Is it permissible to continue one's studies and obtain a doctorate that requires field visits lasting six hours without a mahram, despite the pressing need for work and difficult financial circumstances?

A woman is not permitted to travel without a mahram. This is supported by authentic hadiths, including the Prophet's (peace and blessings be upon him) saying: "A woman should not travel except with a mahram." This ruling applies to anything considered travel and is not restricted to a specific distance. The variations in wording in the hadiths are due to the different questioners and circumstances. Therefore, you are not permitted to pursue studies in a specialization that necessitates travel without a mahram, because preserving one's religion takes precedence over obtaining such an education.