Thermal conductivity common use in the construction and textile industries. The construction industry makes use of units such as the R-value (resistance) and the U-value (transmittance). Although related to the thermal conductivity of a material used in an insulation product, R- and U-values are dependent on the thickness of the product. Likewise the textile industry has several units including the tog and the clo which express thermal resistance of a material in a way analogous to the R-values used in the construction industry. There are a number of ways to measure thermal conductivity. Each of these is suitable for a limited range
Construction of a complex null tetrad to the horizon r=0, formula_74 where formula_75 refers to its on-horizon value. The very coordinates used in the adapted tetrad above are actually the Gaussian null coordinates employed in studying near-horizon geometry and mechanics of black holes. Construction of a complex null tetrad Calculations in the Newman–Penrose (NP) formalism of general relativity normally begin with the construction of a complex null tetrad formula_1, where formula_2 is a pair of "real" null vectors and formula_3 is a pair of "complex" null vectors. These tetrad vectors respect the following normalization and metric conditions assuming the spacetime signature formula_4 Only after the tetrad