Equation of State of Neutron Star with Junction Condition Approach in Starobinsky Model Workshop on Dark Physics of the Universe National Center for Theoretical Sciences Dec. 20 th , 2015 PhD student: Wei-Xiang Feng Advisor: Prof. Chao-Qiang Geng NTHU
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Equation of State of Neutron Star with Junction Condition Approach in Starobinsky Model Workshop on Dark Physics of the Universe National Center for Theoretical.
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Equation of Stateof Neutron Star
with Junction Condition Approachin Starobinsky Model
Workshop on Dark Physics of the Universe National Center for Theoretical Sciences
Dec. 20th, 2015PhD student: Wei-Xiang Feng
Advisor: Prof. Chao-Qiang GengNTHU
Outline• Introduction
• The Coupled Ordinary Equations
• Junction & Boundary Conditions
• Numerical Results
• Buchdahl Stability Bound
• Summary
Introduction
Introduction: f(R) model
• Inflation model (Starobinsky model): A. A. Starobinsky “A new type of isotropic cosmological models without singularity”.Phys. Lett. B 91, 99 (1980). A. A. Starobinsky and H-J Schmidt “On general vacuum solution of fourth-order gravity”. Class.Quant.Grav. 4 (1987)
• Neutron star (NS) as a laboratory to test f(R)-theory
• Motivation: A. Ganguly, R. Gannouji, R. Goswami, and S. Ray “Neutron stars in Starobinsky model”10.1103/PhysRevD.89.064019, arXiv:1309.3279v2 [gr-qc]
For different • There exist solutions for and . • General feature: (1) The smaller the , the larger the . (2) The mass (radius) is smaller (bigger) for larger .
Profiles with • Ricci scalar and its derivative match the B.C. of the Schwarzschild vacuum solution.
• Ricci scalar deviates from .
• Mass function deviates much more from GR, whereas the does not. • The effective density matters.• Chandra limit of can be exceeded with .
For different with• Smaller can allow both larger mass and radius.• For ordinary matter, condition is required, therefore, we avoid for with at the center of NS.
Buchdahl Stability Bound
• In GR, we have but not (Buchdahl stability bound)
• Is there a corresponding relation for R2 model?
• In the R2 model with poly-tropic EoS, still holds for . (As we have seen from TABLE I.)
Summary• We have solved this model exactly rather than perturbatively.
• of the EoS is fine-tuned by the central values and hence the f(R) junction conditions.
• There can exist a EoS of with that has a mass exceeding the Chandra limit, i.e.