LONDON — It was a case of the famous interviewing the famous. The BBC aired an interview on Wednesday that was unusual in at least a couple of respects: The man answering the questions was former President Barack Obama, and the man asking them was his friend Prince Harry.

The prince took the seat as a guest editor for BBC Radio 4’s flagship program, “Today,” and broadcast a long-awaited interview in which he questioned the former president about the day he left the White House, his work since leaving office and his plans for the future.

Neither party mentioned President Trump by name, but Mr. Obama’s successor was never far from the conversation. The two men discussed the risks of using social media and the corrosion of civil discourse.

The interview was recorded in Toronto in September, when Prince Harry and Mr. Obama met during the Invictus Games, a sporting competition for injured military members and veterans.

The highlights of the interview:

Since leaving office in January, Mr. Obama has more time on his hands. He gets to wake up later, spend more time with his family and take control of his day, something he says he couldn’t do as president. But the things that are important to him have not changed.

Now that he no longer has the authority that came with being president, Mr. Obama said he relies on persuasion rather than legislation.

“A lot of the things that still motivate me and move me continue to this day,” he added.

While neither man mentioned Mr. Trump directly, they discussed the role of social media in leadership,…