In this work, we propose the modeling of static wormholes within the $f(R,T)$ extended theory of gravity perspective. We present some models of wormholes, which are constructed from different hypotheses for their matter content, i.e., different relations for their pressure components (radial and lateral) and different equations of state. The solutions obtained for the shape function of the wormholes obey the necessary metric conditions. They show a behavior similar to those found in previous references about wormholes, which also happens to our solutions for the energy density of such objects. We also apply the energy conditions for the wormholes’ physical content.

F(R, T) gravity is an extended theory of gravity in which the gravitational action contains general terms of both the Ricci scalar R and the trace

In this work, I present exact cosmological solutions from Wesson’s induced matter model applied to a general 5D metric in \(f(R,T)\) theory of gravity. The non-conservation of the energy-momentum tensor, predicted by \(f(R,T)\) theory, allows the derivation of a relation that describes the time evolution of the extra coordinate, revealing its compactification. It is shown that such a compactification could induce the effects of an accelerated expansion in the observable universe.

Wormholes are tunnels connecting two different points in space-time. In Einstein’s general relativity theory, wormholes are expected to be filled by exotic matter, i.e., matter that does not satisfy the energy conditions and may have negative density. We propose, in this paper, the achievement of wormhole solutions with no need for exotic matter. In order to achieve so, we consider a gravity theory that starts from linear and quadratic terms on the trace of the energy-momentum tensor in the gravitational action. We show that by following this formalism, it is possible, indeed, to obtain nonexotic matter wormhole solutions.