Instability of compact stars with a nonminimal scalar-derivative coupling

Abstract

For a theory in which a scalar field $\varphi$ has a nonminimal derivative coupling to the Einstein tensor $G_{\mu \nu }$ of the form $\varphi G_{\mu \nu }{\nabla }^{\mu }{\nabla }^{\nu }\varphi$, it is known that there exists a branch of static and spherically-symmetric relativistic stars endowed with a scalar hair in their interiors. We study the stability of such hairy solutions with a radial field dependence $\varphi (r)$ against odd- and even-parity perturbations. We show that, for the star compactness $\mathcal{C}$ smaller than $1/3$, they are prone to Laplacian instabilities of the even-parity perturbation associated with the scalar-field propagation along an angular direction. Even for $\mathcal{C}>1/3$, the hairy star solutions are subject to ghost instabilities. We also find that even the other branch with a vanishing background field derivative is unstable for a positive perfect-fluid pressure, due to nonstandard propagation of the field perturbation $\delta \varphi$ inside the star. Thus, there are no stable star configurations in derivative coupling theory without a standard kinetic term, including both relativistic and nonrelativistic compact objects.

arXiv comment17 pages, 8 figures, published version

References in corpus (53)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Dynamics of dark energy
• Modified Gravity and Cosmology
• Testing General Relativity with Present and Future Astrophysical Observations
• Beyond the Cosmological Standard Model
• Generalized G-inflation: Inflation with the most general second-order field equations
• From k-essence to generalised Galileons
• Black holes, gravitational waves and fundamental physics: a roadmap
• Tensor-scalar gravity and binary-pulsar experiments
• The relativistic pulsar-white dwarf binary PSR J1738+0333 II. The most stringent test of scalar-tensor gravity
• Black hole hair in generalized scalar-tensor gravity
• Action functionals for relativistic perfect fluids
• General second order scalar-tensor theory, self tuning, and the Fab Four
• Black holes in scalar-tensor gravity
• Dressing a black hole with a time-dependent Galileon
• Black hole hair in generalized scalar-tensor gravity: An explicit example
• Further stable neutron star models from f(R) gravity
• A no-hair theorem for the galileon
• Analytical representations of unified equations of state for neutron-star matter
• Black holes with non-minimal derivative coupling
• Asymptotically locally AdS and flat black holes in Horndeski theory
• Constraints on Perturbative f(R) Gravity via Neutron Stars
• Asymptotically flat black holes in Horndeski theory and beyond
• Dark energy in Horndeski theories after GW170817: A review
• Neutron Stars in f(R) Gravity with Perturbative Constraints
• Analytical representations of unified equations of state of neutron-star matter
• I-Love-Q, Spontaneously: Slowly Rotating Neutron Stars in Scalar-Tensor Theories
• Black hole perturbation in the most general scalar-tensor theory with second-order field equations I: The odd-parity sector
• Non-perturbative and self-consistent models of neutron stars in R-squared gravity
• Black hole perturbation in the most general scalar-tensor theory with second-order field equations II: the even-parity sector
• Neutron stars in general second order scalar-tensor theory: the case of non-minimal derivative coupling
• Neutron stars in scalar-tensor theories of gravity and catastrophe theory
• Exact black hole solutions in shift symmetric scalar-tensor theories
• Solutions in the scalar-tensor theory with nonminimal derivative coupling
• Slowly rotating neutron stars in the nonminimal derivative coupling sector of Horndeski gravity
• On neutron stars in f(R) theories: small radii, large masses and large energy emitted in a merger
• Black Holes in Bi-scalar Extensions of Horndeski Theories
• Rapidly rotating neutron stars in scalar-tensor theories of gravity
• Stability of Schwarzschild-like solutions in f(R,G) gravity models
• Neutron star transition to strong-scalar-field state in tensor scalar gravity
• Neutron stars in Horndeski gravity
• Instability of hairy black holes in shift-symmetric Horndeski theories
• Slowly Rotating Relativistic Stars in Scalar-Tensor Gravity
• Black holes in a cubic Galileon universe
• Cosmological perturbations of a perfect fluid and noncommutative variables
• Scaling solutions and weak gravity in dark energy with energy and momentum couplings
• Linear perturbation analysis of hairy black holes in shift-symmetric Horndeski theories: Odd-parity perturbations
• Neutron stars in $f(R)$ gravity and scalar-tensor theories
• A no-hair theorem for stars in Horndeski theories
• Effective field theory of modified gravity on the spherically symmetric background: leading order dynamics and the odd-type perturbations
• Axial quasinormal modes of static neutron stars in the nonminimal derivative coupling sector of Horndeski gravity: spectrum and universal relations for realistic equations of state
• Stability of relativistic stars with scalar hairs

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• Stability of neutron stars in Horndeski theories with Gauss-Bonnet couplings
• Truly Lorentzian quantum cosmology
• Anti-de Sitter neutron stars in the theory of gravity with nonminimal derivative coupling
• Even-parity stability of hairy black holes in $U(1)$ gauge-invariant scalar-vector-tensor theories