What Causes the Increase in Area of Black Hole Horizons?

In summary, the conversation discusses the increase in mass and area of a black hole when a photon falls into it. The equations show that the increase in mass is directly proportional to the Planck constant and inversely proportional to the Schwarzschild radius, while the increase in area is always one square Planck length for each piece of information that falls in. However, there is a discrepancy in the equations as they involve the initial radius, meaning the increase in area may not be the same for all black holes.
  • #1
schaefera
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From another post on this forum, we have an excerpt of Susskind's "The Black Whole War":



To figure the increase in mass, let's figure the energy of the photon and then convert that to an equivalent mass.

Photon energy is E = hf and if wavelength is Rs/SUB], from v = f x wavelength, frequency (f) is c/Rs/SUB] so E = hf becomes hc/Rs/SUB]. (1)

From E =mc2, dividing energy by c2 gives mass, so the change in mass becomes h/Rsc. (2)

The Schwarzschild radius is given by Rs - 2MG/c2 (3)

and substituting the above change in mass for the photon, substituting (2) in (3) increases the radius 2hG/Rsc3...



Later on, the book says that solving the equations for the increase in area of the black hole horizon, you can see that the area is always increasing by one square Planck length for each piece of information which falls in, regardless of the black hole's size. But don't the equations all involve R(s), meaning that the increase in area is not always the same for all black holes? For example, the increase in radius involves the initial radius itself.
 
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1. What is a black hole?

A black hole is a region in space with such a strong gravitational pull that nothing, including light, can escape from it. It is formed when a massive star collapses in on itself, creating a singularity at its center.

2. How are black holes related to entropy?

Black holes are related to entropy through the second law of thermodynamics, which states that the total entropy of a closed system will always increase over time. As matter falls into a black hole, its entropy increases, causing the overall entropy of the universe to also increase.

3. Can anything escape from a black hole?

Once something crosses the event horizon of a black hole, it is impossible for it to escape. This includes light, which is why black holes appear black. However, some particles can escape through processes like Hawking radiation.

4. Do black holes violate the laws of physics?

No, black holes do not violate the laws of physics. They are a natural consequence of the theory of general relativity and are consistent with other laws of physics, such as the conservation of energy and momentum.

5. Are there different types of black holes?

Yes, there are different types of black holes based on their mass and properties. The most common types are stellar black holes, which are formed from the collapse of a single massive star, and supermassive black holes, which are found at the center of most galaxies and can be billions of times more massive than our sun.

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