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By hybrid density functional theory, we have investigated anisotropies in the electronic, optical, and mechanical properties of the body centered tetragonal C(4) phase of carbon. We predict a strong electronic anisotropy associated with the in-plane carbon-carbon covalent bonds and the zigzag carbon chains along the c-direction (out-of-plane), which results in a state-resolved directional distribution of valence electrons at the top of the valence band. The calculated adsorption spectra display highly anisotropic features which are already manifested at ambient pressure by a substantial difference (2 eV) for the absorption edges between the in-plane and out-of-plane components of the tetragonal cell. Similar anisotropic features in the elastic compressibility are also discussed. (C) 2010 American Institute of Physics. [doi:10.1063/1.3479478]