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The large scatters of luminosity relations of gamma-ray bursts (GRBs) havebeen one of the most important reasons that prevent the extensive applicationsof GRBs in cosmology. In this paper, we extend the two-dimensional (2D)luminosity relations with $\tau_{\mathrm{lag}}$, $V$, $E_{\mathrm{peak}}$, and$\tau_{\mathrm{RT}}$ as the luminosity indicators to three dimensions (3D)using the same set of luminosity indicators to explore the possibility ofdecreasing the intrinsic scatters. We find that, for the 3D luminosityrelations between the luminosity and an energy scale ($E_{\mathrm{peak}}$) anda time scale ($\tau_{\mathrm{lag}}$ or $\tau_{\mathrm{RT}}$), their intrinsicscatters are considerably smaller than those of corresponding 2D luminosityrelations. Enlightened by the result and the definition of the luminosity(energy released in units of time), we discussed possible reasons behind, whichmay give us helpful suggestions on seeking more precise luminosity relationsfor GRBs in the future.

Gamma-ray Burst Luminosity Relations: Two-dimensional versus Three-dimensional Correlations