entropy is greater than the entropy at the beginning of the evaporation. I am looking for an example of a quantitative result for the entropy of the black hole after evaporation (or the entropy difference between the beginning and the end of the evaporation). You can use your favorite theory (General relativity, f(R), String theory, Loop Quantum Gravity, etc..), you can use your favorite kind of black hole (Schwarzschild, rotating, charged, extremal, BTZ, etc... ), and you can use your favorite dimension (from 4 to 11...), but I am looking for a quantitative result.
 
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  • #2
I would try a semiclassical description (Hawking radiation + classical spacetime; after evaporation this is Hawking radiation + flat spacetime). For Hawking radiation the entropy calculation is done using Bose-Einstein statistics for non-interacting photons of given temperature. There are two problems: i) one has to adapt the standard plane wave formalism to (distorted) spherical waves (have a look at Hawking's paper); ii) geometry and therefore temperature are not constant.
 
  • #3
Don't all our current theories break down for a black hole smaller than a Planck mass (or a ratio thereof, such as √∏), thus we can't arrive at a quantitative (integrative) value for the entropy of complete evaporation?
 
  • #4
ryan albery said:
Don't all our current theories break down for a black hole smaller than a Planck mass (or a ratio thereof, such as √∏), thus we can't arrive at a quantitative (integrative) value for the entropy of complete evaporation?
The semiclassical calculation (Hawking) is certainly invalid; there are proposals for microscopic state counting in LQG or string theory (but I think that evaporation with thermal radiations + corrections is not understood); anyway - why not try to calculate the BH entropy using Bekensteins formula, and then calculate the entropy for the thermal radiation?
 
  • #5
Does the Planck scale represent the realm where the horizon of a black hole is basically the same as the singularity itself, at least in regards to entropy?

With a sense of humor I hope others can appreciate, the theory I choose to answer this question in is that the universe has a ground state energy/entorpy (or related frequency) that's closely proportional to the Planck mass. Taking that same mass/energy/frequency for my Schwarzschild black hole, then the entropy change for such a black hole evaporating is quantitatively zero. Funny, that same ground state also gives (in a space domain) a value for dark energy that's pretty close to what we observe.

I obviously think I might need some help with my thinking.
 
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  • #6
Typically, black hole entropy calculations assume it all resides at the event horizon. I'm unconvinced that is correct.
 

FAQ: Entropy of a black hole after evaporation

What is the concept of entropy in relation to black hole evaporation?

The concept of entropy in relation to black hole evaporation refers to the measure of disorder or randomness in a system. As a black hole evaporates, its entropy increases, leading to a decrease in its size and eventual disappearance.

How does the entropy of a black hole change during the process of evaporation?

The entropy of a black hole increases as it evaporates, reaching a maximum value before it eventually disappears completely. This is due to the release of Hawking radiation, which carries away energy and decreases the mass of the black hole.

Can the entropy of a black hole ever decrease?

No, according to the second law of thermodynamics, the entropy of a closed system can never decrease. This means that the entropy of a black hole can only increase as it emits Hawking radiation and eventually evaporates.

Is there a limit to the maximum entropy of a black hole?

There is no known limit to the maximum entropy of a black hole. However, as a black hole evaporates, its entropy approaches a value known as the Bekenstein-Hawking entropy, which is proportional to the surface area of the event horizon.

What happens to the information contained in a black hole as its entropy increases?

As the entropy of a black hole increases, the information contained within it becomes more and more scrambled and difficult to retrieve. This is known as the "information paradox" and is still a topic of much debate and research in the field of black hole physics.

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