Gravitational potential gradient in accelerated reference frames?

[bkercso]

TL;DR Summary

Is there any speed-of-time gradient there?

Hi,

Could you please help me to clarify the following problem? In the gravitational field of a mass, the force on a body in steady state comes from the gradient of the gravitational potential - or the gradient of speed of time. But what about accelerated reference frames? I assume that there is no speed-of-time gradient, right? However, we state that the two type of field are indistunguishable, ie. the same.

 

[Ibix]

I assume that there is no speed-of-time gradient, right?

You assume wrongly. Calling it a "speed of time" isn't the best way of doing it, but clocks along the length of an accelerating rocket do tick at different rates consistent with a "gravitational redshift".

However, we state that the two type of field are indistunguishable, ie. the same.

That's not quite accurate. The equivalence principle says that being at rest in a gravitational field and accelerating in flat spacetime are locally indistinguishable. But that doesn't affect my answer above.