In this case you should avoid Backbiting or ghaybah الغيبة.
... And do not spy or backbite each other. Would one of you like to eat the flesh of his brother when dead? You would detest it. And fear Allah ; indeed, Allah is Accepting of repentance and Merciful. (49:12)
A short definition could be found in this well known hadith.
According Imam an-Nawawi backbiting is defined as follows (My own translation take it with care, who may find mistakes is free to correct them)
فأما الغيبة: فهي ذكرك الإنسان بما فيه مما يكره، سواء كان في بدنه، أو دينه أو دنياه، أو نفسه، أو خَلْقه، أو خُلُقه، أو ماله، أو ولده، أو والده، أو زوجه، أو خادمه، أو مملوكه، أو عمامته، أو ثوبه، أو مشيته، وحركته وبشاشته وخلاعته، وعبوسه، وطلاقته، أو غير ذلك مما يتعلق به، سواء ذكرته بلفظك أو كتابك، أو رمزت، أو أشرت إليه بعينك، أو يدك، أو رأسك، أو نحو ذلك
Backbiting (in the context of Islam) means: That you say something about your brother that he dislikes, no matter if it was something about or on his body, or religion, his life (donya), his desires (nafs), his creation (appearance), his character, his wealth or money, his children, his parents, his spouse(s), his servants, his slaves or fraught, his turban, his tissue, his walk, his movements, his smile or frown, his ease or hardship... no matter if you say it or write or indicate it, with your eyes, hand or head or any similar way
So falling into ghaybah is very easy, as the grey zone between halal and haram here is very tiny and it's very hard to avoid it.
An-Nawawi added that ghaybah is allowed for shar'i goals if it wouldn't be possible to do something only using backbiting and quoted six reasons (all of them can be evidenced with ahadith) among them is:
تحذير المسلمين من الشر ونصيحتهم
warning Muslims from an evil and advising them.
he also divided this case in examples:
- consultation if one wants to get married or deal with somebody etc. the consulted person should say the truth.
- to help and advise a scholar in case he didn't know he was dealing with an evil person.
- if somebody holds a position he is not accomplishing his duties the right way one should inform about him.
beside this the other 5 reasons are (see also this fatwa in Arabic):
- to beef (if somebody mistreated you),
- to seek help to guide somebody to avoid evil deeds,
- when asking for fatwa (similar case to beef),
- if somebody is doing bad deeds and evil things without any care an doesn't hide it, and gets some help or pay from the government due to legal reasons one should inform the authorities
- to introduce somebody: For example if somebody was well known by a special property: like al-'Amash (the blear eyed) الأعمش, al-'Araj (the cripple) الأعرج, al-Assam (the deaf) الأصم ... note this are all surnames of known scholars you may find in narrator chains of almost all sunni hadith collections!
On the other hand in at-Tabarni's al Kabir we may find this hadith (which has a sound narrator chain):
كان رسول الله صلى الله عليه وسلم يقول: اللهم إني أعوذ بك من يوم السوء، ومن ليلة السوء، ومن ساعة السوء، ومن صاحب السوء، ومن جار السوء في دار المقام
The Messenger of Allah, peace and blessings be upon him, would say, “O Allah, I seek refuge in you from an evil day, from an evil night, from an evil hour, from an evil companion, and from an evil neighbor in the final abode.”
Bad friends or evil companions are something one should avoid, so helping people to avoid them should be considered as a good deed.
If possible you must avoid naming this person while warning as you may find in ahadith words like:
What has happened to these people that they say so and so ... (Sahih Muslim)
or
What is the case of people who make conditions that are not in Allah's Book? ... (Jami' at-Tirmdihi)
Where our Messenger avoided calling them by name.
Beside all of this don't ever add something that might not be true if you talk about anybody! Only say what you are 200% or at least 100% sure of!
Read also this fatwa about the definition and ruling about backbiting.
This fatwa in Arabic says there's no backbiting if you don't point (by any means at the person you are talking about)-> avoid calling them by name.
This was my major source in Arabic.
There's something i forgot in my original answer, but as it is important due to the word you used in your post, so I'm adding it now.
Note that accusing somebody to be an adulterer is a very grave accusation, as in Islam if you don't have at least four witnesses (four men or for each missing man two women, the accuser himself doesn't count) for that, you should be hardly punished according the shari'a. See (24:4-5 and 24:23) for the accusation of chaste women, which applies also for men. The Quran mentioned women in first place as falsely accusing them is more grave!
Note that those witnesses must have witnessed the act themselves (either seeing it, or maybe hearing it -with no doubt-), which usually would be hard! Of course if the person himself admits it freely then the witnesses won't be necessary
Please be aware of this and read this hadith!
