Does a relativistic rotating mass bend light through its gravitational field?

[Phymath]

What if someone set up an experiment, where they sped up a mass of high density in a circle ethier by making its radius smaller and smaller, until the large mass is moving near the speed of light, then at an extremely small highet above this rotating mass you set off a high frequency laser light, theorticly shouldn't the mass of the moving object increase, because of SR, thus having a larger gravitational field, and then the grav field should bend the laser light. It is most likely such a small divergence that it is unmeasureable but wouldn't we expect to see this? According to the force eqaution..

$$E = mc^2 = hf \ F = \frac{G m_1 m_2}{r^2}$$
$$m = hf/c^2$$ the grav force is acting on the "mass" of the light
$$F = \frac{G m_1 hf}{r^2c^2} \ m' = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}$$
$$F(m_o,v,f,r) = \frac{Gh}{c^2} \frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}} \frac{f}{r^2}$$

which can of course broken into a relation of v to the rotational frequencey of the mass. Also as is my understanding that a grav field effects clocks, so that in this synethic grav field that anything moving through it would have its relative time slow down. ie see everyone else moving slower then they are.

 

[Phymath]

am I to assume that all of this seems sound? and that this Force should be expected

 

[Chronos]

You cannot plug in a mass value for photons this way without breaking Lorentz invariance. Experimental tests have constrained Lorentz invariance violations to no more than one part in 10E20.

 

[Phymath]

what is Lorentz invariance?

 

[Phymath]

i believe u find the Schwarzschild Radius by stating that the "mass" of a photon is hf/c^2 so that a grav field acts on anything with energy.

$$U = \frac{G m_1 m_2}{r} \ m_2 = \frac{hf}{c^2}$$
$$\frac{1}{2} m v^2 = \frac{G m hf}{rc^2}$$
$$\frac{hf}{c^2} v^2 = \frac{2 G m hf}{rc^2} \ v = c$$
$$c^2 = \frac{2 G m}{r} \ r = \frac{2Gm}{c^2}$$ <- Schwarzschild Radius