A computer tomograph (1) for X-ray imaging includes a rotationally fixed gantry (2) that is displaceable at most in the axial direction (z). A plurality of X-ray emitters (3) and X-ray detectors (4) is arranged in the gantry (2) in a fixed manner about a central geometrical axis (z), in each case opposite to one another and offset with respect to each other in the direction of the central axis (z). The X-ray emitters (3) have cathodes (5) as electron emitters, which are separately connected to emitter controls (25) and cooperate with a common extraction grid (26) connected upstream of at least one focusing electrode (27). In comparison to conventional computer tomographs having rotating or rigidly arranged technical X-ray components, the computer tomograph (1) has a light and compact design.