Gautama Maharishi is a sage mentioned in Hindu mythology and is not specifically related to the Ramayana. However, there are some stories and references to Gautama Maharishi in the Ramayana.
One of the most well-known stories involving Gautama Maharishi is the story of Ahalya, his wife. Ahalya was cursed by Gautama Maharishi to turn into a stone due to her infidelity with Indra, the king of gods. Later, when Lord Rama and his wife Sita were on their way to the forest during their exile, they met Gautama Maharishi. Gautama Maharishi recognized Lord Rama as an incarnation of Lord Vishnu and requested him to restore his wife Ahalya to human form. Lord Rama granted his wish and touched the stone with his foot, which brought Ahalya back to life.
Another incident involving Gautama Maharishi takes place during Lord Rama’s coronation ceremony. When Lord Rama was being crowned as the king of Ayodhya, Gautama Maharishi was present there along with other sages and saints. Gautama Maharishi praised Lord Rama’s qualities and offered his blessings to him.
In summary, Gautama Maharishi is a sage mentioned in Hindu mythology, and while he is not specifically related to the Ramayana, there are a few stories and references to him in the epic.