Einstein–Yang–Mills solitons: The role of gravity

Abstract

The canonical Bartnik-McKinnon solitons are regular solutions of the coupled Einstein-Yang-Mills system in which gravity may balance the repulsive nature of the Yang-Mills field. We examine the role played by gravity in balancing the system and determine its strength. In particular, we obtain an analytic lower bound on the fundamental mass-to-radius ratio, max r {2m(r)/r} > 2/3, which is a necessary condition for the existence of globally regular Einstein-Yang-Mills solitons.Our analytical results are in accord with numerical calculations.

Lower bound on the compactness of isotropic ultracompact objects

“…where, for spatially regular asymptotically flat spacetimes, the radially dependent metric functions {C, δ} are characterized by the small-r [20] C(r → 0) = O(r 2 ) and δ(0) < ∞…”

“…and large-r [20,21] C(r → ∞) → 0 and δ(r → ∞) → 0 (4) functional behaviors. The spatial behavior of these radially-dependent static metric functions is determined by the Einstein equations G µ ν = 8πT µ ν .…”

Self-gravitating field configurations: The role of the energy–momentum trace

“…In Section 4 we shall prove that matter configurations which are characterized by a non-negative energy-momentum trace are necessarily highly relativistic objects. In particular, we shall derive a lower bound on the compactness (mass-to-radius ratio [11,12]) of these extended physical objects. In Section 5 we shall prove that the curved spacetime geometries which describe these self-gravitating objects necessarily possess (at least) two photon-spheres, compact hypersurfaces on which massless particles can follow null circular geodesics.…”

“…The line element describing the spacetime geometry takes the following form in Schwarzschild coordinates [12][13][14][15] …”

“…Note that Eqs. (12) and (15) imply T ≤ 2ρ, an inequality which restricts the value of α to the regime [19,20]:…”