  A simple generalization to Einstein's general relativity (GR) was recently
proposed which allows a correction term $T_{\alpha\beta}T^{\alpha\beta}$ in the
action functional of the theory. This theory is called Energy-Momentum Squared
Gravity (EMSG) and introduces a new coupling parameter $\eta$. EMSG resolves
the big bang singularity and has a viable sequence of cosmological epochs in
its thermal history. {Interestingly, in the vacuum EMSG is equivalent to GR,
and its effects appear only inside the matter-energy distribution. More
specifically, its consequences appear in high curvature regime. Therefore it is
natural to expect deviations form GR inside compact stars. In order to study
spherically symmetric compact stars in EMSG, we find the relativistic governing
equations. More specifically, we find the generalized version of the
Tolman-Oppenheimer-Volkov equation in EMSG. Finally we present two analytical
solutions, and two numerical solutions for the field equations. For obtaining
the numerical solutions we use polytropic equation of state which is widely
used to understand the internal structure of neutron stars in the literature.
Eventually we find a mass-radius relation for neutron stars. Also, We found
that EMSG, depending on the central pressure of the star and the magnitude of
free parameter $\eta$, can lead to larger or smaller masses for neutron stars
compared with GR. Existence of high-mass neutron stars with ordinary polytropic
equation of state in EMSG is important in the sense that these stars exist in
GR provided that one use exotic equation of states.
