Time-periodic solutions of the Einstein’s field equations I: general framework

Abstract

In this paper, we develop a new method to find the exact solutions of the Einstein's field equations by using which we construct time-periodic solutions. The singularities of the time-periodic solutions are investigated and some new physical phenomena, such as the time-periodic event horizon, are found. The applications of these solutions in modern cosmology and general relativity are expected.

Compact Time and Determinism for Bosons: Foundations

“…In fact, only null sources j (x, t), or eventually sources with the same periodicity of the field, are compatible with static space-time periodicities of the field itself. 10 In the boundary terms the field acts similarly to a source term and the variation of periodicity of the field propagates in agreement with relativistic causality. This aspect is related to the dynamic and local nature of the compactification already discussed in (11) and can be interpreted in terms of the Huygens-Fresnel principle.…”

“…From these considerations we finally check that the four-momentum of the foundamental level and the space-time compactification radiuses can be written respectively asp μ = (Ē/c,p) and R μ = (cR t , R x ), where |R x | = R x = /|p|. Generalizing the de Broglie hypothesis, the foundamental compactification conditions (11) and (10) can be written with the following notation…”

Time-periodic solutions of the Einstein’s field equations II: geometric singularities

“…This work is a continuation of our previous work [3]. As in [3], we still consider the time-periodic solutions of the following vacuum Einstein's field equations…”

Physical characters of KLS time-periodic universe

“…From the Finkelstein diagram, we can see that r = 0 is a null curve. The Finkelstein diagram is a section (θ, φ) constant of space-time, any point describes the two-off dimensional surface whose topology structure is ds 2 …”

“…Recently, Kong et al [2][3][4] are the first to address exact time-periodic solutions in general relativity by solving the vacuum Einstein's field equations. In particular, Kong et al [4] constructed a new time-periodic solution of the vacuum Einstein's field equations.…”