Lorentzian wormholes in Eddington-inspired Born-Infeld gravity

Abstract

We show that it is possible to construct a wide class of Lorentzian wormholes in Eddington-inspired Born-Infeld gravity with a stress energy which does not violate the weak or null energy condition.The wormholes exist in a certain region of the parameter space. In fact, it is shown that there is a critical value of a parameter defined in our work, below which we have wormholes. Above the critical value, we have a regular black hole spacetime. We put a restriction on the equation of state parameter α (p θ = αρ) to have wormholes. We also put a lower limit on both the theory parameter |κ| and the throat radius, to restrict the tidal acceleration (at the throat) below one Earth gravity.As a special case of our general solution, we retrieve the wormhole supported by an electric field for a charge-to-mass ratio greater than the critical value Q M c ≈ 1.144.

Born–Infeld inspired modifications of gravity

“…This highlights the fact that two similar wormhole structures can show very different properties regarding the behaviour of curvature invariants. This can also be observed in the case of wormholes supported by anisotropic fluids found in [327] and discussed in section 4.3, whose Euclidean embedding for the model with α = 3/4 in Eqs. (4.84) and (4.85) is also depicted in Fig.16.…”

“…For the wormhole geometry (4.79) one has [344] R0ĵ0p = γ/(2ǫ + r 2 0 ) (where γ = (1 − v 2 /c 2 ) −1/2 and v = ± |g rr /g tt |dr/dt), which is finite for any nonvanishing ǫ, and thus the presence of a throat at r 0 may avoid the infinitely large tidal forces found in the EB black hole. Shaikh [327] also uses an anisotropic fluid (4.72) to investigate wormhole structures within EiBI gravity, taking the equations of state p r = −ρ and p t = αρ (where 0 ≤ α ≤ 1 in order for the energy conditions to be satisfied). This approach differs from the one of Harko et al [194] in the gauge used for the line elements:…”

“…(2.57) can be explicitly written for this case, giving a set of three independent differential equations. Together with the fluid conservation equation, one can obtain the following solutions for the components of the line element (for ǫ < 0) as [327] ψ(r) = 1 + r 2(α+1) 0 r 2(α+1) .…”

“…In Fig.14 the metric components for the case α = 3/4 are depicted, where this transition between traversable wormholes and regular black holes with a horizon is observed. Following the analysis of Tamang et al [344], Shaikh also discusses the tidal forces upon an observer travelling through the wormhole [327]. Using the tidal acceleration 2(1−f ) 2 | r 0 = (1 − x)/r 0 > 0, which is satisfied if x < 1, implying that the wormhole throat r 0 < |ǫ| 1/2 ).…”

Massive charged BTZ black holes in asymptotically (a)dS spacetimes

“…Among various motivations for studying BI theory, one can point out obtaining BI effective action in superstring theory and absence of singularity for D-branes [86][87][88][89][90][91], and also Eddington-inspired BI theory's applications in gravitation and cosmology [92][93][94][95][96][97][98]. In addition, the functional form of BI nonlinear theory of electrodynamics has been employed as gravitational theory as well [99,100].…”