Blackhole mass = Hawking temperature x Entropy?

In summary, according to Blackhole thermodynamics, a black hole's entropy is proportional to its surface area and it has a temperature called the Hawking temperature. Multiplying the Hawking temperature by the entropy gives a thermal energy, which can be considered as the mass/energy of the black hole itself. This is in line with the holographic principle, which states that the internal state of a black hole is described by its surface area. If the holographic principle also applies to the Universe, then the Universe can be seen as a maximum entropy object with its entropy determined by its expanding event horizon. This leads to a relationship between the mass and radius of the Universe that implies a linearly expanding model that follows the Hubble equation. This model
  • #1
johne1618
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According to Blackhole thermodynamics a black hole has an entropy that is proportional to its surface area and a temperature called the Hawking temperature.

If one multiplies the Hawking temperature by the entropy one gets a thermal energy.

Would this energy be equal to the mass/energy of the black hole itself?

John
 
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  • #2
Actually I answered my own question.

By integrating the thermodynamic relation:

dU = T dS

where T is the Hawking temperature and S is the black hole entropy one obtains the relation:

G M / R = c^2 / 2

which is the Scwartzchild radius relation for a black hole.

Thus the whole of the mass of a black hole can be considered as the thermal energy of its event horizon. This is in accord with the holographic principle that the internal state of a black hole is completely described by the state of its surface area.
 
  • #3
If the holographic principle also applies to the Universe as a whole then the Universe is a maximum entropy/information object like a black hole with its entropy determined by the surface area of its expanding event horizon.

If we assume that this event horizon has a Hawking temperature and that its surface thermal energy equals the mass/energy of the Universe then the above analysis again applies so that we again get the relationship:

G * M / R = c^2 / 2

where now M and R is the mass and radius of the Universe.

If you plug this relation into the Friedman equations one finds that it implies a spacially flat linearly expanding model of the Universe that exactly obeys the Hubble equation. This model is both simple and elegant and also fits the current Universe expansion data pretty well.
 

FAQ: Blackhole mass = Hawking temperature x Entropy?

1. What is the relation between black hole mass, Hawking temperature, and entropy?

The equation "Blackhole mass = Hawking temperature x Entropy" is known as the Bekenstein-Hawking formula. It describes the fundamental relationship between the mass, temperature, and entropy of a black hole, as predicted by the theory of general relativity.

2. How does the Bekenstein-Hawking formula connect to the laws of thermodynamics?

The Bekenstein-Hawking formula is consistent with the laws of thermodynamics, specifically the second law which states that the entropy of a closed system cannot decrease. In the case of a black hole, the entropy always increases with the mass and temperature, as described by the formula.

3. What is the significance of the Hawking temperature in the Bekenstein-Hawking formula?

The Hawking temperature is a temperature assigned to a black hole based on its surface gravity, which is a measure of its strength of gravity at the event horizon. This temperature is proportional to the mass of the black hole and inversely proportional to its entropy, as described by the Bekenstein-Hawking formula.

4. Can the Bekenstein-Hawking formula be used to calculate the mass, temperature, or entropy of a black hole?

Yes, the Bekenstein-Hawking formula can be used to calculate the mass, temperature, or entropy of a black hole. However, it is important to note that the formula is an approximation and does not account for quantum effects, so it may not be accurate for extremely small or massive black holes.

5. Are there any real-world applications of the Bekenstein-Hawking formula?

While the Bekenstein-Hawking formula was originally developed to describe theoretical properties of black holes, it has since been used in various fields such as string theory, quantum gravity, and cosmology. It has also been used in the study of black hole thermodynamics and the relationship between black holes and entropy in the universe.

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