The White Oak (Imperfect Darkness #1) by Kim White

In The White Oak, the first book in the Imperfect Darkness series, Cora Alexander falls through a sinkhole and enters the underworld still alive. Her living presence threatens the tyrannical rule of Minos and the infernal judges who have hijacked the afterlife and rebuilt it, trapping human souls in a mechanical, computer-controlled city that lies at the core of the earth. To survive, Cora must rely on her untrustworthy guide, Minotaur, an artificial intelligence built by Minos. She is helped by a mysterious voice, and by Sybil, underworld librarian and author of each person's book of life. Sybil's collection holds the key to humankind's intertwined life stories. When Cora's own book is destroyed, Sybil gives her a magical golden pen and sends her to the underworld city to write her own destiny. Along the way, Cora finds the ghost of her dead brother, Lucas, a genius programmer who alone is capable of finding the chink in Minos's armor. But will he be able to get Cora out alive, or will they both succumb to the seemingly inescapable underworld trap?