Ellis--Bronnikov wormhole in Quasi-topological Gravity

TL;DR

This work constructs higher-dimensional Ellis--Bronnikov traversable wormholes in $D>4$ quasi-topological gravity with a phantom scalar field and analyzes how higher-curvature corrections, parameterized by $\alpha$ and truncation order $N$, and the spacetime dimension $D$ affect the wormhole geometry, mass $M$, scalar charge $\mathcal{D}$, and near-throat properties. By reducing the field equations to a throat-adapted coordinate system with functions $A(r)$ and $p(r)$ and introducing the integration constant $\mathcal{D}$ via $N(l)f(l)l^{D-2}\phi'(l)=\sqrt{\mathcal{D}}$, the authors perform detailed numerical studies over parameter spaces. They find that larger $\alpha$ generally increases $M$ and suppresses $\mathcal{D}$ and NEC violation, while higher truncation order $N$ weakens mass growth and further reduces phantom-field dependence; a horizon-like dip in $-g_{tt}$ can emerge at the throat and the Kretschmann scalar $K$ typically decreases with stronger corrections. Dimensional effects show $D=6$ can yield significantly larger masses and different curvature and energy-condition behaviors compared to $D=5$, with embedding diagrams confirming throat modulation by $\alpha$ and $N$. The results suggest quasi-topological gravity as a viable framework for wormholes and point to future work on 4D realizations, stability analyses, and broader quasi-topological constructions.

Abstract

We construct higher-dimensional traversable wormholes in quasi-topological gravity (QTG) supported by a phantom scalar field. Using a static, spherically symmetric ansatz, we numerically analyze how quasi-topological gravity corrections affect the geometry and physical properties of the wormhole solutions. The resulting wormhole solutions are symmetric about the throat. Negative mass can arise for certain choices of parameters. For certain parameter ranges, the scalar charge $\mathcal{D}$ of the phantom field rapidly decreases with increasing the higher-curvature coupling parameter $α$ and approaches zero. Moreover, by changing $α$, the overall level of the Kretschmann scalar is also lowered. Finally, for sufficiently large $α$, $-g_{tt}$ becomes close to zero near the throat, exhibiting a ``horizon''-like structure.

Figures (14)

• Figure 1: For $D=5$, the total mass $M$ (top row) and the scalar charge $\mathcal{D}$ (bottom row) as functions of the coupling parameter $\alpha$. Different curves correspond to different truncation orders $N$ and different coefficient configurations $\{\alpha_n\}$.
• Figure 2: The function $-g_{tt}\equiv e^{(D-3)A(r)}$ (panels (a)--(c)) and the quantity $\alpha\psi$ (panel (d)) as functions of the radial coordinate $x$. Different curves correspond to different truncation orders $N$ and representative values of $\alpha$, with the coefficients chosen as $\alpha_n=\alpha^{\,n-1}$.
• Figure 3: The function $-g_{tt}$ for different values of $\alpha$. Solid curves correspond to $\alpha_n=\alpha^{\,n-1}$, while dashed curves correspond to $\alpha_n=\frac{1-(-1)^n}{2}\alpha^{\,n-1}$.
• Figure 4: The distribution of the Kretschmann scalar $K$ as a function of the radial coordinate $x$. Solid curves correspond to $\alpha_n=\alpha^{\,n-1}$, while dashed curves correspond to $\alpha_n=\frac{1-(-1)^n}{2}\alpha^{\,n-1}$.
• Figure 5: The variation of NEC ($-T^t_t+T^r_r$) violation with the radial coordinate $x$. Panels (a)--(c) correspond to different truncation orders $N$, with the coefficients chosen as $\alpha_n=\alpha^{\,n-1}$.