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Finslerian Wormholes in squared trace gravity

Z. Nekouee, B. R. Yashwanth, Manjunath Malligawad, S. K. Narasimhamurthy, S. K. J. Pacif, Kazuharu Bamba

Abstract

We investigate traversable wormholes in squared-trace extended gravity within the framework of Finsler-Randers geometry equipped with the Barthel connection. The Einstein-Hilbert action is modified by terms involving the trace of the energy-momentum tensor and its square, generating effective anisotropies through matter-curvature coupling. The resulting field equations are studied under barotropic equations of state with exponential and power-law shape functions. Finslerian anisotropy introduces novel pressure dynamics that enable the classical energy conditions to be satisfied in specific parameter domains. Our analysis shows that the Barthel connection significantly extends the parameter space for non-exotic, physically viable wormholes compared to purely Riemannian models. These findings suggest that Finslerian modifications provide a powerful mechanism for realizing realistic wormhole structures, offering new perspectives on anisotropic and geometrically enriched space-time configurations in extended gravity.

Finslerian Wormholes in squared trace gravity

Abstract

We investigate traversable wormholes in squared-trace extended gravity within the framework of Finsler-Randers geometry equipped with the Barthel connection. The Einstein-Hilbert action is modified by terms involving the trace of the energy-momentum tensor and its square, generating effective anisotropies through matter-curvature coupling. The resulting field equations are studied under barotropic equations of state with exponential and power-law shape functions. Finslerian anisotropy introduces novel pressure dynamics that enable the classical energy conditions to be satisfied in specific parameter domains. Our analysis shows that the Barthel connection significantly extends the parameter space for non-exotic, physically viable wormholes compared to purely Riemannian models. These findings suggest that Finslerian modifications provide a powerful mechanism for realizing realistic wormhole structures, offering new perspectives on anisotropic and geometrically enriched space-time configurations in extended gravity.

Paper Structure

This paper contains 13 sections, 32 equations, 7 figures, 2 tables.

Table of Contents

  1. I. Introduction
  2. II. Geometric Structures Induced by Barthel Connections in Finsler Spaces
  3. III. Conceptual Framework
  4. IV. Finslerian Perspectives on Wormhole Geometry
  5. V. Wormhole Configurations and their Compatibility with Energy Conditions
  6. A. Case 1:
  7. B. Case 2:
  8. C. Anisotropy Factor
  9. VI. A Geometric Measure of Exoticity in Traversable Wormholes
  10. A. Case 1:
  11. B. Case 2:
  12. VII. Conclusions
  13. Acknowledgements

Figures (7)

  • Figure 1: Embedding surfaces in two and three dimensions constructed from the exponential shape function $b(r)=r\textrm{e}^{-2(r-r_0)}$ and its behavior at $r_0 = 0.5$.
  • Figure 2: Satisfaction of all energy conditions (NEC, WEC, SED, DEC) at $r_0=0.5$ and $\xi<-1$.
  • Figure 3: Embedding surfaces in two and three dimensions constructed from the power-law shape function $b(r)=\sqrt{r_0r}$ and its behavior at $r_0 = 1$.
  • Figure 4: Satisfaction of all energy conditions (NEC, WEC, SED, DEC) at $r_0=1$ and $\xi<-1$.
  • Figure 5: Depictions of the pressure anisotropy ($\triangle p$).
  • ...and 2 more figures