Neutron stars in $f(mathcal{R,T})$ gravity using realistic equations of state in the light of massive pulsars and GW170817

In this work we investigate neutron stars (NS) in $f(mathcal{R,T})$ gravity for the case $R+2lambdamathcal{T}$, $mathcal{R}$ is the Ricci scalar and $mathcal{T}$ the trace of the energy-momentum tensor. The hydrostatic equilibrium equations are solved considering realistic equations of state (EsoS). The NS masses and radii obtained are subject to a joint constrain from massive pulsars and the event GW170817. The parameter $lambda$ needs to be negative as in previous NS studies, however we found a minimum value for it. The value should be $|lambda|lesssim0.02$ and the reason for so small value in comparison with previous ones obtained with simpler EsoS is due to the existence of the NS crust. The pressure in theory of gravity depends on the inverse of the sound velocity $v_s$. Since, $v_s$ is low in the crust, $|lambda|$ need to be very small. We found that the increment in the star mass is less than $1%$, much smaller than previous ones obtained not considering the realistic stellar structure, and the star radius cannot become larger, its changes compared to GR is less than $3.6%$ in all cases. The finding that using several relativistic and non-relativistic models the variation on the NS mass and radius are almost the same for all the EsoS, manifests that our results are insensitive to the high density part of the EsoS. It confirms that stellar mass and radii changes depend only on crust, where the EoS is essentially the same for all the models. The NS crust effect implying very small values of $|lambda|$ does not depend on the theorys function chosen, since for any other one the hydrostatic equilibrium equation would always have the dependence $1/v_s$. Finally, we highlight that our results indicate that conclusions obtained from NS studies done in modified theories of gravity without using realistic EsoS that describe correctly the NS interior can be unreliable.