Does mass increase with gravitational acceleration like it does with driven acceleration?

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If an object increases mass with acceleration due to the energy driving force converting to mass then is it true also when there is no driving force but gravitational tug acting to accelerate the object?
 
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No, an object increase mass due to the link of space and time according to theory of relativity. This increase is a relative effect.
 
tanzanos said:
If an object increases mass with acceleration due to the energy driving force converting to mass then is it true also when there is no driving force but gravitational tug acting to accelerate the object?
Could you be thinking about the Pound and Rebka Mossbauer Effect experiment at Harvard in which photons from an iron-57 source falling from the roof to the basement of the phyics building gained a measurable amount of energy? In this case there was no mass gained, but the photon energy gain was due to gravity.
 
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Bob S said:
Could you be thinking about the Pound and Rebka Mossbauer Effect experiment at Harvard in which photons from an iron-57 source falling from the roof to the basement of the phyics building gained a measurable amount of energy? In this case there was no mass gained, but the photon energy gain was due to gravity.
So gravitational tug causes an object to gain energy but that energy does not convert to mass? What happens to this energy?
 
tanzanos said:
So gravitational tug causes an object to gain energy but that energy does not convert to mass? What happens to this energy?
For photons, E2=(pc)2 + (m0c2)2, so for photons with zero rest mass, the energy increase is equal to the momentum increase; E = pc.