Speed of light in a gravitational field

[gc]

I'm just curious, is there a way to calculate the speed of light in a gravitational field? From my understanding, light travels slower in a gravitational field and the speed is zero in a black hole. Is there an equation to determine the speed of light on earth (not including slowing down due to air) compared to the speed of light in a vacuum? The closest I could find was this which says that c'=co(1 + V/c^2)

where V is the potential energy - GMm/r

At the schwarzschild radius, r=2GM/c^2, the speed of light would be 0.5c. However, we know that the speed of light in a black hole is zero. Am I missing something here?

[Spyman]

The reason for the qualification 'properly defined' above is that the speed of light depends upon the vantage point (frame of reference) of the observer. When we say that the speed of light is decreased, we mean from the perspective of an observer fixed relative to the black hole and at an essentially infinite distance. On the contrary, to an observer free falling into the black hole, the speed of light, measured locally, would be unaltered from the standard value of c.

From your link: -> http://www.physlink.com/Education/AskExperts/ae13.cfm?CFID=22213950&CFTOKEN=50980107

 

What do you mean with: "the speed of light in a black hole is zero" ?

 

I am not an expert on GR but I think your "missing thing" is: "relative the vantage point of the observer".

 

And lightspeed in vacuum = (not including slowing down due to air), you probably meant flat space.

 

 

EDIT(1):

 

The formula c'=c_o(1 + V/c²) is NOT CORRECT:

The idea of bending light was revived in Einstein's 1911 paper "On the Influence of Gravitation on the Propagation of Light". Oddly enough, the quantitative prediction given in this paper for the amount of deflection of light passing near a large mass was identical to the old Newtonian prediction, δ = 2m/r₀. There were several attempts to measure the deflection of starlight passing close by the Sun during solar eclipses to test Einstein's prediction in the years between 1911 and 1915, but all these attempts were thwarted by cloudy skies, logistical problems, the First World War, etc. Einstein became very exasperated over the repeated failures of the experimentalists to gather any useful data, because he was eager to see his prediction corroborated, which he was certain it would be. Ironically, if any of those early experimental efforts had succeeded in collecting useful data, they would have proven Einstein wrong! It wasn't until late in 1915, as he completed the general theory, that Einstein realized his earlier prediction was incorrect, and the angular deflection should actually be twice the size he predicted in 1911.

http://www.mathpages.com/rr/s6-03/6-03.htm

 

 

EDIT(2):

 

Gravitational time dilation formula: (outside a non-rotating sphere)

[math]

t_0=t_f \sqrt{\ 1- \frac{2GM}{rc^2}}

[/math]

 

t₀ is the proper time between events A and B for a slow-ticking observer within the gravitational field,

t_f is the proper time between events A and B for a fast-ticking observer distant from the massive object,

G is the gravitational constant,

M is the mass of the object creating the gravitational field,

r is the radial coordinate of the observer,

c is the speed of light

http://en.wikipedia.org/wiki/Gravitational_time_dilation