A theoretical study is presented on the characteristics of terahertz antennas formed by metallic single-walled carbon nanotube (SWCNT) dipoles. The Boltzmann transport equation and Maxwell's equations are combined with boundary conditions of the electron distribution function, in order to formulate a wavenumber-domain integral equation for the current, which considers the spatial dispersion and provides higher level of accuracy and generality than existing approaches. Through proper approximations of that equation, the same spatial integral equations from several other studies can be drawn. The radiation properties of the SWCNT antenna are derived from the wavenumber-domain current. Numerical results are given for short dipole antennas and those with length close to the half wavelength in free space. They are compared to the results calculated by other methods. We also investigate the frequency dependence of conductance under different values of relaxation frequency and find the increase of relaxation frequency leads to strong attenuation of surface-wave resonances.