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It is shown that the theoretical arguments for the unavoidable collapse ofmassive stars, which are valid within standard general relativity, are notvalid in extended gravity. In particular a calculation is reported of neutronstars within a theory obtained from an Einstein-Hilbert action involving afunction of $R^{2}-1/2R_{\mu \nu}R^{\mu \nu}$ added to the Ricci scalar $R$.The calculation suggests that within that theory there are stable neutron starswith arbitrarily high baryon number.

Can modified gravity prevent the gravitational collapse to black hole?