How to perform authentication without central server in P2P? How can one be sure that the man who you're talking with is the one who you think he is? i.e. How can one perform authentication in P2P network without a central trust server or Certificate Authority?

I'm just wondering how someone can make distributed (peer-to-peer) overlay network or chat using DHT for finding peers (like BitTorrent Chat has done).

BitTorrent chat uses DHT to find some information about peers and then to connect to them directly. I think it uses assymetric cryptography, as well. But this doesn't solve the problem of somebody trying to perform a MiTM attack by putting a lot of incorrect data about peers into the DHT (i.e. incorrect peer IP addresses or public keys).
For P2P authentication, you can go for web of trust concept. Simply this means, if someone is trusted by people you can trust, you can also trust that unknown person. In OpenPGP, a certificate can be signed by other users who trust the association of that public key with the person or entity listed in the certificate. So trust relationships can be propagated.
In addition This presentation discusses about P2P authentication, including authentication methods without central server. It proposes web of trust and few other concepts. Also I found a survey about this topic. You can choose a method according to your requirements. Hope this helps.