Scalar Field Vanishes Research Articles

Perturbations to generalized kink-like topological defects in AdS

We explore perturbations to a kink-like (codimension 1) topological defect whose world brane is AdSq embedded into AdSq+1. Previously, we found solutions in the limit the mass of the scalar field vanishes. In this article we extend a calculation previously done in AdS2 to higher-dimensional embedding spaces and find that all perturbations to the mass of the field are stable to first order as expected in a theory with topological defects. We find that the equation of motion to the correction strongly resembles a problem well-known in quantum mechanics.

Spontaneously Scalarized Kerr Black Holes in Extended Scalar-Tensor-Gauss-Bonnet Gravity.

We construct asymptotically flat, spinning, regular on and outside an event horizon, scalarized black holes (SBHs) in extended scalar-tensor-Gauss-Bonnet models. They reduce to Kerr BHs when the scalar field vanishes. For an illustrative choice of nonminimal coupling, we scan the domain of existence. For each value of spin, SBHs exist in an interval between two critical masses, with the lowest one vanishing in the static limit. Non-uniqueness with Kerr BHs of equal global charges is observed; the SBHs are entropically favoured. This suggests that SBHs form dynamically from the spontaneous scalarization of Kerr BHs, which are prone to a scalar-triggered tachyonic instability, below the largest critical mass. Phenomenologically, the introduction of BH spin damps the maximal observable difference between comparable scalarized and vacuum BHs. In the static limit, (perturbatively stable) SBHs can store over 20% of the spacetime energy outside the event horizon; in comparison with Schwarzschild BHs, their geodesic frequency at the ISCO can differ by a factor of 2.5 and deviations in the shadow areal radius may top 40%. As the BH spin grows, low mass SBHs are excluded, and the maximal relative differences decrease, becoming of the order of a few percent for dimensionless spin j≳0.5. This reveals a spin selection effect: non-GR effects are only significant for low spin. We discuss if and how the recently measured shadow size of the M87 supermassive BH constrains the length scale of the Gauss-Bonnet coupling.

Stability of gravitating charged-scalar solitons in a cavity

We present new regular solutions of Einstein-charged scalar field theory in a cavity. The system is enclosed inside a reflecting mirror-like boundary, on which the scalar field vanishes. The mirror is placed at the zero of the scalar field closest to the origin, and inside this boundary our solutions are regular. We study the stability of these solitons under linear, spherically symmetric perturbations of the metric, scalar and electromagnetic fields. If the radius of the mirror is sufficiently large, we present numerical evidence for the stability of the solitons. For small mirror radius, some of the solitons are unstable. We discuss the physical interpretation of this instability.

Black hole perturbation in nondynamical and dynamical Chern-Simons gravity

Chern-Simons gravitational theories are extensions of general relativity in which the parity is violated due to the Chern-Simons term. We study linear perturbations on the static and spherically symmetric background spacetime both for nondynamical and dynamical Chern-Simons theories. We do not make an assumption that the background Chern-Simons scalar field vanishes, which has been adopted in the literature. By eliminating nondynamical variables using their constraint equations, we derive the reduced second order action from which a set of closed evolution equations containing only dynamical variables are immediately obtained and therefore the number of propagating degrees of freedom as well. It is found that ghost is present both for the nondynamical case and for the dynamical case unless the background Chern-Simons scalar field vanishes. It is also found that if the background scalar field vanishes, ghost degrees of freedom are killed and all the modes propagate at the speed of light.

Gravitational signature of Schwarzschild black holes in dynamical Chern-Simons gravity

Dynamical Chern-Simons gravity is an extension of General Relativity in which the gravitational field is coupled to a scalar field through a parity-violating Chern-Simons term. In this framework, we study perturbations of spherically symmetric black hole spacetimes, assuming that the background scalar field vanishes. Our results suggest that these spacetimes are stable, and small perturbations die away as a ringdown. However, in contrast to standard General Relativity, the gravitational waveforms are also driven by the scalar field. Thus, the gravitational oscillation modes of black holes carry imprints of the coupling to the scalar field. This is a smoking gun for Chern-Simons theory and could be tested with gravitational-wave detectors, such as LIGO or LISA. For negative values of the coupling constant, ghosts are known to arise, and we explicitly verify their appearance numerically. Our results are validated using both time evolution and frequency domain methods.

