For Hazel the idea of drowning resonates both on a literal and a metaphorical level, and it ties directly into novel’s most prominent symbol, water. On the literal side, the metastatic tumors in her lungs cause them to fill with fluid, which is the reason she's rushed to the intensive care unit midway through the novel. But drowning appears in other ways as well. When Hazel wakes one night with incredible pain in her head and has to go to the ICU, she describes it like being on the shore with waves crashing overhead, but being unable to drown. Drowning also appears in the T.S. Eliot poem “The Love Song of J. Alfred Prufrock” that Hazel recites parts of for Augustus. As they have their dinner and champagne in Amsterdam, she says the concluding lines of the poem: “We have lingered in the chambers of the sea / By sea-girls wreathed with seaweed red and brown / Till human voices wake us, and we drown.” She doesn't point it out at the time, but it's possible that the poem reminds her of her own situation. In these instances, drowning is a clear reference to the death Hazel fears, a threat she contends with constantly because of the tumors in her lungs. Finally, once Augustus dies, she uses the same analogy to describe how she feels having lost him. She compares it to being smashed by waves and unable to drown, meaning there’s no relief to her pain.
The characters in the novel, notably Augustus and Hazel, frequently use metaphors as a shorthand they can use to talk about emotionally overwhelming subjects. Augustus, for instance, describes shooting “existentially fraught” free throws on the day before the amputation of his leg. The free throws in this instance become a metaphor for Augustus's sense of purpose, since prior to his amputation he was an all-star basketball player, and losing his leg meant an end to sports. He suddenly began to question why this activity was so important, but the implication is that he suddenly began wondering what his purpose might be more broadly. He also fashions a symbol that is uniquely his own: He often keeps an unlit cigarette in his mouth in order to symbolize his control over a thing that can kill him, namely cancer. This is the exact form of control neither Augustus, nor Hazel, nor Isaac has when it comes to their cancers, and it's fitting that Augustus relies on the significance of the cigarette symbol to give him strength in times of fear and uncertainty. Hazel has her own frequently used metaphor. She likens herself to a grenade when she imagines the pain she will cause to her loved ones when she dies. In each instance the metaphor allows the character to deal with the subject at hand, Hazel's impending death for example, without having to call it by name.
Existentialism isn't so much a set of clearly defined principles as a convenient term for referring to a set of thinkers and artists, many with widely varying beliefs, who all examined how one can find meaning when life and death are potentially meaningless. This conundrum is precisely the one the novel's characters face. Frequently they question whether their lives have meaning if they die young of cancer, before having accomplished anything significant, and how they can then find meaning in their lives. In one notable episode, after Augustus dies Hazel thinks of her first encounter with him, when she said the problem of life isn’t that it leads to oblivion, but that there’s no evident meaning in that oblivion. Appropriately, then, there are recurring references to existentialist thoughts and thinkers throughout the novel, like the names of the rooms in the hotel in Amsterdam, which are all existential philosophers. The made-up novel An Imperial Affliction also ties into the motif as it raises questions about authenticity and value that were also concerns of existentialism. (See the entry in “Symbols” on An Imperial Affliction for a more detailed explanation.)
More significantly, existentialism comes up in the thoughts and fears of Hazel and particularly Augustus as they try to evaluate what meaning their lives have. Early on, for instance, Augustus refers to shooting “existentially fraught” free throws just before he had his leg amputated, and from what he tells Hazel it's clear that he was questioning his sense of purpose and meaning. Augustus eventually reveals that he wants to perform some heroic sacrifice, like diving on a grenade to save a group of kids as he does in the video game he plays with Isaac, in order to give his life and death meaning. When his cancer returns, he struggles with the realization that he'll never perform that kind of act, and Hazel's response is to marvel at Augustus's “existential curiosity.” Augustus is thus forced to wonder whether his life and death will be meaningful at all. Hazel takes offense to this questioning, arguing that an ordinary life without a heroic death, as hers will be, isn't necessarily without meaning, and Augustus comes to recognize that meaning is something he has to determine for himself. It’s a line of thought very much in keeping with existentialism.