Kinematics and dynamics of null hypersurfaces in the Einstein-Cartan spacetime and related thermodynamic interpretation

TL;DR

This paper develops a geometric framework for null hypersurfaces in Einstein-Cartan spacetime with torsion, linking their dynamics to thermodynamic concepts such as temperature and entropy in a covariant manner.

Contribution

It introduces a covariant geometric construction of null hypersurfaces with torsion, deriving their dynamics and establishing a thermodynamic interpretation of Einstein-Cartan equations.

Findings

Null hypersurface geometry with torsion is explicitly constructed.

The dynamics relate to thermodynamic quantities like temperature and entropy.

Einstein-Cartan equations on null surfaces have a thermodynamic interpretation.

Abstract

A general geometric construction of a generic null hypersurface in presence of torsion in the spacetime (Riemann-Cartan background), generated by a null vector $l^a$, is being developed here. We then explicitly define and structure various corresponding kinematical quantities. The dynamics of the null surface, particularly given by $\hat{G}_{ab}k^al^b$, is also discussed. The later one is constructed under the {\it geodesic constraint} condition. This yields a relation among the rate of change of expansion scalar corresponding to auxiliary null vector $k^a$ and various kinematical entities on the null surface. Using this relation we show that the Einstein-Cartan-Kibble-Sciama equation (which provides the dynamics of the metric and the torsion tensor) on this null hypersurface acquires a thermodynamic interpretation. The thermodynamic entities like temperature, entropy density, energy and pressure are properly identified. In the whole analysis we adopt the geometrical field interpretation of torsion and all discussions are done in a covariant manner.