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We consider a particular effect which can be expected in scenarios ofdeviations from Special Relativity induced by Planckian physics: the loss ofadditivity in the total energy of a system of particles. We argue about thenecessity to introduce a length scale to control the effects of non-additivityfor macroscopic objects and consider white dwarfs as an appropriate laboratoryto test this kind of new physics. We study the sensitivity of the mass-radiusrelation of the Chandrasekhar model to these corrections by comparing theoutput of a simple phenomenological model to observational data of whitedwarfs.

Testing energy non-additivity in white dwarfs