What sorts of restrictions do universities place on romantic or sexual relationships between faculty and graduate students, and what are the underlying issues that motivate these restrictions?
For example, suppose the student has previously taken a class from the professor but has no plans for further academic contact. What other factors could help determine whether a relationship would be allowed or considered appropriate?
To give one data point on how this issue is actually framed and enforced by universities (or at least public universities in the US), let me quote from my university's Campus Administrative Manual:
An individual may not initiate or participate in institutional decisions involving a direct benefit or penalty to someone with whom that individual has had a sexual relationship.
Relationships such as those between supervisors and their subordinate employees are inherently asymmetric. Current or past sexual relationships can adversely affect decisions, distort judgments, and undermine morale. Any university employee who participates in academic supervisory or administrative decisions concerning another employee with whom he or she has or has had a sexual relationship has a conflict of interest in these situations.
Accordingly, no individual shall initiate or participate in institutional decisions involving a direct benefit or penalty (employment, retention, promotion, tenure, salary, leave of absence, etc.) to a person with whom that individual has or has had a sexual relationship. He or she must take specific actions to remove himself or herself from all decisions and actions that may influence the career or status of the other employee.
[...]
In cases where a conflict [of interest] is identified, the UEO [Unit Executive Officer] must develop a Supervisory Relationship Management Plan that redirects decision-making and bypasses involved parties. Such procedures must be agreed to in writing and approved through all administrative levels. For changes in existing positions that might create a supervisory relationship in the same unit, review and approval is also required.
[...]
The appropriate human resources office will conduct periodic compliance reviews. Failure to abide by this policy constitutes misconduct, subject to discipline under applicable University procedures.
tl;dr: Sexual relationships between students and faculty are not per se forbidden, but the conflicts of interest they create — either real or perceived — must be carefully and explicitly managed by multiple layers of campus administration.
It is worth emphasizing that these policies are invoked not only for sexual relationships that are generally considered inappropriate, such as undergraduates and their instructors, or graduate students and their advisors, but also with married (and formerly married) couples.
Is it allowed to have a sexual relationship between a Professor and a graduate student?
This depends on the university's rules. Pretty much every plausible set of rules you can think of is used somewhere: everything is allowed (well, generally not explicitly, but by not having rules for this at all), nothing is allowed, it's allowed only if they are in different departments, it's allowed only if the professor is not teaching or supervising the student, etc. If this issue is relevant to your life, then you need to figure out which rules apply.
On the other hand, I'd say it's always a bad idea if the student and professor are in the same department or even related fields, regardless of whether the university's rules allow it. You could have a secret relationship, but it's wise to avoid awkward or troublesome secrets in your professional life (and all the problems of a known relationship will be magnified if you are discovered in a secret relationship). On the other hand, if other people in your department are aware of your romantic involvement, then it is almost certain to lead to complications. For example, the student will eventually need letters of recommendation, some of which will be written by colleagues of the professor. If they write honest letters, can they feel confident that what they wrote won't make it back to the professor? Probably not, so they will feel constrained in what they write. People reading the letters will realize this, so nothing positive will be taken quite as seriously. And letters of recommendation are just one issue - the relationship will keep coming up in different areas.
When you take into account all the important points made in other answers (power differentials, what happens if the relationship ends, improper appearances and effects on reputation, etc.), it's not hard to see why there are often rules against this.
The key issue of whether it is ethical or not reduces the question: Is there a potential for a perceived imbalance of power that can be abused?
If the professor and graduate student are in separate departments, I think it is not an issue because a professor of one department has no power to influence any matters pertaining to the graduate student's academic life.
If they two are of the same field, things can get a bit delicate. Speculation of an improper relationship alone can be devastating to one's reputation even if unfounded. We all know that politics play a role in one's success in a department.
If one is maintaining a mentor-apprentice relationship (teacher-student, or advisor-mentee) and romantic relationship with the same person, it is difficult to determine whether certain actions (benefiting or detrimental to the apprentice or mentor) are biased due to emotion. Furthermore, if the romantic relationship terminates, it is difficult to continue the mentor-apprenticeship relation.
While technically not "illegal", you have to ask yourself the question "is there a potential for a perceived imbalance in power in the relationship?". If so, I strongly advise against it.
Official Answer: It depends on the tenets of your institution.
Real Answer: No. Never with an active student at your institution.
Relationships may sometimes be allowed between former students and faculty by the letter, but I cannot think of when it would be advisable for a faculty member to have a relationship with a student. Why not?
If there is ever a chance of you having power over their academic progress, it is at best a conflict of interest and at worst a setup for sexual harassment case. If you're looking for a great reason to have your tenure file silently quashed by a dean, this is a great way to do it.
Even if you have no direct power over a student, there is the possibility that other students could complain if there is indirect influence (e.g., if you have connections to other faculty who do have power over that student or over rival students). Even an indirect connection to the student has the potential for allegations of bias or preference.
You do not know the future and may run into a conflict later (e.g., student takes a course in your department, invited to work on a funded grant with member of their department). At that point, you're hosed. Even if ended the relationship as soon as the conflict became evident, the prior history of the relationship still exists. Alternatively, you could hurt your own (or the student's) academic trajectory by declining these opportunities. At the point where you are hurting a students' academic trajectory, it's unethical.
It looks bad on the institution. How many administrators would want it known that any of their professors are dating any of their students? If you were a parent looking at a school for your kid, all else being equal, would you want the one where faculty are dating students? Imagine if the relationship goes sour and you end up in shouting matches with a student in your office/lab (or theirs!). In that light, dating a student is an anti-service to the institution.
If the student is really going to be the love of your life, you can wait until they're graduated to start a relationship. If not, then it's certainly not worth the risk (even if your name is Professor Carlos Danger).
This sort of thing used to be allowed decades ago, where it wasn't uncommon for the (almost entirely male) faculty to end up marrying female grad students. As we've become more aware of the power structures and negative externalities involved, it's become much less permissible. Rightly so, in my opinion. No school is bigger than 100,000 students and most students you meet will be done in 3-4 years maximum. Given the risks (bias, bad press, potential lawsuits by the student or their peers), I don't think it's an undue restriction to not date a few thousand people rotating over a few years.
It depends on what allowed means. Many things are legal but not advisable.
Traditionally the teacher-student relationship is Platonic. It also often continues beyond the class that brings the two together. If that relationship morphs into something else, it can appear improper even if nothing is technically awry. We all know how important appearance is in university relations.
There is a further wrinkle. Do you mean an exclusively sexual relationship? That can create the appearance of a quid pro quo.
To second @Charles, this is an interesting question precisely because it is a delicate topic. For example, it appears that the OP is male and discussing a female professor. How would our reactions change if the genders were reversed? Or, if both were the same gender?
