TY - JOUR

T1 - Stability of relativistic stars with scalar hairs

AU - Kase, Ryotaro

AU - Kimura, Rampei

AU - Sato, Seiga

AU - Tsujikawa, Shinji

N1 - Funding Information:
R. Kase is supported by the Grant-in-Aid for Young Scientists B of the JSPS No. 17K14297. S. T. is supported by the Grant-in-Aid for Scientific Research Fund of the JSPS No. 19K03854.
Publisher Copyright:
© 2020 American Physical Society.

PY - 2020/10

Y1 - 2020/10

N2 - We study the stability of relativistic stars in scalar-tensor theories with a nonminimal coupling of the form F(φ)R, where F depends on a scalar field φ and R is the Ricci scalar. On a spherically symmetric and static background, we incorporate a perfect fluid minimally coupled to gravity as a form of the Schutz-Sorkin action. The odd-parity perturbation for the multipoles l≥2 is ghost-free under the condition F(φ)>0, with the speed of gravity equivalent to that of light. For even-parity perturbations with l≥2, there are three propagating degrees of freedom arising from the perfect-fluid, scalar-field, and gravity sectors. For l=0, 1, the dynamical degrees of freedom reduce to two modes. We derive no-ghost conditions and the propagation speeds of these perturbations and apply them to concrete theories of hairy relativistic stars with F(φ)>0. As long as the perfect fluid satisfies a weak energy condition with a positive propagation speed squared cm2, there are neither ghost nor Laplacian instabilities for theories of spontaneous scalarization and Brans-Dicke (BD) theories with a BD parameter ωBD>-3/2 (including f(R) gravity). In these theories, provided 0

AB - We study the stability of relativistic stars in scalar-tensor theories with a nonminimal coupling of the form F(φ)R, where F depends on a scalar field φ and R is the Ricci scalar. On a spherically symmetric and static background, we incorporate a perfect fluid minimally coupled to gravity as a form of the Schutz-Sorkin action. The odd-parity perturbation for the multipoles l≥2 is ghost-free under the condition F(φ)>0, with the speed of gravity equivalent to that of light. For even-parity perturbations with l≥2, there are three propagating degrees of freedom arising from the perfect-fluid, scalar-field, and gravity sectors. For l=0, 1, the dynamical degrees of freedom reduce to two modes. We derive no-ghost conditions and the propagation speeds of these perturbations and apply them to concrete theories of hairy relativistic stars with F(φ)>0. As long as the perfect fluid satisfies a weak energy condition with a positive propagation speed squared cm2, there are neither ghost nor Laplacian instabilities for theories of spontaneous scalarization and Brans-Dicke (BD) theories with a BD parameter ωBD>-3/2 (including f(R) gravity). In these theories, provided 0

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U2 - 10.1103/PhysRevD.102.084037

DO - 10.1103/PhysRevD.102.084037

M3 - Article

AN - SCOPUS:85093527678

VL - 102

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 8

M1 - 084037

ER -