Quasitopological magnetic brane coupled to nonlinear electrodynamics

In this paper, we are eager to construct a new class of ($n+1$)-dimensional static magnetic brane solutions in quasitopological gravity coupled to nonlinear electrodynamics such as exponential and logarithmic forms. The solutions of this magnetic brane are horizonless and have no curvature. For $\rho$ near $r_{+}$, the solution $f(\rho )$ is dependent on the values of parameters $q$ and $n$, and for larger $\rho$, it depends on the coefficients of LoveLock and quasitopological gravities $\lambda$, $\mu$, and $c$. The obtained solutions also have a conic singularity at $r=0$ with a deficit angle that is only dependent on the parameters $q$, $n$, and $\beta$. We should remind the reader that the two forms of nonlinear electrodynamics theory have similar behaviors on the obtained solutions. At last, by using the counterterm method, we obtain conserved quantities such as mass and electric charge. The value of the electric charge for this static magnetic brane is obtained as zero.

Figure 1

$f(\rho )$ vs $\rho$ with $M=5$, $\beta =10$, $n=4$, $\lambda =-0.01$, $\mu =0.4$, and $c=-0.01$.

Figure 2

$f(\rho )$ vs $\beta$ with $M=1$, $q=2$, $n=4$, $\lambda =0.01$, $\mu =1.1$, and $c=-0.02$.

Figure 3

$f(\rho )$ vs $\rho$ for EN electrodynamics.

Figure 4

$f(\rho )$ vs $\rho$ with $M=5$, $q=3$, $\beta =10$, $\lambda =-0.01$, $\mu =0.4$, and $c=-0.1$ for EN electrodynamics.

Figure 5

$\delta \varphi$ vs $r_{+}$ with $\beta =5$ and $n=4$.

Figure 6

$\delta \varphi$ vs $r_{+}$ with $q=1$ and $n=4$ for EN electrodynamics.

Figure 7

$\delta \varphi$ vs $r_{+}$ with $q=2$ and $\beta =4$ for EN electrodynamics.