Black Hole

A black hole is an object so massive that even light cannot escape from it. This has been approached with the idea of an effective 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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Gravity and the Photon

The relativistic energy expression attributes a mass to any energetic particle, and if applied to 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.

*The idea of "gravitational potential energy" for a photon is currently being challenged with the point of view that the observed clock rate discrepancies are due to the local curvature of the space time. This gives the frequency differences without postulating gravitational properties for the photon.

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


*The idea of "gravitational potential energy" for a photon is currently being challenged with the point of view that the observed clock rate discrepancies are due to the local curvature of the space time. This gives the frequency differences without postulating gravitational properties for the photon.

Schwarzschild radius
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