A damping device for being situated between a housing wall of a housing of a thermal gas turbine and a casing ring is provided. The casing ring includes an area radially internal with regard to a rotation axis of a rotor of the thermal gas turbine and facing rotating moving blades of the gas turbine. The damping device includes at least sectionally a porous damping structure. A method for manufacturing this type of damping device as well as to a thermal gas turbine, in particular an aircraft engine, in which this type of damping device is situated in a housing of the gas turbine between a housing wall and a casing ring are also provided.