THE KUZNETSOV TENSOR AND THE INTERNAL DYNAMICS OF SPACETIME

This paper examines the concept of the internal dynamics of spacetime based on the introductionand analysis of the Kuznetsov tensor, a generalized tensorial object designed to describe theevolution of geometry under conditions of singularities, entropy concentrations, andnonequilibrium states. In contrast to traditional approaches in general relativity, where thedynamics of spacetime are determined exclusively by the metric and the energy-momentumtensor, the proposed formalism emphasizes internal tensorial structures that govern the directionand character of geometric evolution.The Kuznetsov tensor is interpreted as a tool that enables spacetime to be analyzed “from theinside,” that is, through the processes that generate and transform the metric itself rather thanthrough its observable manifestations alone. This perspective allows for a natural description ofregimes in which standard geometric representations become insufficient, including regions ofhigh curvature, breakdowns of connectivity, and anomalous entropy dynamics.The paper discusses the relationship between the Kuznetsov tensor and modified geometricflows, as well as its role in the generalization of entropy functionals used to analyze the stabilityand evolution of spacetime structures. It is shown that the internal dynamics governed by thistensor do not violate fundamental physical laws but instead provide an alternative geometricperspective in which singularities and extreme regimes admit a regular and consistentdescription.The results obtained may be of interest for research in mathematical physics, spacetimegeometry, and theoretical frameworks aimed at unifying gravitational dynamics withinformational and entropic processes.