Why is Prince Hamlet considered a Gothic tragic hero?
Hamlet technically wouldn't be called a gothic, as that genre officially began in 1764 with Horace Walpole's novel Castle of Otranto, so technically Hamlet is not a Gothic hero. However, Hamlet does include gothic elements, such as an eerie opening setting in the fogs of the castle at night, the supernatural in the form of the frightening ghost of Hamlet's father, and, in Prince Hamlet, elements of the uncanny and heightened emotionality.
As for Hamlet himself, he exhibits the heightened emotionality and tortured soul of a gothic hero. He is pushed to brink of suicide and madness by his encounter with the ghost and the revelation that his uncle murdered his father. His long soliloquies reveal the anguished and unstable state of his psyche. There's not all that much difference between him and, say, Roderick Usher in Poe's classic Gothic tale, "The Fall of the House of Usher."
The uncanny, which Freud defined as the unheimlich (unhomelike) in his essay "The Uncanny," permeates Hamlet's psyche and everywhere affects the atmosphere of Denmark. Something is "rotten" in the state of Denmark, starting with the eerie opening rumors of war preparations through to the corrupt state of the royal court, where Hamlet can trust nobody. He feels anything but "at home" in his childhood home, where almost everything, especially the people around him, now seem diseased to him. Unsurprisingly, Hamlet even shows up in a graveyard, examining the skull of Yorick.
Finally, doubling is an aspect of the Gothic hero, and Hamlet in some ways is the double of his father. They share the same name—Hamlet—and Claudius tries to treacherously murder both of them. Yorick, the court fool who used to ride Hamlet around on his back, also acts as a double of sorts for Hamlet: Hamlet realizes looking at his skull that death is the great leveler that will come for princes as well as fools. The corpse is a key figure representing the uncanny, because it is at once both human and eerily inhuman, a reminder of the mortality we try so hard to repress. Thus Hamlet's encounter with Yorick—and shortly after, the dead Ophelia—reinforces Hamlet's identification with the uncanny and foreshadows his own death.
There was a movement in British literature in the 19th century that was termed "Gothic." It contained supernatural elements, dark and foreboding settings and often included direct or symbolic representations of man's subconscious desires -- usually emphasizing the passionate, chaotic and irrational.
Technically, Hamlet cannot be considered "Gothic," since it was written nearly 200 years before this movement in literature and theatre, however, you could certainly draw similarities between Hamlet and the Gothic.
- Hamlet spends the majority of the play examining his own behaviour and, by extension the motives and behaviour of other characters and even mankind. This could be seen as the sort of internal investigation of the subconscious explored in Gothic works.
- The ghost lends the element of the supernatural and the opening of the play is in the classically Gothic "dark and stormy night" style.
- Hamlet's investigation of madness (though he is in fact pretending madness) fits the subject as well.
The amazing thing about Hamlet (and the strongest testament to the play and character's longevity) is that he is so fully developed as a man seeking truth and meaning in the world, that he could be described to fit any movement in literature you might care to suggest, including the Gothic.