Non-gravitating scalar field in the FRW background

We study interacting scalar field theory non-minimally coupled to gravity in the FRW background. We show that for a specific choice of interaction terms, the energy-momentum tensor of the scalar field vanishes, and as a result the scalar field does not gravitate. The naive space dependent solution to equations of motion gives rise to singular field profile. We carefully analyze the energy-momentum tensor for such a solution and show that the singularity of the solution gives a subtle contribution to the energy-momentum tensor. The space dependent solution therefore is not non-gravitating. Our conclusion is applicable to other space-time dependent non-gravitating solutions as well. We study hybrid inflation scenario in this model when purely time dependent non-gravitating field is coupled to another scalar field.

SHORT STRINGS IN THE ABELIAN HIGGS MODEL

We consider the monopole–antimonopole static potential in the confining phase of the Abelian Higgs model and in particular the corrections to the Coulomb-like potential at small distances r. By minimizing numerically the classical energy functional, we observe a linear in r, stringy correction even at distances much smaller than the apparent physical scales. We argue that this term is a manifestation of the condition that the monopoles are connected by a mathematically thin line along which the scalar field vanishes. These short strings modify the operator product expansion as well. Implications for QCD are discussed.

Newman-Penrose constants and the tails of self-gravitating waves.

We study the properties of the decay of a self-gravitating radiation field by analyzing the relation between behavior in the weak field regime, test field behavior in a Schwarzschild background, and strong field behavior. Our model consists of a spherically symmetric scalar field incident on a reflecting barrier, which allows all these regimes to be treated on a common nonsingular manifold. Our primary conclusion, in the curved space case, is that there are two distinct types of late decay determined by whether or not the Newman-Penrose constant for the scalar field vanishes. For the nonvanishing case, the radiation tail decays as $\frac{1}{t}$, with respect to Bondi time, but there are also ln $\frac{t}{{t}^{2}}$ corrections, as well as the exponentially decaying contributions associated with quasinormal modes.

Pair condensation in massless scalar electrodynamics

Motivated by the instabilities of the vacuum to bound-state pair production at large coupling in both abelian and non-abelian gauge theories, we examine the stability of the vacuum of a constrained version of massless scalar electrodynamics to the formation of a scalar pair condensate. The trial states are constructed by analogy with the BCS ground state of super-conductivity and are such that the vacuum expectation value of the scalar field vanishes. Analysis of the minimization equation for the energy density indicates that there are two phases as a function of the coupling constant. Under the constraint that the vacuum expectation value of the scalar field be zero, we find what, for small coupling, the perturbative vacuum minimizes the energy, while for large coupling a condensate of particle-antiparticle pairs is energetically favored. After discussing the relation of our results to the phase structure of unconstrained scalar electrodynamics, we speculate on possible implications for QCD.

Closed anisotropic cosmological models

From observation, it appears that the anisotropy of our universe is small. Because of this, most workers have assumed isotropy during the entire evolution of their cosmological models of our universe. Such models are in accord with observations of the present state of our universe but do not explain the isotropy. Recently, Misner suggested that the early universe could have been anisotropic and the present universe highly isotropic if the anisotropy damped out sufficiently rapidly during the expansion of our universe. In this paper we give a new exact solution to Einstein's equations representing homogeneous nonisotropic cosmological models of a closed universe containing electromagnetic and scalar fields. This solution reduces to (1) a generalization of Brill's electromagnetic universe when the scalar field vanishes, (2) Taub-NUT-M space when both these fields vanish. The solutions also satisfy the scalar tensor equations and represent (1) a universe containing electromagnetic fields and (2) a source-free solution to the scalar-tensor equations representing a closed universe.

Space-Time Structure of a Static Spherically Symmetric Scalar Field

Bergmann and Leipnik have derived some special solutions of the general-relativistic field equations in which the metric has the Schwarzschild or the Minkowski form, although a scalar field is assumed to be present. It will be shown that in reality this scalar field vanishes.