Do I always have to specify absolute path for objects instantiated from std::fstream class? In other words, is there a way to specify just relative path to them
The behaviour is OS specific. Therefore, the best way to handle this IMHO is to make it somebody else's problem. Read the path to the file to open as a string from the user (e.g: command line argument, config file, env variable etc..) then pass that string directly to the constructor of fstream. Document that this is how your program behaves.
I wrote more about path manipulation here: https://stackoverflow.com/a/40980510/2345997