Choosing the appropriate effective mass definition for gravitational response of quasiparticles

Establish a principled criterion for selecting the appropriate effective mass definition to use when computing the gravitational response of quasiparticles in condensed matter systems within Einstein’s field equations, resolving the ambiguity among definitions such as the band-curvature effective mass m = ℏ²/𝔈″, the optical/cyclotron effective mass m = ℏ²k/𝔈′, and the bare (rest) mass inferred from the relativistic dispersion limit 𝔈(0)/c².

Background

The authors analyze several effective mass definitions used in condensed matter physics, including the quasi-classical band-curvature mass and the optical/cyclotron mass, and compare them to the bare mass limit derived from relativistic dispersion relations. While they appeal to the Equivalence Principle to motivate a choice, they explicitly note that at present there is no definitive method for choosing the proper mass definition for gravitational calculations involving quasiparticles. Resolving this ambiguity is essential for consistent modeling of how condensed matter excitations contribute to space-time curvature through the stress-energy tensor.