You are using an incorrect expression for acceleration which is valid for classical cases only. That is, $\ a = \frac{\ v^2}{\ x}$ 

These pages from Hartle's book Gravity will help. See example 5.6, equation 5.52 and whats written after it. You'll get the answer. 

Just use $\ a = \frac{\ v^2 \gamma}{\ x}$ to get the correct answer.

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  [1]: https://i.sstatic.net/EuVJj.jpg
  [2]: https://i.sstatic.net/VuKbx.jpg