Production of hollow carbon fibers and hollow carbon particles includes baking and carbonization of polymer particles having a specified volume after deformation. A metal-deposited carbon fiber with metal deposited inside and/or outside the hollow carbon fiber is applicable to electron discharge devices. The thickness and crystallinity of the graphite layer can be freely controlled. Since almost no by-product is generated, separation and refining using a solvent is not required. A hollow carbon particle of desired shape can be produced at a high yield rate. The hollow carbon fiber represented by a carbon nano-tube can be controlled in such a way that a low resistance and uniform shape are provided so that there is an increase in the amount of electrons discharged from the hollow carbon fiber. Use of this hollow carbon fiber as an electron discharge source provides an excellent electron discharge device characterized by stable pixels.