general relativity - Is there a maximum possible acceleration?

I'm thinking equivalence principle, possibilities of unbounded space-time curvature, quantum gravity.

Answer

The spit horizon in a Rindler wedge occurs at a distance $d~=~c^2/g$ for the acceleration $g$. In spatial coordinates this particle horizon occurs at the distance $d$ behind the accelerated frame. Clearly if $d~=~0$ the acceleration is infinite, or better put indefinite or divergent. However, we can think of this as approximating the near horizon frame of an accelerated observer above a black hole. The closest one can get without hitting the horizon is within a Planck unit of length. So the acceleration required for $d~=~\ell_p$ $=~\sqrt{G\hbar/c^2}$ is $g~=~c^2/\ell_p$ which gives $g~=~5.6\times 10^{53}cm/s^2$. That is absolutely enormous. The general rule is that Unruh radiation has about $1K$ for each $10^{21}cm/s^2$ of acceleration. So this accelerated frame would detect an Unruh radiation at $\sim~10^{31}K$. This is about an order of magnitude larger than the Hagedorn temperature. We should then use the string length instead of the Planck length $4\pi\sqrt{\alpha’}$ and the maximum acceleration will correspond to the Hagedorn temperature.