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To the best of our knowledge, there are no specific calculations ofgravity-darkening exponents for white dwarfs in the literature. On the otherhand, the number of known eclipsing binaries whose components are tidallyand/or rotationally distorted white dwarfs is increasing year on year.  Our main objective is to present the first theoretical approaches to theproblem of the distribution of temperatures on the surfaces of compact starsdistorted by rotation and/or tides in order to compare with relevantobservational data.  We find discrepancies between the gravity-darkening exponents calculated withour methods and the predictions of the von Zeipel theorem, particularly in thecases of cold white dwarfs; although the discrepancy also applies to highereffective temperatures under determined physical conditions. We find physicalconnections between the gravity-darkening exponents calculated using ourmodified method of triangles strategy with the convective efficiency (definedhere as the ratio of the convective to the total flux). A connection betweenthe entropy and the gravity-darkening coefficients is also found: variations ofthe former cause changes in the way the temperature is distributed on distortedstellar surfaces.  On the other hand, we have generalised the von Zeipel theorem for the case ofhot white dwarfs. Such a generalisation allows us to predict that, undercertain circumstances, the value of the gravity-darkening exponent may besmaller than 1.0, even in the case of high effective temperatures.

Rotationally and tidally distorted compact stars A theoretical approach to the gravity-darkening exponents for white dwarfs