Tilted Lemaitre-Tolman-Bondi Spacetimes: Hydrodynamic and Thermodynamic Properties

Abstract

We consider Lemaitre-Tolman-Bondi spacetimes from the point of view of a tilted observer, i.e. one with respect to which the fluid is radially moving. The imperfect fluid and the congruence described by its four-velocity, as seen by the tilted observer is studied in detail. It is shown that from the point of view of such tilted observer the fluid evolves non-reversibly (i.e. with non-vanishing rate of entropy production). The non-geodesic character of the tilted congruence is related to the non-vanishing of the divergence of the 4-vector entropy flow. We determine the factor related to the existence of energy-density inhomogeneities and describe its evolution, these results are compared with those obtained for the non-tilted observer. Finally, we exhibit a peculiar situation where the non-tilted congruence might be unstable.