You can still get sludge even with the use of synthetic motor oil.
But when you use synthetic motor oil it lessens the chance of your vehicles engine getting sludge buildup.
Although synthetic oil can last longer than conventional motor oil it still needs changed every 8,000 to 12,000 miles.
Also always change your engine oil filter every time you change the oil as I've known some people to just change the oil and not the filter and then have problems later on.
The oil filter is also very important to keeping the engine operating properly as it filters contaminants that can damage the bearings.
The best way to check for engine sludge is to open up the valve covers on the engine and if your engine has engine sludge there will usually be a lot of engine sludge or at least some sludge around the valves under the valve covers.
Or you can use a camera that you can stick down into the engine valve covers to check for engine sludge that way as well.
Sometimes engine sludge can splatter on the outsides of the engine but not always and the engine sludge will usually appear in small clumps.
Engine sludge usually occurs due to not changing the oil often enough or just driving around town for short trips and not getting the engine up to a high enough temperature.
An engine needs to get up to operating temp and drive down the highway to help evaporate moisture from the engine to also prevent engine sludge.
Engine sludge if not removed can cause damage to the engine eventually due to the engine sludge potentially blocking the oil passages so that the oil does not get through.
To prevent engine sludge change your oil every 3,000 to 5,000 miles and take your vehicle on highway driving trips.
Driving on the highway for longer trips is much better for your vehicle than short trips in town.