Process for producing hollow bodies comprising fibre-reinforced ceramic materials, where cores whose shape corresponds to that of the hollow spaces are produced in a first step, a green body is produced in a second step by introducing the abovementioned cores and a press moulding compound into a mould, where the press moulding compound comprises carbon fibres and/or carbon threads and pitch and/or resins, the green body is cured in a third step by heating under pressure, and then carbonised in a fourth step by heating in the absence of oxidants to form a C/C body, which latter can be infiltrated with liquid metal with retention of its shape in a fifth step, with at least partial formation of carbides, where the cores comprise a material which is non-meltable but undergoes at least sufficient shrinkage above the curing temperature of the shaping by pressing of the press moulding compound for the shrunken core to be able to be taken out from the carbonised body; hollow bodies produced by this process and also their use as brake disks, clutch disks and friction disks