The concept of Relative Receiver Autonomous Integrity Monitoring (RRAIM) using time differential carrier phase measurements is investigated in this paper. The precision of carrier phase measurements allows for mitigation of integrity hazards by implementing RRAIM monitors with tight thresholds without significantly affecting continuity. In order to avoid the need for cycle ambiguity resolution, time differences in carrier phase measurements are used as the basis for detection. In this work, we examine RRAIM within the context of the GNSS Evolutionary Architecture Study (GEAS), which explores potential architectures for aircraft navigation utilizing the satellite signals available in the mid-term future with GPS III. The objectives of the GEAS are focused on system implementations providing worldwide coverage to satisfy LPV-200 operations, and potentially beyond. In this work, we study two different GEAS implementations of RRAIM. General formulas are derived for positioning, fault detection, and protection level generation to meet a given set of integrity and continuity requirements.