Why would Hamlet fear suicide if he knew of life after death?

Question

Prince Hamlet describes his fear of death in poetic phrases.

To be or not to be, that is the question: ...
              To die, to sleep;
To sleep, perchance to dream—aye, there's the rub:
For in that sleep of death, what dreams may come,
When we have shuffled off this mortal coil,
Must give us pause.     (III.i.64, 72–76)

He even claims that nobody has knowledge of what may come after death.

But that the dread of something after death,
The undiscovered country, from whose bourn
No traveller returns, puzzles the will,
And makes us rather bear those ills we have, Than fly to others that we know not of.     (III.i.86–90)

^{Hamlet, Act 3, Scene 1}

The young prince has good reason to believe that the soul lives after death. He does know somewhat what dreams may comes for a traveler has returned from that undiscovered country, his father, King Hamlet.

The ghost says he will soon be tormented until the crimes of his life are purged away. The ghost is also forbidden from telling the conditions of his torment.

Ghost of King Hamlet: I am thy father's spirit,
Doom'd for a certain term to walk the night,
And for the day confined to fast in fires,
Till the foul crimes done in my days of nature
Are burnt and purged away. But that I am forbid
To tell the secrets of my prison-house,
I could a tale unfold whose lightest word
Would harrow up thy soul, freeze thy young blood (I.v.14–21)

^{Hamlet, Act 1, Scene 5}

If young Hamlet believes himself to be pure of heart and who has never committed a crime against anyone, then he should not fear the torments his father's spirit endures.

So why would Prince Hamlet fear death?

Answer 1

Because suicide is a mortal sin

According to the Church, suicide is a sin against God, because only God has the right to bring life and decide death. Suiciders didn't receive a Christian burial: they were not allowed to be buried in hallowed ground and there was no mass sung for anyone who committed suicide. They have been excommunicated from the Church and condemned to Hell and since they've "stolen their life" from the Lord, their goods were often confiscated. ^source

So while Hamlet knows that there is life after death (as any Christian at this time would), he is afraid that his fate would be much worse than his father's one.

Please note, that Hamlet does believe in what the Church says regarding salvation and damnation: in the act 3 scene 3, the prince has a chance to kill Claudius, but Hamlet holds his hand: Claudius is praying, so if he was killed at this moment, he would go straight to heaven (even while being a murderer), while his father has to suffer for his sins, because he had no chance to redeem them.

Answer 2

The great doubter Hamlet is never certain regarding the identity of the Ghost. At least two possible choices are available to him, the Devil or the ghost of his father. By orchestrating The Mousetrap, Hamlet settles on at least determining whether the Devil/ghost is telling the truth about Claudius’s guilt. Therefore, the Prince does not have direct proof of a person’s return from “the undiscovered country.” This, in addition to God’s “canon 'gainst self-slaughter” (1.2.135), would make suicide a very dangerous option indeed for Hamlet.