Just for fun, but with a plot... the Doctor going places without a companion. (I always like exploring how he acts right after he's lost a companion, especially 10 and 12).
"I don't believe a word."
The Doctor, of course, believed everything. But he couldn't let her knew that.
The woman looked formidible, or would have to anyone who wasn't 10,000+ years old. Entire galaxies spun like ethereal glitter in her eyelashes. Stars burned and twinkled as a thousand million pin pricks on her literally black skin. She had no hair, and the stuff her fingernails were made out of looked like gold.
"Well, let's suppose I was meeting a black hole. Why would it come to me?" He had always thought he'd known about black holes, and he hated not being right. Besides, she looked nothing like his idea of a black hole.
The woman folded her arms. "First you have to understand that 'black hole' is just your word for 'another universe'. I keep balance in the Sejoris-"
"The Sejoris? Hah! Never heard of it!" The Doctor made a I-gotcha face and pointed at her. "And this idea of universes on your... on your skin? So what happens if you get a facelift, or need to scratch your-"
She frowned. "That's just it." As she raised one hand to her face, little glittery black specks flurried off her cheek and away into the atmosphere like dandruff.
The Doctor put his serious face on. "Oh. I see."
"I tried to contact other timelords, but it was impossible. They're all on another frequency entirely," she said.
"Yeah, I know." The Doctor put on his sonic glasses and grabbed her hands and squeezed them. "I'm scanning for alien life forms. Alien tech. I knew a guy once-"
A shrill beep cut him off. "Oh. Oh."
He leaned in, close enough to smell her neck, glasses still on. "There's something in your chest area. Lungs, heart, I don't know." He squinted one and a half eyes shut, dusting off his hands on his pants as he squinted. "It's hiding itself from me. Could be dark matter, but seeing as I have no rear end of a clue what dark matter is..."
The Doctor leaned back, folded his glasses and put them back into his pocket, eyebrows slightly raised. "I'm not actually a Doctor of anything, you know. So you can stop looking at me like that, like I can fix everything, because I can't."
"I didn't say you could," Sejoris replied coldly. "I thought you might be able to diagnose it." With that, she crossed her arms into some unrecognizable symbol and vanished.