Non-exotic wormholes in $f(R,L_m)$ gravity

TL;DR

The paper addresses the longstanding issue that traversable wormholes in General Relativity require exotic matter by exploring wormholes in extended $f(R,L_m)$ gravity, which couples curvature and matter. It analyzes two representative forms, a linear model $f(R,L_m)=\alpha\frac{R}{2}+\beta L_m$ and a nonlinear model $f(R,L_m)=\frac{R}{2}+L_m^\alpha$, using a variational derivation of the field equations for an anisotropic fluid and imposing a constant redshift function with a power-law shape function $b(r)=r^m$. The results show that the linear model can yield non-exotic solutions when $\alpha/\beta<0$ for suitable $m$, while the nonlinear model admits parameter regions where NEC, WEC, and SEC can hold (though DEC may fail), with concrete examples such as $b(r)=1/r^3$ and $\alpha=-2$; the power-law shape also leads to a linear EoS $p=\omega\rho$ and non-isotropic, EC-respecting wormholes in certain regimes. Overall, the work demonstrates that curvature–matter coupling in $f(R,L_m)$ gravity can alleviate the need for exotic matter in wormhole configurations and highlights directions for future observational and solar-system tests to assess viability.

Abstract

In the present analysis, we examine the potential existence of generalized wormhole models within the framework of newly developed extended $f(R,L_m)$ gravity. We investigate both a linear model, $f(R,L_m)=αR+βL_m$, and a non-linear model, $f(R,L_m)=\frac{R}{2}+ L^α_m$, to analyze traversable wormholes. By employing the variational approach, we derive modified versions of the field equations under the influence of an anisotropic matter source. A power-law shape function is applied, resulting in a linear equation of state for both radial and lateral pressures. Furthermore, we explore solutions characterized by a variable equation of state parameter. It was observed that the violation of energy conditions is influenced by the parameters $α$ and $β$. A wide range of non-exotic wormhole solutions was discovered, dependent on the specific parameters of the model. We demonstrate that wormholes with power-law shape functions yield solutions that comply with the energy conditions in both linear and non-linear forms of $f(R, L_m)$. It is shown that the non-exotic wormhole solutions obtained within this framework are not isotropic.

Figures (2)

• Figure 1: The graph depicts the correlation between $S_1(\alpha, m)$ and the variables $\alpha$ and $m$. It is clear that $S_1$ is positive within a certain range of $\alpha$ and $m$ (a), while $S_1$ is negative in a different range (b).
• Figure 2: The graph depicts the functions $\rho(r)$(red), $H(r)$(green), $H_1(r)=H_3(r)$(yellow), $H_2(r)$(blue), and $H_4(r)$(violet) plotted against the radial coordinate for the shape function $b(r)=1/r^3$ within the framework of $f(R, L_m)=R/2+L_m^{-2}$. It is evident that all ECs, except for the DEC, are satisfied. See the text for details.