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Effects of gravitational correction through the introduction of U bosons on neutron stars with antikaon condensation are studied in the relativistic mean held theory. How the global properties of neutron stars, redshift and the momentum of inertia are modified by gravitational correction and antikaon condensation are discussed here. Results show that antikaon condensation can occur at the core of pulsar PSR J1614-2230. Gravitational correction and antikaon condensation influence each other, and when coupling constant of U bosons and baryons becomes very high, effects of antikaon condensation almost vanish. Moreover, both the redshift and the momentum of inertia of neutron stars are sensitive to the constant of U bosons. Combining with observation data, we can provide a further constraint on coupling constant of U bosons.

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