# The scalarized Raychaudhuri identity and its applications

## TL;DR

This paper introduces a scalarized form of the Raychaudhuri identity, enabling new applications in cosmology, black-hole thermodynamics, and Einstein equations reformulation.

## Contribution

It presents a novel scalarization of the Raychaudhuri identity that broadens its applicability in various physical and cosmological contexts.

## Key findings

- Scalarization links the Raychaudhuri identity to relativistic temperature and scalar fields.
- Applications include cosmological background dynamics and black-hole thermodynamics.
- Reformulation of Einstein equations into Klein-Gordon form in thermodynamic space.

## Abstract

We show that the covariant Raychaudhuri identity describing kinematic characteristics of space-time admits a representation involving a geometrical scalar $\xi$ which, depending on circumstances, might be related to, e.g., relativistic temperature or cosmological scalar field. With an appropriately chosen spacetime deformation tensor (fixing the symmetry of a problem under consideration), such scalarization opens a wide scope for physical applications. We consider few such applications including dynamics of cosmological (anti)scalar background, non-variational deduction of the field equations, scalar and black-hole thermodynamics and the reshaping of the Einstein equations into the Klein-Gordon equation in thermodynamic Killing space.