Black Hole Entropy: Is S=A/4 robust ?

In summary, black hole entropy is a measure of the disorder within a black hole and is calculated using the formula S=A/4, where S is the entropy and A is the surface area of the black hole's event horizon. This equation has been extensively studied and is considered robust, but some physicists argue it may not hold true in certain cases. The equation is significant in black hole thermodynamics as it links it to classical thermodynamics and provides a theoretical basis for black hole entropy. Understanding black hole entropy is crucial for understanding black holes and their role in the universe, leading to advances in quantum gravity and implications for our understanding of space and time.
  • #1
Pacopag
197
4
I would like to use the formula S=A/4 to find the entropy of a black hole. But before I go ahead and believe that formula, there are a couple of subtleties that are troubling me.

First of all, in just about every "classical" treatment of black hole thermodynamics, there is usually the underlying assumption that the spacetime is 4-dimensional, and asymptotically flat. Does anyone know if the above formula S=A/4 holds in higher-dimensional spacetimes that aren't asymptotically flat?

Thanks.
 
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  • #2
S=A/4 is valid in higher dimensions. I am not sure about asymptotic flatness.
 
  • #3


The formula S=A/4, also known as the Bekenstein-Hawking formula, is a fundamental result in black hole thermodynamics. It relates the entropy (S) of a black hole to its surface area (A). This formula has been extensively studied and tested, and it has been found to hold in a wide range of scenarios. However, as with any scientific theory, there are certain subtleties and limitations that need to be taken into consideration.

One of the main concerns with the formula S=A/4 is its applicability in higher-dimensional spacetimes that are not asymptotically flat. As mentioned in the post, most classical treatments of black hole thermodynamics assume a 4-dimensional spacetime that is asymptotically flat. This means that at large distances from the black hole, the spacetime looks like flat Minkowski space. However, in higher-dimensional spacetimes, this assumption may not hold.

There have been studies that have investigated the validity of the Bekenstein-Hawking formula in higher-dimensional and non-asymptotically flat spacetimes. Some studies have found that the formula still holds in certain cases, while others have suggested modifications or corrections to the formula. However, the overall consensus is that the formula S=A/4 is robust and holds in a wide range of scenarios, including higher-dimensional and non-asymptotically flat spacetimes.

It is important to note that the Bekenstein-Hawking formula is a semi-classical result, meaning it is derived from a combination of classical and quantum theories. As such, it may not fully capture the behavior of black holes in extreme scenarios, such as in the case of quantum gravity or near the singularity. Further research and investigations are needed to fully understand the applicability of the formula in these scenarios.

In conclusion, while there may be some subtleties and limitations to the Bekenstein-Hawking formula, it is a well-established result in black hole thermodynamics. It has been extensively tested and found to hold in a wide range of scenarios, including higher-dimensional and non-asymptotically flat spacetimes. However, as with any scientific theory, further research and investigations are needed to fully understand its limitations and applicability in extreme scenarios.
 

1. What is black hole entropy?

Black hole entropy is a measure of the disorder or randomness within a black hole. It is related to the number of microstates or configurations that a black hole can exist in.

2. How is black hole entropy calculated?

Black hole entropy is calculated using the famous formula S=A/4, where S is the entropy, and A is the surface area of the black hole's event horizon in units of the Planck area.

3. Is S=A/4 a robust equation for black hole entropy?

The equation S=A/4 has been extensively studied and has been found to be robust in various scenarios. However, some physicists argue that it may not hold true in certain cases, such as when considering quantum corrections or the effects of string theory.

4. Why is S=A/4 significant in black hole thermodynamics?

The equation S=A/4 is significant because it establishes a link between black hole thermodynamics and the laws of classical thermodynamics. It also provides a theoretical basis for the concept of black hole entropy.

5. How does black hole entropy contribute to our understanding of the universe?

Black hole entropy is a crucial aspect of understanding the behavior of black holes and their role in the universe. It has also led to significant advances in the field of quantum gravity and has implications for our understanding of the nature of space and time.

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