Mamzer from a rape

Question

During the pogroms a married Jewish woman is raped by a Cossack. Is the child born of this rape a Mamzer?

Does the intercourse of a married Jewish woman with a non-Jew have to be consensual for the child to be a Mamzer?

Answer 1

Let's start with the definition of a mamzer, e.g., from chabad.org

the Hebrew term mamzer [...] refers only to the offspring of people whose relationship would be punishable with karet (excision). This includes many close-blood relatives or a woman who was concurrently married to someone other than the child’s father.

The Rambam lists these punishable relations in chapter 1 of Hilchot Issurei Biah. They don't include relations with non-Jews.

As such the offspring of the rape of a Jewish woman by a non-Jew is not a mamzer.

Even if the man was a Jew, the offspring would only be a mamzer if the man and woman were prohibited to marry each other (see Hilchot Issurei Biah 15:1)

Answer 2

H. Issurei Biah 15:1

איזה הוא "ממזר" (דברים כג,ג) האמור בתורה: זה הבא מערווה מן העריות--חוץ מן הנידה, שהבן ממנה פגום ואינו ממזר; אבל הבא על שאר העריות--בין באונס בין ברצון, בין בזדון בין בשגגה--הוולד ממזר. ואחד זכרים ואחד נקבות, אסורין לעולם--שנאמר "גם דור עשירי, לא יבוא" (שם), כלומר לעולם

What is meant by a "mamzer"? The term refers to a person conceived from a forbidden sexual relationship. A niddah is an exception. A son conceived from such relationships is blemished, but is not a mamzer. When, however, a person enters into any other forbidden sexual relationships, whether through rape, or willingly, whether deliberately or inadvertently, the offspring produced is a mamzer. Both males and females are forbidden forever, as it states: "even the tenth generation" (Deuteronomy 23:3) i.e., the prohibition is everlasting.

However H. Issurei Biah 15:3-4 elaborates that:

גוי ועבד הבא על בת ישראל, הוולד כשר--בין בפנויה בין באשת איש, בין באונס בין ברצון… זה הכלל: בן הבא מן העבד, או מן הגוי, או מן השפחה, או מן הגויה--הרי הוא כאימו, ואין משגיחין על האב

When a gentile or a servant enter into relations with a Jewish woman, the child is acceptable. This applies whether the woman is unmarried or married, whether she was raped or engaged in relations willingly... This is the general principle: When a child is born from a servant, a gentile, a maid-servant, or a female gentile, he is like his mother. We are not concerned with the father.

SA EH 4:19 similarly records the halakhah as follows:

עכו"ם ועבד שבאו על הממזרת הולד ממזר ואם באו על בת ישראל בין פנויה בין אשת איש הולד כשר ופגום לכהונה

If a gentile or a slave cohabit with a female mamzer, the offspring is a mamzer. If they cohabit with a Jewish woman, whether she is single or married, the offspring is permitted [to marry into the congregation], but is considered damaged with regard to marrying a Kohen.