A locally finite model for gravity

TL;DR

This paper introduces a finite-degree-of-freedom classical gravity model using straight strings in locally flat space-time sections, offering a simplified setting for studying complex gravitational interactions and potential quantum extensions.

Contribution

It presents a novel gravity model with finite degrees of freedom in finite regions, facilitating analytical solutions and insights into classical and quantum gravity.

Findings

Exact solutions in finite domains

Model generates infinite fractals globally

Potential for analytical and quantum gravity studies

Abstract

Matter interacting classically with gravity in 3+1 dimensions usually gives rise to a continuum of degrees of freedom, so that, in any attempt to quantize the theory, ultraviolet divergences are nearly inevitable. Here, we investigate matter of a form that only displays a finite number of degrees of freedom in compact sections of space-time. In finite domains, one has only exact, analytic solutions. This is achieved by limiting ourselves to straight pieces of string, surrounded by locally flat sections of space-time. Globally, however, the model is not finite, because solutions tend to generate infinite fractals. The model is not (yet) quantized, but could serve as an interesting setting for analytical approaches to classical general relativity, as well as a possible stepping stone for quantum models. Details of its properties are explained, but some problems remain unsolved, such as a complete description of the most violent interactions, which can become quite complex.