Wormholes in 4D Einstein–Gauss–Bonnet gravity

Abstract Recent times witnessed a significant interest in regularizing, a $$ D \rightarrow 4 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>D</mml:mi><mml:mo>→</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math> limit, of EGB gravity initiated by Glavan and Lin [Phys. Rev. Lett. 124, 081301 (2020)] by re-scaling GB coupling constant as $$\alpha /(D-4)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi><mml:mo>/</mml:mo><mml:mo>(</mml:mo><mml:mi>D</mml:mi><mml:mo>-</mml:mo><mml:mn>4</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math> and taking limit $$D \rightarrow 4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>D</mml:mi><mml:mo>→</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math> , and in turn these regularized 4 D gravities have nontrivial gravitational dynamics. Interestingly, the maximally or spherically symmetric solution to all the regularized gravities coincides in the 4 D case. In view of this, we obtain an exact spherically symmetric wormhole solution in the 4 D EGB gravity for an isotropic and anisotropic matter sources. In this regard, we consider also a wormhole with a specific radial-dependent shape function, a power-law density profile as well as by imposing a particular equation of state. To this end, we analyze the flare-out conditions, embedding diagrams, energy conditions and the volume integral quantifier. In particular our −ve branch results, in the limit $$\alpha \rightarrow 0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi><mml:mo>→</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math> , reduced exactly to vis- $$\grave{a}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mi>a</mml:mi><mml:mo>`</mml:mo></mml:mover></mml:math> -vis 4D Morris-Thorne of GR.

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