A cooling system, comprising: a rotor (202, 302); a bearing assembly (238, 338) mounted to the rotor (202, 302); a static aft bearing structure (240, 340) surrounding the bearing assembly (238, 338) and including a cylindrical section defining a cavity within which the bearing assembly (238, 338) is disposed; an outer casing (272, 372) surrounding the static aft bearing structure (240, 340) and defining a portion of an exhaust pathway; the cooling system characterized in that the cooling system further comprises: a plurality of hollow struts (254, 354, 356, 358) extending from the static aft bearing structure (240, 340) towards the outer casing (272, 372) and through the exhaust pathway, each hollow strut including an outer radial end extending through an opening in the outer casing to receive cooling air from a cool air source and to provide a pathway for the cooling air to flow into the cavity; and a center-body cap disposed over an end of the static aft bearing structure (240, 340), the center-body cap including a rim configured to create a low pressure region at an interface between the static aft bearing structure (240, 340) and the center-body cap, wherein the low pressure region has a pressure that is lower than a pressure within the cavity; wherein: the cylindrical section of the static aft bearing structure has an aft end; the aft end is relatively blunt and creates a step, when the rim is disposed within the aft end; and a slit (292, 592) is included between the aft end and the rim, so that the cooling air is drawn from the cool air source through the plurality of hollow struts into the cavity. a rotor (202, 302); a bearing assembly (238, 338) mounted to the rotor (202, 302); a static aft bearing structure (240, 340) surrounding the bearing assembly (238, 338) and including a cylindrical section defining a cavity within which the bearing assembly (238, 338) is disposed; an outer casing (272, 372) surrounding the static aft bearing structure (240, 340) and defining a portion of an exhaust pathway; a plurality of hollow struts (254, 354, 356, 358) extending from the static aft bearing structure (240, 340) towards the outer casing (272, 372) and through the exhaust pathway, each hollow strut including an outer radial end extending through an opening in the outer casing to receive cooling air from a cool air source and to provide a pathway for the cooling air to flow into the cavity; and a center-body cap disposed over an end of the static aft bearing structure (240, 340), the center-body cap including a rim configured to create a low pressure region at an interface between the static aft bearing structure (240, 340) and the center-body cap, wherein the low pressure region has a pressure that is lower than a pressure within the cavity; wherein: the cylindrical section of the static aft bearing structure has an aft end; the aft end is relatively blunt and creates a step, when the rim is disposed within the aft end; and a slit (292, 592) is included between the aft end and the rim, so that the cooling air is drawn from the cool air source through the plurality of hollow struts into the cavity. the cylindrical section of the static aft bearing structure has an aft end; the aft end is relatively blunt and creates a step, when the rim is disposed within the aft end; and a slit (292, 592) is included between the aft end and the rim, so that the cooling air is drawn from the cool air source through the plurality of hollow struts into the cavity.