Time-periodic universes

TL;DR

This paper introduces a novel time-periodic vacuum solution to Einstein's equations, revealing a universe with intrinsic periodicity and singularities, including black hole phenomena, expanding understanding of dynamic spacetime structures.

Contribution

The paper presents the first explicit time-periodic vacuum solution with singularities, demonstrating intrinsic periodicity and black hole features in Einstein's equations.

Findings

The solution exhibits infinite curvature at certain points.

It describes a universe with intrinsic time periodicity.

New singularities and black hole phenomena are identified.

Abstract

In this letter we construct a new time-periodic solution of the vacuum Einstein's field equations whose Riemann curvature norm takes the infinity at some points. We show that this solution is intrinsically time-periodic and describes a time-periodic universe with the "black hole". New physical phenomena are investigated and new singularities are analyzed for this universal model.