Finite lifespan of solutions of the semilinear wave equation in the Einstein-de Sitter spacetime

TL;DR

This paper proves that solutions to the massless self-interacting scalar field equation in the Einstein-de Sitter universe have finite lifespan for certain nonlinearities, highlighting limitations of solution longevity in curved spacetime models.

Contribution

It establishes finite lifespan results for solutions of the semilinear wave equation in the Einstein-de Sitter spacetime, specifically for the $ p$ model with $1< p<4$.

Findings

Solutions have finite lifespan for $1< p<4$ in Einstein-de Sitter spacetime.

The result applies to the massless self-interacting scalar field equation.

Highlights limitations of solution longevity in curved spacetime models.

Abstract

We examine the solutions of the semilinear wave equation, and, in particular, of the $\varphi ^p$ model of quantum field theory in the curved space-time. More exactly, for $1< p<4$ we prove that solution of the massless self-interacting scalar field equation in the Einstein-de Sitter universe has finite lifespan.