Self-gravitating scalar breathers with negative cosmological constant

TL;DR

This paper explores time-periodic, localized scalar field solutions in anti-de Sitter space within Einstein's gravity, revealing discrete families, stability limits, and analytical solutions across dimensions.

Contribution

It provides a detailed numerical phase space analysis of AdS breathers and derives small amplitude solutions analytically for any dimension.

Findings

Discrete families of solutions indexed by frequency and mode number

Breathers are stable up to a critical central density

Analytical small amplitude solutions are obtained for arbitrary dimensions

Abstract

Breather-type (time-periodic and spatially localized) solutions with spherical symmetry are investigated in a massless scalar field theory coupled to Einstein's gravity with cosmological constant in $d$ spatial dimensions imposing anti de Sitter (AdS) asymptotics on space-time. Using a code constructed with the Kadath library that enables the use of spectral methods, the phase space of breather solutions is explored in detail for $d=3$ and $d=4$. It is found that there are discrete families of solutions indexed by an integer and by their frequency. Using a time evolution code these AdS breathers are found to be stable for up to a critical central density, in analogy to boson stars. Using an analytical perturbative expansion small amplitude breathers are worked out for arbitrary dimensions $d$.