Necessary conditions for having wormholes in f(R) gravity

Understand

For a generic $f(R)$ which admits a polynomial expansion of at least third order (i.e.

• $\frac{d^{3}f}{dR^{3}}\neq 0$) we find the near-throat wormhole solution.
• Necessary conditions for the existence of wormholes in such $f(R)$ theories are derived for both zero and non-zero matter sources.
• A particular choice of energy-momentum reveals that the wormhole geometry satisfies the weak energy condition (WEC).