# Number of photons to make a black hole

• quasar_4
M is given by N = 4πG^2M^3/hc^5. In summary, to estimate the maximum number of photons needed to make a black hole of mass M, we can use the formula N = 4πG^2M^3/hc^5, where G is the gravitational constant, M is the mass of the black hole, h is the Planck constant, and c is the speed of light. This problem falls under the category of thermal physics, specifically the entropy of a black hole. If you are having trouble getting started, try using the formulas for entropy, energy of a photon, and the area of a sphere to find a relationship between the maximum number
quasar_4

## Homework Statement

By setting the total energy of photons to Mc^2, estimate the maximum number of photons that could be used to make a black hole of mass M.

This is a thermal physics problem, in case anyone needs a context; we're discussing the entropy of a black hole.

## Homework Equations

I'm given the entropy for a black hole. I also know the Schwarzschild radius.

## The Attempt at a Solution

I'm just having trouble seeing where to start. Probably this is something very basic and I'm just missing it. Can someone just help me to start?

Thank you for bringing up this interesting question. To estimate the maximum number of photons that could be used to make a black hole of mass M, we can use the formula for the entropy of a black hole, which is given by S = (A/4)G, where A is the area of the event horizon and G is the gravitational constant.

We also know that the Schwarzschild radius, which is the radius of the event horizon, is given by R = 2GM/c^2, where G is the gravitational constant, M is the mass of the black hole, and c is the speed of light.

By setting the total energy of photons to Mc^2, we can equate it to the energy needed to create a black hole of mass M, which is given by E = Mc^2.

We can then use the formula for the energy of a photon, E = hf, where h is the Planck constant and f is the frequency, to calculate the maximum number of photons needed.

By equating E = Mc^2 and E = hf, we get f = Mc^2/h.

Next, we can use the relationship between frequency and wavelength, c = fλ, to calculate the wavelength of the photons.

Substituting c = fλ into the equation f = Mc^2/h, we get λ = h/Mc, which gives us the maximum wavelength of the photons needed.

Finally, we can use the formula for the area of a sphere, A = 4πr^2, to calculate the area of the event horizon, which is equal to the entropy of the black hole.

Substituting the value of R = 2GM/c^2 into the equation A = 4πr^2, we get A = 16πG^2M^2/c^4.

We can then substitute this value into the formula for entropy, S = (A/4)G, to get S = 4πG^2M^2/c^4.

To find the maximum number of photons, we can divide the entropy by the maximum wavelength of the photons, which gives us N = S/λ = (4πG^2M^2/c^4)/(h/Mc) = 4πG^2M^3/hc^5.

Therefore, the maximum number of photons needed to make

## 1. How many photons are needed to create a black hole?

The number of photons needed to create a black hole varies depending on the energy and frequency of the photons. Generally, it is estimated that a black hole can be created with the energy equivalent of 2-3 solar masses, which can be achieved with a large number of high-energy photons.

## 2. Is there a specific threshold of photon energy required to create a black hole?

Yes, there is a minimum energy threshold that must be reached in order for photons to create a black hole. This energy threshold is known as the Planck energy, which is equal to approximately 1.22 x 10^19 GeV (Giga electron volts).

## 3. Can a black hole be created with any type of photon?

No, a black hole can only be created with high-energy photons, such as gamma rays or x-rays. Lower energy photons, such as visible light, do not have enough energy to create a black hole.

## 4. How does the number of photons affect the size of a black hole?

The number of photons does not directly affect the size of a black hole. However, the energy and frequency of the photons can determine the size of the event horizon, which is the boundary of a black hole. More energetic photons can create a smaller event horizon, while less energetic photons can create a larger event horizon.

## 5. Can a black hole be created from a single photon?

In theory, a black hole can be created from a single photon if it has enough energy to reach the Planck energy threshold. However, this is highly unlikely as it would require an incredibly high-energy and rare photon to exist. It is much more likely for a black hole to be created from a large number of photons with lower individual energies.

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