Direct imaging of exoplanets requires establishing and maintaining a high-contrast dark field (DF) within the science image to a high degree of precision (10(-10)). Current approaches aimed at establishing the DF, such as electric field conjugation (EFC), have been demonstrated in the lab and have proven capable of high-contrast DF generation. The same approaches have been considered for the maintenance of the DF as well. However, these methods rely on phase diversity measurements, which require field modulation; this interrupts the DF and consequently competes with the science acquisition. We introduce and demonstrate spatial linear dark field control (LDFC) as an alternative technique by which the high-contrast DF can be maintained without modulation. Once the DF has been established by conventional EFC, spatial LDFC locks the high-contrast state of the DF by operating a closed loop around the linear response of the bright field (BF) to wavefront variations that modify both the BF and the DF. We describe the fundamental operating principles of spatial LDFC and provide numerical simulations of its operation as a DF stabilization technique that is capable of wavefront correction within the DF without interrupting science acquisition. (c) The Authors.