Are private conversion without involving a Rabbi possible? Like converting a Christian without making it public, not even to rabbis thus doing the conversion rituals on our own?
Yes and no. The only way to convert to Judaism is to follow the procedures provided by Jewish law, which require a beis din of three Jews. However, in practice, the three Jews are rabbis, since there are a limited number of widely-recognized batei din, all of which are composed solely of rabbis, and few Orthodox rabbis will recommend or arrange a conversion that is not going to be widely accepted.
Note that it would be possible to "convert" them to Noahidism (since no procedure is required to become a Noahide.) Noahides believe in Judaism but only follow those commandments required of non-Jews.
Adel, this is a question near and dear to my heart as I am a convert. See my bio and the links thereto by clicking on my signature line below.
The fundamental requirements for Orthodox Jewish conversion are (according to my own experiences and in accordance with the text of Rabbi Maurice Lamm's book, Becoming a Jew, (Jonathan David Publ. 1991), p 119): • The conversion candidate, after a peeriod of study with an Orthadox rabbi, goes before a beis din -- an ad hoc "court" made up of three observant adult males who qualify as judges; Usually the beis din is made up of rabbis. The beis din will question the would-be convert on motives, knowledge, secular/family impact, and other topics. In my experience, the rabbis will show a high level of deference to their colleague's assertions that the candidate is ready and worthy of conversion. In my experience, a rabbi will not take someone to the beis din until they demonstrate working knowledge of Hebrew, the kosher dietary laws, and Sabbath observance and sufficient understanding to know when they need to ask questions of a rabbi when they don't know what to do. • Male candidates approved by the beis din then undergo circumcision or, if already circumsized, hatafat dam b'ris, which is the drawing of a symbolic drop of blood from there. • Everyone accepted for conversion must be immersed in a mikvah (ritual bath). The rabbis personally supervise the immersion of the male converts and, in the case of female converts, they stand outside the door and rely on a female attendant's testimony that the convert immersed herself in accordance with the law.
When the temple is rebuilt, the convert will be liable for a korban (offering) before being able to take part in any other Temple-related ceremonies. Talmud Kerisos 8b.
The big issue that divides Orthodox, Conservative and Reform Jews, and even among Orthodox rabbis, are (a) the requirements related to the convert's personal commitments to observe Jewish law and (b) the make-up of the beis din. Whereas once upon a time, when Jewish communities were more compact and stable, it was practicable to have members of the beis din include non-rabbis who were widely known to be knowledgeable of Jewish law and particularly observant and G-d fearing. Another factor that made that possible and practical was the fact that the convert would stay in the community where he or she converted, and there was no particular benefit in converting, so it was assumed that anyone who wanted to convert was sincere.
Times change. Conversion to Judaism now has advantages with the reestablishment of the state of Israel -- e.g. any Jew (including converts accepted as Jewish by the government) have financial incentives to immigrate, and non-Jews living in Israel can become citizens if they convert. Accordingly, the Israeli rabbinate -- even back when I converted 34 years ago -- have not been happy with the non-permanent, local beis dins accepted for conversions in the US and some other countries. The Israeli rabbinate felt that it was impossible for them to know every rabbi overseas, much less observant lay persons, and therefore they could not rely on the signatures that might appear on a certificate of conversion.
To make American conversions more acceptable within Israel, the Rabbinical Council of America has set up standardized policies and procedures for conversions, and a system of regional courts to substitute for the ad hoc local beis dins. See the RCA article on the topic here.
So, to summarize, my answer to your question is that while there is, in theory, a method available for converting without rabbis, it is not practical.
Technically, yes, but this is highly discouraged.
The conversion process requires 3 things, all of which need to be done in the presence of 3 observant Jews (beit din):
As the 3 Jews on the beit din don't need to be formally ordained, it is possible to convert without involving a rabbi. However, in practice, the conversion would likely not be accepted by the general Jewish public nor by any Rabbinate or synagogue.
I don't understand the reason for not "making it public." One of the primary purposes of conversion is to join the Jewish People. Becoming part of this community and tradition necessitates making your entrance (ie. conversion) public.
An analogous case would be a private wedding. Technically, in order to get married, all I need are two observant Jews to witness it (and a ring, and ketubah, and an empty room for 10 minutes), and we'll be halachically married. But just because it can be done doesn't mean it's a good idea.