Wormholes in 4D Einstein-Gauss-Bonnet gravity with BEC Dark Matter density profile

TL;DR

This work investigates traversable wormholes in four-dimensional Einstein-Gauss-Bonnet gravity with a phenomenological Bose-Einstein condensate density profile as the matter source. By adopting a static, spherically symmetric ansatz with a constant redshift function, the authors derive the wormhole shape function $\mathcal{S}(r)$ and the corresponding energy density and pressures from the modified field equations, enforcing throat, flaring-out, and asymptotic-flatness conditions. They analyze the embedding diagram, proper radial distance, and the volume integral quantifier to quantify exotic matter, and perform an anisotropy and stability study via the adiabatic sound speed $C_s^2$. The results reveal parameter regimes, notably $\alpha \in [-4, -4.222]$, where energy conditions can be satisfied at the throat, and a throat-stable solution exists at $\alpha = -0.0512471$, demonstrating that non-relativistic BEC matter can support stable traversable wormholes in this modified gravity setting, with potential implications for realistic wormhole configurations in higher-curvature theories.

Abstract

The existence of Traversable Wormhole (TW) in the 4D Einstein-Gauss-Bonnet (4D-EGB) gravity is explored with phenomenological Bose-Einstein Condensates (BEC) dark matter density profile. In the framework of 4D EGB gravity, which one obtains by regularizing the higher-dimensional EGB gravity in the limit $D \to 4$ is considered to obtain a spherically symmetric TW. The Gauss-Bonnet coupling parameter ($α$) in this case is rescaled to $α\to \fracα{D-4}$. Considering the energy density profile of non-relativistic BEC matter, the shape function of the WH geometry and the Null energy condition (NEC) are determined with a constant redshift function. The applicability of realistic flaring-out condition and asymptotic flatness conditions are studied here and the domain of model parameters for realistic scenario is determined. We analyze the embedding diagram of the WH obtained here with proper radial distance, volume integral quantifier, and anisotropy. We obtained WH which is stable at the throat when $α= -0.0512471$ for a set of model parameters, which is estimated from sound speed measurement. The energy conditions are investigated, and it is noted that there is a range of Gauss-Bonnet coupling parameter $α\in [-4,-4.222]$, at which the energy conditions, including NEC, are obeyed at the throat. We explore NEC for other values of $α$ and found that it is not satisfied. The other energy conditions are also violated. A new result is thus obtained with 4D Einstein-Gauss-Bonnet gravity with BEC Dark Matter profile. We determine the parameter space for which the WH solution exists in the proposed modified gravity model.

Figures (12)

• Figure 1: Shape function for different model parameters: $(R_{BE},r_0,\alpha) = (6,2,1)$(Top-left plot), $(R_{BE},r_0,\rho_0) = (6,2,0.0025)$(Top-right plot), & $(R_{BE},\rho_0,\alpha) = (6,0.0025,1)$(Bottom plot)
• Figure 2: Asymptotic flatness condition for different model parameters: $(R_{BE},r_0,\alpha) = (6,2,1)$(Top-left plot), $(R_{BE},r_0,\rho_0) = (6,2,0.0025)$(Top-right plot), & $(R_{BE},\rho_0,\alpha) = (6,0.0025,1)$(Bottom plot)
• Figure 3: flaring-out condition for different model parameters: $(R_{BE},r_0) = (6,2)$(Top-left plot), $(R_{BE},\alpha) = (6,1)$(Top-right plot), & $(R_{BE},\rho_0) = (6,0.0025)$(Bottom plot). Red area suggests: $\mathcal{S}'(r) \geq 1$, which is unacceptable.
• Figure 4: Embedding diagram of the WH for different model parameters: $(R_{BE},r_0,\alpha,\rho_0) = (6,3,1,0.0025)$(top-left and bottom-left plots), & $(R_{BE},r_0,\alpha,\rho_0) = (6,1,-1,0.0025)$(top-right and bottom-right plots)
• Figure 5: Proper radial distance of the WH for different model parameters: $(R_{BE},r_0,\alpha) = (6,2,2)$(left plot), & $(R_{BE},r_0,\rho_0) = (6,2,0.0025)$(right plot)