Junction conditions and thin shells in perfect-fluid f (R, T) gravity

In this work we derive the junction conditions for the matching between two spacetimes at a separation hypersurface in the perfect-fluid version of f(R, T) gravity, not only in the usual geometrical representation but also in a dynamically equivalent scalar-tensor representation. We start with the general case in which a thin shell separates the two spacetimes at the separation hypersurface, for which the general junction conditions are deduced, and the particular case for smooth matching is considered when the stress-energy tensor of the thin shell vanishes. The set of junction conditions is similar to the one previously obtained for f(R) gravity but features also constraints in the continuity of the trace of the stress-energy tensor T-ab and its partial derivatives, which force the thin shell to satisfy the equation of state of radiation sigma = 2p(t). As a consequence, a necessary and sufficient condition for spherically symmetric thin shells to satisfy all the energy conditions is the positivity of its energy density s. For specific forms of the function f(R, T), the continuity of R and T ceases to be mandatory but a gravitational double layer arises at the separation hypersurface. The Martinez thin-shell system and a thin shell surrounding a central black hole are provided as examples of application.