According to an article by Professor Tzvi Zohar of Bar Ilan University, which has aroused fervent debate in religious Zionist circles, the answer is yes, but only if the relationship is based on mutual respect and the woman immerses herself in a mikve [ritual bath].
Zohar's article, which appears in the latest edition of Akdamot, an academic journal on Jewish thought published by Beit Morasha, analyzes the opinions of leading halachic authorities from the Middle Ages, such as Nachmanides, to the modern era, such as Rabbi Ya'acov Emden, and shows that many permitted sexual relations without marriage.
In the arrangement, sanctioned by Jewish law according to these opinions, the woman becomes a pilegesh, or concubine. Neither the man nor the woman has any obligations or rights. Both must adhere to family purity laws in accordance with halacha.
According to halacha, a man is not allowed to come into physical contact with a woman after she has menstruated until she has immersed herself in a mikve. This prohibition is called nida.
Young religious men and women who are committed to the halacha need no longer struggle with their libido, argues Zohar. All those hormones can be channeled into a kosher communion that is free of marital obligations.
The article sparked major interest.
"Never since we first established Akdamot ten years ago has there been so much interest in an article," said Avi Berholz, Akdamot's chief editor. "The rabbis are angry at us for publishing an article which they feel undermines the Jewish family," said Berholz. "But more liberal elements within religious Zionism thank us for presenting this opinion."
Rabbi Ohad Tohar-Lev, who heads the Israeli program at Lindenbaum (Bruria), a yeshiva for young women aged 18 to 22, said that he fears the article will encourage more young religious people to have sexual intercourse before marriage.
"It legitimizes licentiousness," said Tohar-Lev, who, as a head of an institution that prepares religious women for army service, is considered liberal.
"There are certain laws that are best kept secret. Zohar's article will give some young people the justification they were looking for. Nobody wants to be a sinner."
Y., 21, a student at Lindenbaum, said that she has single religious friends who already know about Zohar's solution and have used it.
"The woman simply goes to a mikve before having sex and that's it."
But Y. said that many of her friends, while committed to orthodoxy, do not adhere to the rules of nida.
"I do not know whether they have intercourse. But I see them touching one another."