Multitemporal generalization of Schwarzschild solution

TL;DR

This paper extends the Schwarzschild solution to multiple time dimensions, integrating geodesic equations, proposing multitemporal Newton laws for extended objects, and presenting a scalar-vacuum generalization.

Contribution

It introduces a multitemporal generalization of Schwarzschild solution, including geodesic integration and Newton laws for extended objects, and extends to scalar-vacuum scenarios.

Findings

Integrated geodesic equations for multitemporal metrics

Proposed multitemporal Newton laws for extended objects

Presented scalar-vacuum generalization of the solution

Abstract

The $n$-time generalization of Schwarzschild solution is considered. The equations of geodesics for the metric are integrated. The multitemporal analogues of Newton laws for the extended objects described by the solution are suggested. The scalar-vacuum generalization of the solution is also presented.