Modeling wormholes in $f(R,T)$ gravity

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.

Figure 1

The shape function $b(r)$, with $A=1$ and $n=-0.4$.

Figure 2

Violation of the NEC, $\rho +p_r\le 0$, with $A=1$ and $\lambda =-12$.

Figure 3

The NEC, $\rho +p_l\ge 0$, with $A=1$ and $\lambda =-12$.

Figure 4

The DEC, $\rho \ge |p_r|$, with $A=1$ and $\lambda =-12$.

Figure 5

The DEC, $\rho \ge |p_l|$, with $A=1$ and $\lambda =-12$.

Figure 6

$b(r)$ with $b_0=1$ and $\omega =10$.

Figure 7

Violation of the NEC, $\rho +p_r\le 0$, with $b_0=1$ and $\lambda =-12$.

Figure 8

Validity region of the NEC, $\rho +p_l\ge 0$, with $b_0=1$ and $\lambda =-12$.

Figure 9

Validity of the DEC, $\rho \ge |p_r|$, with $b_0=1$ and $\lambda =-12$.

Figure 10

Violation of the DEC, $\rho \ge |p_l|$, with $b_0=1$ and $\lambda =-12$.

Figure 11

$b(r)$ with $r_0=1,B=4$ and $m=2$.

Figure 12

Violation of the NEC, $\rho +p_r\le 0$, with $r_0=1$, $B=4$ and $\lambda =-12$.

Figure 13

The NEC, $\rho +p_l\ge 0$, with $r_0=1$, $B=4$ and $\lambda =-12$.

Figure 14

Validity of the DEC, $\rho \ge |p_r|$, with $r_0=1$, $B=4$ and $\lambda =-12$.

Figure 15

Violation of the DEC, $\rho \ge |p_l|$, with $r_0=1$, $B=4$ and $\lambda =-12$.