Why are capacitors used when obtaining dual power supply from a single power supply and how to know the values?
At the end of the day, this circuit forms a low pass filter. The corner frequency is: \$f_o = \dfrac{1}{2\pi RC}\$. The capacitors are there to help stabilize the virtual ground. Practically \$1-10\mu F\$ with \$R=10k\Omega\$ is a good place to start. If your virtual ground is noisy relative to the system ground, look at the spectral content, and adjust R and C values to minimize it.