Combined Rastall and rainbow theories of gravity with applications to neutron stars

The possibility of modifications on general relativity is investigated. We propose an alternative theory of gravity constructed with the combination of Rastall and rainbow theories. The hydrostatic equilibrium equations are obtained in order to test the new theory in neutron stars, whose mass-radius diagrams are obtained using modern equations of state of nuclear matter derived from relativistic mean field models and compared with the ones computed by the Tolman-Oppenheimer-Volkoff equations. Different sets of parameters are used and the obtained results confronted with accepted masses and radii values, including important astrophysical objects as the quiescent LMXB NGC 6397 and the double neutron system J0737. We conclude that substantial modifications are obtained even for very small alterations on the two free parameters, making the reproduction of astrophysical observations an easier task.

Figure 1

Mass-radius relation for a family of hadronic stars described with the IU-FSU EoS. We analyze the effects caused by varying the Rainbow parameter $\mathrm{\Sigma }$ (left) while keeping the other parameter fixed and the effects of varying the Rastall parameter $\lambda$ (right) while keeping $\mathrm{\Sigma }$ fixed.

Figure 2

IU-FSU EoS (solid line) and corresponding RR EoS (dashed line) obtained with the parameters named ${\mathrm{RR}}_{\lambda 4}$ in Table 1.

Figure 3

Mass-radius relation for a family of hadronic stars described with the QMC EoS. We analyze the effects caused by varying the rainbow parameter $\mathrm{\Sigma }$ (left) while keeping the other parameter fixed and the effects of varying the Rastall parameter $\lambda$ (right) while keeping $\mathrm{\Sigma }$ fixed.

Figure 4

Mass-radius relation for a family of hadronic stars described with the $\mathrm{QMC}\omega \rho$ EoS. We analyze the effects caused by varying the Rainbow parameter $\mathrm{\Sigma }$ (left) while keeping the other parameter fixed and the effects of varying the Rastall parameter $\lambda$ (right) while keeping $\mathrm{\Sigma }$ fixed.