The geophysics of extrasolar planets is a scientific topic often regarded as standing largely beyond the reach of near-term observations. This reality in no way diminishes the central role of geophysical phenomena in shaping planetary outcomes, from formation, to thermal and chemical evolution, to numerous issues of surface and near-surface habitability. We emphasize that for a balanced understanding of extrasolar planets, it is important to look beyond the natural biases of current observing tools, and actively seek unique pathways to understand exoplanet interiors as best as possible during the long interim prior to a time when internal components are more directly accessible. Such pathways include but are not limited to: (a) enhanced theoretical and numerical modeling, (b) laboratory research on critical material properties, (c) measurement of geophysical properties by indirect inference from imprints left on atmospheric and orbital properties, and (d) the purpose-driven use of Solar System object exploration expressly for its value in comparative planetology toward exoplanet-analogs. Breaking down barriers that envision local Solar System exploration, including the study of Earths own deep interior, as separate from and in financial competition with extrasolar planet research, may greatly improve the rate of needed scientific progress for exoplanet geophysics. As the number of known rocky and icy exoplanets grows in the years ahead, we expect demand for expertise in exogeoscience will expand at a commensurately intense pace. We highlight key topics, including: how water oceans below ice shells may dominate the total habitability of our galaxy by volume, how free-floating nomad planets may often attain habitable subsurface oceans supported by radionuclide decay, and how deep interiors may critically interact with atmospheric mass loss via dynamo-driven magnetic fields.
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