What I understand is that anti-radiation missiles are accurate and long range.
So, assume that a fighter aircraft is 100% invisible on radar. However, its radar is transmitting energy continuously which can be detected and targeted using anti-radiation missiles. As Wikipedia suggests there is Russian air-to-air anti radiation missile (Vympel R-27EP).
Wouldn't such a missile neutralize the stealth technology? And why don't we have any other examples of such weaponry other than Russian one?
There are many anti-radiation missiles in many arsenals, they are designed for air to ground missions, attacking surface to air missile radars from a long distance. I don't know whether it would be possible for an anti-radiation missile to hit an air target.
If we assume it is possible your idea has a significant flaw in that stealth aircraft turn off their radars when they are on a stealth mission. Running a radar is like holding a flare in the middle of a field on a dark night, which is why they don't do it, at least not using conventional radars.
Some stealth airplanes don't even have a radar, for instance the F117. Typically attacks were done using GPS for precision navigation to the target, which is then attacked using precision munitions like laser guided bombs or GPS guided bombs or missiles.
Nowadays here are advanced radar systems that spread signals over multiple frequencies which will blend in with other signals, and can be directed in specific directions to avoid being detected. If a radar beam isn't pointing towards a sensor then the radar won't be detected.
If the stealth aircraft's radar were continually transmitting, then, yes, the other stealth features would be completely useless, and missiles would easily home in on them and shoot them down. Which is why the radar on stealth aircraft are very rarely used.
Anti-radiation missiles are much more dangerous against ground radars precisely because they are in a fixed position. If the crew turns off the radar, then the missile just has to remember where it last saw the radar, and attack that point. The same can't be said for an aircraft's radar, because they are by definition mobile. Thus an air-to-air missile would have to rely on the element of surprise, basically sneaking up on the enemy plane so they don't realize they're being attacked (and thus have a chance to turn off their radar) until its too late. Which means in turn that its usually better to keep the radar off all the time unless you have some specific need for it, and even then, use it as sparingly as possible.
Note that the same is true, albeit to a lesser extent, for non-stealth aircraft. You can detect another aircraft's radar from a lot further away than it can detect you, so if you have the radar on all the time, you're basically advertising your position to an enemy that you might not even be able to detect. So the only time military aircraft use their radar is if they know they've already been spotted, if they're deliberately playing dumb to act as bait for an ambush, or if they judge that giving away their position is an acceptable trade-off for greater awareness.
Yes, but such aircraft can turn off their active emissions (radar, EM jammer, communications etc etc.). And AESA radars can be very select about in which directions it emit to not make the aircraft detected to known threats.
There is also missiles with Home on Jam capabilities. So if you jam to disguise your position for example, such missiles can home in on the jamming signal. So as a stealth aircraft, it is probably another thing to keep turned off unless you really need it.
As an addition to other answers:
To form a picture of the battlefield situation, the radar system of a stealth aircraft (or any radar for that matter) does not need to transmit all the time. It can blib or burst a signal, or perform a sweep for more resolution, and then hibernate. It can also "listen" to other radar signal sources and echoes and thus image the surroundigs to some extent.
As explained in other answers and especially in the comments, modern warfare is no longer a game of separate units. It is a merged system, and on the NATO side, the "glue" of this matrix is the Link 16 network. Data collected from multiple sources is trasferred via Link 16 and is used to form a very comprehensive and accurate realtime presentation of the battlefield.
The stealth aircraft, or actually any networked battlefield operator has eyes, ears and noses all over the place, they really do not necessarily need to use much of their own. For example, for an F-22 or F-35, information about enemy precense is initially delivered from elsewhere, and they only need to use their own radar to perform a strike, and maybe not even for that. Should the adversary fire the missile in question at them while they were using radar, they can simply switch off the radar transmitter, and they have become invisible. The enemy missile only has their last tx position, and that just won't be of any help.
I don't have rep to comment, so this answer is more of a side note, that stealth fighters have been trackable for decades. The TAMARA radio system from what was Tesla Electronics (former Czechoslovakia) involved a large network of receivers that could correlate reflections from radio signals, and also identify the communication between onboard weapon systems, if I recall correctly. https://en.wikipedia.org/wiki/Tamara_passive_sensor I do remember the Czech premiere appearing in the UK giving assurances to Western powers that Tamara would not be sold because Tesla was to go bankrupt. I think that is what ended up happening.
It's successor VERA is apparently also able to track stealth planes https://en.wikipedia.org/wiki/VERA_passive_sensor
So while it is unrelated to the question of anti radiation missiles, anti radiation missiles are probably not as useful if you have these radar systems already
In theory - yes. In practice - I dont think so.
Conclusion: I don't think so. There are some indications that some of air-to-air missiles have passive guidance mode but I have never heard about combat engagement using such a mode.
