Bearing chamber housing for bearing a shaft of a turbomachine, comprising an additively constructed housing wall and an oil chamber cover, wherein, in each case relative to an axis of rotation of the shaft, the housing wall radially outwardly delimits an oil chamber (22a, 22b) of the bearing chamber housing, and the oil chamber cover, arranged at an axial end of the housing wall, axially delimits a region of the oil chamber, wherein said region is radially inwardly delimited by an inner shell of the bearing chamber housing, and wherein, in each case relative to the axis of rotation of the shaft, the housing wall, in a circumferential segment remote from the axial end, when viewed in an axial section, first comprises an axial extension in an axial portion and then, in a radial portion, springs back radially inwardly as far as the inner shell, so that in the circumferential segment, an outer wall surface of the housing wall that faces away from the oil chamber (22a, 22b), viewed from the outside, forms a pocket, wherein, in the circumferential segment, the housing wall, when viewed in the axial section, extends radially outward obliquely to the axis of rotation in a flank portion which follows the radial portion in the direction away from the axial end of the housing wall, wherein the flank portion and the radial portion together delimit the pocket in the axial direction and, in the radial portion, an inner wall surface of the housing wall that is opposite the outer wall surface axially delimits the region of the oil chamber, specifically axially opposite the oil chamber cover, wherein the inner shell is arranged radially within the region of the oil chamber that is arranged axially between the radial portion of the housing wall and the oil chamber cover, which inner shell forms a bearing receptacle, wherein a connection opening is introduced into the housing wall, which connection opening connects the oil chamber (22a, 22b) to an outer region outside the housing wall, wherein the connection opening is arranged at an axial position with the pocket, wherein the housing wall has an axial and radial extension in a first side wall portion, in which the outer wall surface of the housing wall delimits the pocket in the circumferential direction, and the housing wall also has an axial and radial extension in a second side wall portion, which is offset from the first side wall portion in the circumferential direction, wherein the housing wall delimits a connecting channel in the circumferential direction with its extension in the first and the second side wall portion, which connecting channel connects the region of the oil chamber to a further region of the oil chamber radially inside the pocket. an additively constructed housing wall and an oil chamber cover, wherein, in each case relative to an axis of rotation of the shaft, the housing wall radially outwardly delimits an oil chamber (22a, 22b) of the bearing chamber housing, and the oil chamber cover, arranged at an axial end of the housing wall, axially delimits a region of the oil chamber, wherein said region is radially inwardly delimited by an inner shell of the bearing chamber housing, and wherein, in each case relative to the axis of rotation of the shaft, the housing wall, in a circumferential segment remote from the axial end, when viewed in an axial section, first comprises an axial extension in an axial portion and then, in a radial portion, springs back radially inwardly as far as the inner shell, so that in the circumferential segment, an outer wall surface of the housing wall that faces away from the oil chamber (22a, 22b), viewed from the outside, forms a pocket, wherein, in the circumferential segment, the housing wall, when viewed in the axial section, extends radially outward obliquely to the axis of rotation in a flank portion which follows the radial portion in the direction away from the axial end of the housing wall, wherein the flank portion and the radial portion together delimit the pocket in the axial direction and, in the radial portion, an inner wall surface of the housing wall that is opposite the outer wall surface axially delimits the region of the oil chamber, specifically axially opposite the oil chamber cover, wherein the inner shell is arranged radially within the region of the oil chamber that is arranged axially between the radial portion of the housing wall and the oil chamber cover, which inner shell forms a bearing receptacle, wherein a connection opening is introduced into the housing wall, which connection opening connects the oil chamber (22a, 22b) to an outer region outside the housing wall, wherein the connection opening is arranged at an axial position with the pocket, wherein the housing wall has an axial and radial extension in a first side wall portion, in which the outer wall surface of the housing wall delimits the pocket in the circumferential direction, and the housing wall also has an axial and radial extension in a second side wall portion, which is offset from the first side wall portion in the circumferential direction, wherein the housing wall delimits a connecting channel in the circumferential direction with its extension in the first and the second side wall portion, which connecting channel connects the region of the oil chamber to a further region of the oil chamber radially inside the pocket.