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

TL;DR

This paper analyzes tilted Lemaitre-Tolman-Bondi spacetimes, revealing non-reversible fluid evolution, entropy production, and potential instability of the non-tilted congruence, with implications for understanding inhomogeneities and thermodynamics in cosmological models.

Contribution

It provides a detailed study of tilted observers in LTB spacetimes, highlighting non-reversible thermodynamic behavior and conditions for stability and inhomogeneity evolution.

Findings

Tilted observer perceives non-reversible fluid evolution.

Entropy production is non-zero for tilted congruence.

Non-tilted congruence may be unstable under certain conditions.

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.