It’s the day after tomorrow, and New York City has been cut off from the rest of the world by a biological-weapon attack followed by the invasion of the white-helmeted Eggheads, an army of Islamist lunatics who may or may not be in league with the Chinese, shadowy corporate interests, or Mrs. Winship’s Farm, a rural utopian community of white supremacists. Surviving women are given Auschwitz-style tattoos on the back of the neck and required to cover their heads with identifying blue bonnets when in public or be hanged in Union Square; surviving men—and there are not many—are castrated and worse. Nobody really quite knows what is going on in the rest of the world, but there are rumors of safe havens in Pennsylvania and Ohio.

Such is the world of Through the Yellow Hour, the writer and director Adam Rapp’s claustrophobic new play at the Rattlestick Playwrights Theater downtown. I am an admirer of thes ...