Gravitational Higgs mechanism in neutron star interiors

Abstract

We suggest that nonminimally coupled scalar fields can lead to modifications of the microphysics in the interiors of relativistic stars. As a concrete example, we consider the generation of a non-zero photon mass in such high-density environments. This is achieved by means of a light gravitational scalar, and the scalarization phase transition in scalar-tensor theories of gravitation. Two distinct models are presented, and phenomenological implications are briefly discussed.PACS numbers: 04.50. Kd,04.40.Dg Scalar-tensor theories [1][2][3][4] can be thought of as theories of gravity with an additional scalar field Φ that couples non minimally to the metricg µν but does not couple to the matter fields, Ψ A . The latter couple minimally tog µν only. In this representation, known as the Jordan frame, the action readsand the weak equivalence principle (WEP) is manifest. Here Φ has the interpretation of a varying inverse gravitational constant, S m denotes the matter action, andR is the Ricci scalar ofg µν . One can also reformulate this action in terms of another metric and a redefined scalar field, in the so called Einstein frame. The scalar field and the metric in this frame are related to their Jordan frame counterparts by,where G ⋆ is a bare gravitational constant. The form of A 2 (φ) is determined by the choice of ω(Φ) and the requirement that the kinetic term for φ be canonical. That is, the Einstein frame action readswhere R is the Ricci scalar of g µν . In the absence of matter the theory clearly reduces to general relativity (GR) with a minimally coupled scalar field. In this representation the deviation from GR is encoded in the nonmiminal coupling between the matter and φ. After some manipulations the field equation for the scalar field can be put into the form [1][2][3][4][5] where T is the trace of the Einstein frame stress-energy tensorTheories in which dA(φ 0 )/dφ = 0 for some constant φ 0 , admit GR solutions with a trivial scalar configuration, as the scalar's equation is trivially satisfied and g µν effectively satisfies Einstein's equation with a rescaled gravitational coupling. Note that such theories have ω(Φ 0 ) → ∞ in the Jordan frame, where Φ 0 ≡ Φ(φ 0 ) (see Ref.[6] for a more detailed discussion). Certain theories in this class exhibit a remarkable property dubbed spontaneous scalarization [4,5,7]. It is convenient to expand the logarithmic derivative of the conformal factor around φ = φ 0 asIn and around stars of relatively low densities, such as the Sun, the scalar remains at the trivial configuration, φ = φ 0 , and the metric is that of GR. As a result the theory is indistinguishable from GR in the weak field limit. However, for β 0 < ∼ −4, compact stars above a threshold central density undergo a phase transition and develop a large scalar charge, even in the absence of an external scalar environment [5]. This behaviour is of particular interest as it underscores the importance of constraining deviation from GR in the strong field regime.At the perturbative level spontaneous scalariza...

Black Hole Quasibound States from a Draining Bathtub Vortex Flow

“…That ambiguity is lifted by requiring that the second solution has a vanishing Wronskian (defined as (φ 1 |φ 2 ) = φ * 1 φ 2 − φ * 1 φ 2 ). This defines Bi, and ensures that the connection formula (16) preserves the Wronskian conservation [42]. In other words, T ∈ U (1, 1).…”

Constructing neutron stars with a gravitational Higgs mechanism

“…As discussed in Ref. [10], the model we considered here should be viewed as a toy model whose purpose is to demonstrate the effectiveness of spontaneous scalarization as a Higgs-like mechanism in a simplified setting. Indeed, our results provide strong motivation for exploring more elaborate models, in which the scalar that undergoes scalarization couples with other standard model fields.…”

“…The mechanism resembles the Higgs mechanism and the model of Ref. [10] was intentionally simple and provocative. In principle one can use exactly the same mechanism to modify other aspects of the standard model in the high curvature regime.…”

“…The analysis of Ref. [10] was perturbative. As mentioned earlier, at perturbative level scalarization manifests itself as a tachyonic instability and one can study this instability in order to demonstrate that the model under consideration will exhibit spontaneous scalarization and assess whether it will satisfy criterion (ii) above.…”

“…The purpose of this paper is to revisit the model of Ref. [10] and perform a non-perturbative analysis. We will construct static, spherically symmetric neutron star solutions and we will show that spontaneous scalarization does indeed go through as expected and it endows the photon with a φ-dependent mass.…”