Coordinate singularities of self-interacting vector field theories

Abstract

Self-interacting vectors are seeing a burst of interest where various groups demonstrated that the field evolution ends in finite time. Two nonequivalent criteria have been offered to identify this breakdown: (i) the vector constraint equation cannot be satisfied beyond a point where the breakdown occurs, (ii) the dynamics is governed by an effective metric that becomes singular at the breakdown. We show that (i) identifies a coordinate singularity, and can be removed by a change of coordinates. Hence, it does not signify a physical problem, and cannot determine the validity of a theory.

5 pages, 2 figures. Minor changes to bring into line with published version in PRL

References in corpus (11)

• Nonlinear collective effects in photon-photon and photon-plasma interactions
• The imitation game: Proca stars that can mimic the Schwarzschild shadow
• Spontaneous growth of vector fields in gravity
• Black holes in vector-tensor theories
• Aspects of Nonlinear Effect on Black Hole Superradiance
• The problem with Proca: ghost instabilities in self-interacting vector fields
• Electromagnetism and hidden vector fields in modified gravity theories: spontaneous and induced vectorization
• Vortex String Formation in Black Hole Superradiance of a Dark Photon with the Higgs Mechanism
• A singularity problem for interacting massive vectors
• Instability of vectorized stars
• The well-posedness of the Cauchy problem for self-interacting vector fields

Cited by in corpus (11)

• Spontaneous scalarization
• Proca-Higgs balls and stars in a UV completion for Proca self-interactions
• Fixing the dynamical evolution of self-interacting vector fields
• Pervasiveness of the breakdown of self-interacting vector field theories
• Treatments and placebos for the pathologies of effective field theories
• Self-interactions can (also) destabilize bosonic stars
• Loss of hyperbolicity and tachyons in generalized Proca theories
• Highly compact Proca stars with quartic self-interactions
• Black hole destabilization via trapped quasi-normal modes
• Aspects of time evolution in $p$-form field theories
• Internal symmetry to the rescue: well-posed 1+1 evolution of self-interacting vector fields