New particlelike solutions in modified gravity: the Higgs

New particlelike solutions
in modified gravity:
the Higgs monopoles
André Füzfa
Massimiliano Rinaldi & Sandrine Schlögel
Namur Center for Complex Systems - naXys
University of Namur
Eventuellement suivi de
«!A n’ouvrir qu’en cas de Prix Nobel!»

SOME PARTICLELIKE SOLUTIONS
IN CLASSICAL FIELD THEORY
Part One

Why particlelike solutions?
! Original motivation:
→ Temptative models of elementary particles such as
electron in terms of solutions to classical field equations
→ Naive view since no quantum mechanical aspects…
!Regularization of singularities in classical field
theory for point sources (spherical symmetry)
! Alternatives to black holes
→ Black holes: singular solutions
→ classical regularisation of gravitational singularities
→ new candidates for compact objects (high-energy
astrophysical sources such as quasars, galactic centers,
etc.)

What makes a particlelike solution?
!Spherical symmetry
!Static (Time-independent) equilibrium configurations
!Globally regular (no singularities at r=0 and r->∞)
!Asymptotically flat: vanishing forces at spatial infinity
!Finite-energy/mass
! Stable under perturbations (when possible)

An example in electromagnetism
! Electron: some electrical charge distribution, pointlike at
distance
!Which electric potential? => Maxwell equations
→ For static potential : Poisson equation
V’’r+2V’=0 ; (.)’=d(.)/dr
Distance
The solution V(r) ~ 1/r is singular!
Electric potential
Particlelike solution
Inner
region,
regularity
at r=0
Outer region:
fast decrease when r->∞
So that total energy is bounded
Electron radius
Naive
classical
vision!
Quantum
Mechanics!