Black Hole

A black hole is an object so massive that even light cannot escape from it. This requires the idea of a gravitational mass for a photon, which then allows the calculation of an escape energy for an object of that mass. When the escape energy is equal to the photon energy, the implication is that the object is a "black hole".
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General relativity ideas

Black hole concepts

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Gravity and the Photon

The relativistic energy expression attributes a mass to any energetic particle, and for the photon

The gravitational potential energy is then

When the photon escapes the gravity field, it will have a different frequency

Since it is reduced in frequency, this is called the gravitational red shift or the Einstein red shift.
 Escape energy for a photon
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Escape Energy for Photon

If the gravitational potential energy of the photon is exactly equal to the photon energy then

Note that this condition is independent of the frequency, and for a given mass M establishes a critical radius. Actually, Schwarzchilds's calculated gravitational radius differs from this result by a factor of 2 and is coincidently equal to the non-relativistic escape velocity expression