Here's a topic I thought a lot about many years ago because I was divorced and hoped to some day remarry. Jesus explicitly forbids remarrieage after divorce (Mark 10:11), so it's an issue for a lot of Christians like me. I've never written about it because I'm afraid my views might be a bit self-serving. Maybe I came to my conclusions in a biased way. I wanted to remarry at some point. But I'm going to go ahead and give my thoughts on it anyway because I was just in a conversation about it today, and it is fresh on my mind.
First, we have to think about what God considers a marriage or when God considers two people to be married. I don't think a legal contract is necessary for a marriage to be binding in God's eyes. I doubt many people in the ancient world had legal contracts they called marriages. Throughout most of history, marriage has just begun with some sort of ceremony followed by cohabiting. Sometimes there's not even a ceremony. A man just takes a woman into his home, and she becomes his wife.
So I don't know what the necessary and sufficient conditions are for God to consider a couple to be married. Living together alone doesn't seem sufficient, and getting a legal contract doesn't seem necessary. Maybe it's just a matter of whether the couple agrees that they are married. But if one thinks they are and the other doesn't, who knows? Or maybe they both do, but one changes their mind and says, "I don't think we were ever married." I don't know what to think in those situations.
In the Mosaic law, if somebody committed the crime of having sex with somebody who was not already married or betrothed to somebody else, the "punishment" was that they had to marry them (Exodus 22:16). I used to think this passage, as well as some others, indicated that sex was the thing that made two people married. It would explain why the Bible doesn't explicitly forbid extra-marital sex.
I changed my mind about that after reading an article by J. Budziszewski called "The Revenge of Conscience." In this article, Budziszewski pointed out a lot of the crazy things people do when they behave contrary to what they intuitively know is right. That article had a lot to do with why I now put so much confidence in my moral intuitions. Before that, I had come to the conclusion that there was no such thing as pre-marital sex because to have sex is to become married in God's eyes. I had reasoned this out through the scriptures, but it didn't sit well with my moral intuitions. It still seemed wrong to me for two peopel to have sex if they weren't already married. So after reading Budziszewski's article, I decided my moral intuitions were correct. The Bible doesn't have to explicitly forbid something before we can know that it's wrong. But besides that, the Bible at least implies that pre-marital sex is wrong when it says things like, "It is better to marry than to burn with passion" (1 Corinthians 7:9).
Nevertheless, I think that of all the sexual crimes we can commit, the least of them is extra-marital sex. But that's not really the subject of this post, so no need to talk about that anymore.
Anywho, maybe you have an obligation to marry the person you have sex with if you're not already married since that's what Exodus 22:16 requires. On the other hand, the fact that the Mosaic laws has this requirement doesn't automatically mean any Christian has the same requirement. The Mosaic law was given specifically to the nation of Israel. But it can still act as a guide for how God views marriage, so it may still have some relevance. I said more about this in "Christians and the Mosaic Law."
Let's look at all the things the New Testament says about divorce and remarriage.
Matthew 5:31-32 "Now it was said, ‘Whoever sends his wife away is to give her a certificate of divorce’; but I say to you that everyone who divorces his wife, except for the reason of sexual immorality, makes her commit adultery; and whoever marries a divorced woman commits adultery."
Matthew 19:9 "And I say to you, whoever divorces his wife, except for sexual immorality, and marries another woman commits adultery."
Mark 10:11-12 "And He said to them, 'Whoever divorces his wife and marries another woman commits adultery against her; and if she herself divorces her husband and marries another man, she is committing adultery.'"
Luke 16:18 "Everyone who divorces his wife and marries another commits adultery, and he who marries one who is divorced from a husband commits adultery."
1 Corinthians 7:10-11 " But to the married I give instructions, not I, but the Lord, that the wife is not to leave her husband (but if she does leave, she must remain unmarried, or else be reconciled to her husband), and that the husband is not to divorce his wife."
1 Corinthians 7:39 "A wife is bound as long as her husband lives; but if her husband dies, she is free to be married to whom she wishes, only in the Lord."
Romans 7:2-3 "For the married woman is bound by law to her husband as long as he is alive; but if her husband dies, she is released from the law concerning the husband. So then, if while her husband is alive she gives herself to another man, she will be called an adulteress; but if her husband dies, she is free from the law, so that she is not an adulteress if she gives herself to another man."
From all these passages, we can see that (1) it is wrong to get a divorce, but (2) if you do get a divorce, you should not remarry because then you'd be committing adultery, and (3) if your spouse dies, then you are free to remarry. Notice, though, that in all the prohibitions about divorce and remarriage, Matthew is the only one that adds the phrase, "except for reason of sexual immorality." Many people, myself, included, think this means that if your spouse commits adultery against you, then you are free to divorce and to remarry.
Now, suppose you got a divorce, and it was not because of adultery. You'd think that would mean you can never remarry. But I think there's a loop hole in which you can remarry. We Christians are typically averse to loop holes, but I can't see any flaw in it. Jesus said that anybody who divorces their wife, except for sexual immorality, and marries another woman, commits adultery (Matthew 19:9). This seems to suggest that if your marriage ended because of adultery that you're free to remarry. There are some Christians who disagree with that, but that is how I see it.
Well, you can only commit adultery against somebody if you are still married to them in some sense. So this must mean that even if you get a divorce, God still considers you to be bound to each other. Otherwise, it would be impossible to commit adultery against each other. The definition of adultery is having sex with somebody else's spouse or being married and having sex with somebody who is not your spouse.
So, here's the loop hole. If you have separated from your spouse and gotten a legal divorce, and neither of you have had a sexual relationship with anybody else, then you're still bound to each other. But as soon as either of you has sex with somebody else, adultery has occurred, and the other person is free to remarry. So the loop hole is that all you have to do is wait for your ex to either remarry or at least have sex with somebody else. Once they do, you are free to remarry because they will have committed adultery against you. If adultery frees you to remarry when it happens while you're still together, then it seems to me it would accomplish the same thing if you were not still together.
This makes good sense to me because imagine that your ex remarries. Obviously, you can't be bound to your ex if they marry somebody else. In fact, in the Mosaic law, if your ex remarries, then divorces, you cannot take your ex back because God considers that detestable (Deuteronomy 24:1-4). So if your ex is married to somebody else, then you can't possibly still be bound to your ex. If you're not bound to your ex, then you can't possibly commit adultery against them by remarrying. So I think if your ex remarries before you do, then you are free to remarry.
You're still guilty of something, though, if you were the one who initiated the divorce. According to Jesus, it would mean you caused her to commit adultery. By divorcing her without good cause (like unfaithfulness), you put her in a vulnerable position. Most of us don't want to be alone, so the temptation to remarry is very strong. But if she initiated the divorce, then you can't be blamed for her committing adultery.
Although my thoughts about divorce and remarriage might be influence by my own biases, I am nevertheless about 99% confident in my conclusion. My only reservation is in the slight possibility that I am wrong to interpret the exception Jesus made in cases of sexual immorality as meaning that if your spouse commits adultery against you, that you are free to divorce and remarry. And the only reason I have any reservation about that at all is simply because there are smarter Christians than me who have a different interpretation. I don't find their arguments the least bit persuasive, but since I'm fallible, and they're smarter than me, they could be right, and I could be wrong.