Pervasiveness of the breakdown of self-interacting vector field theories

Abstract

Various groups recently argued that self-interacting vector field theories lack a well-defined time evolution when the field grows to large amplitudes, which has drastic consequences for models in gravity and high energy theory. Such field amplitudes can be a result of an external driving mechanism, or occur intrinsically, due to large values of the field and its derivatives in the initial data. This brings a natural question: is small amplitude initial data guaranteed to evolve indefinitely in these theories in the absence of an outside driving term? We answer this question in the negative, demonstrating that arbitrarily low amplitude initial data can still lead to the breakdown of the theory. Namely, ingoing spherically symmetric wave packets in more than one spatial dimensions grow as an inverse power of the radius, and their amplitudes can generically reach high enough values where time evolution ceases to exist. This simple example further establishes the pervasiveness of the pathology of self-interacting vector field theories.

5 pages, 1 figure. Published version in PRD

References in corpus (15)

• 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
• Nonlinear studies of binary black hole mergers in Einstein-scalar-Gauss-Bonnet gravity
• 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
• Destabilization of black holes and stars by generalized Proca fields
• Vortex String Formation in Black Hole Superradiance of a Dark Photon with the Higgs Mechanism
• A singularity problem for interacting massive vectors
• Spontaneously vectorized Einstein-Gauss-Bonnet black holes
• Instability of vectorized stars
• Coordinate singularities of self-interacting vector field theories
• The well-posedness of the Cauchy problem for self-interacting vector fields

Cited by in corpus (8)

• Fixing the dynamical evolution of self-interacting vector fields
• Conformally and Disformally Coupled Vector field Models of Dark Energy
• Scalaroca stars: coupled scalar-Proca solitons
• Treatments and placebos for the pathologies of effective field theories
• Loss of hyperbolicity and tachyons in generalized Proca theories
• Aspects of time evolution in $p$-form field theories
• Black hole destabilization via trapped quasi-normal modes
• Internal symmetry to the rescue: well-posed 1+1 evolution of self-interacting vector fields