Some recent papers have claimed the existence of static, spherically symmetric wormhole solutions to gravitational field equations in the absence of ghost (or phantom) degrees of freedom. We show that in some such cases the solutions in question are actually not of wormhole nature while in cases where a wormhole is obtained, the effective gravitational constant G_eff is negative in some region of space, i.e., the graviton becomes a ghost. In particular, it is confirmed that there are no vacuum wormhole solutions of the Brans-Dicke theory with zero potential and the coupling constant ω> -3/2, except for the case ω= 0; in the latter case, G_eff < 0 in the region beyond the throat. The same is true for wormhole solutions of F(R) gravity: special wormhole solutions are only possible if F(R) contains an extremum at which G_eff changes its sign.
We reconsider the issue of whether scalar-tensor theories can admit stable wormhole configurations supported by a non-trivial radial profile for the scalar field. Using a recently proposed effective theory for perturbations around static, spherically symmetric backgrounds, we show that scalar-tensor theories of "beyond Horndeski" type can have wormhole solutions that are free of ghost and gradient instabilities. Such solutions are instead forbidden within the more restrictive "Horndeski" class of theories.
We consider disformal transformations in a subclass of Horndeski theory in which a scalar field is kinetically coupled to the Einstein tensor. We apply a disformal transformation on a seed hairy black hole solution of this theory and we show that there is a transition of a black hole to a wormhole. We also show that the null energy condition is violated in the wormhole configuration and we study the stability of the wormhole solution by calculating the time evolution of scalar perturbations in this geometry.
We obtain a large class of Lorentzian wormhole spacetimes in scalar-tensor gravity, for which the matter stress energy does satisfy the weak energy condition. Our constructions have zero Ricci scalar and an everywhere finite, non-zero scalar field profile. Interpreting the scalar-tensor gravity as an effective on-brane theory resulting from a two-brane Randall--Sundrum model of warped extra dimensions, it is possible to link wormhole existence with that of extra dimensions. We study the geometry, matter content, gravitational red-shift and circular orbits in such wormholes and argue that our e…
We show that the cold horizon of the extremal Reissner-Nordström can be considered as the throat of a thin-shell wormhole with zero total exotic matter and positive angular pressure. Such a wormhole is physical and stable against radial perturbations provided an appropriate perfect fluid exists at the throat.
Two critical issues in the study of Morris-Thorne wormholes concerns the stability of such structures, as well as their compatibility with quantum field theory. This note discusses an important subset characterized by zero tidal forces. It is shown that such wormholes (1) are in stable equilibrium using a criterion based on the Tolman-Oppenheimer-Volkoff (TOV) equation and (2) are not in direct conflict with quantum field theory.
Wormholes that meet the flare-out condition violate the weak energy condition in classical general relativity. The purpose of this note is to show that even a slight modification of the gravitational theory could, under certain conditions, avoid this violation for matter threading the wormhole. The first part discusses some general criteria based on the field equations, while the second part assumes a specific equation of state describing normal matter, together with a particular type of shape function. The analysis is confined to wormholes with zero tidal forces.
We consider spinning generalizations of the Ellis wormhole in scalar-tensor theory. Analogous to other compact objects these wormholes can carry a non-trivial scalarization. We determine the domain of existence of the scalarized wormholes and investigate the effect of the scalarization on their properties. Depending on the choice of the coupling function, they may possess multiple throats and equators in the Jordan frame, while possessing only a single throat in the Einstein frame.
Wormholes are tunnels connecting two different points in space-time. In Einstein's General Relativity theory, wormholes are expected to be filled by exotic matter, i.e., matter that does not satisfy the energy conditions and may have negative density. We propose, in this paper, the achievement of wormhole solutions with no need for exotic matter. In order to achieve so, we consider quadratic terms in the trace of the energy-momentum tensor as corrections to the effective energy-momentum tensor of the underlined theory of gravity. We show that by following this formalism, it is possible, indeed…
In order to be traversable, the static Lorentzian wormhole must be made out of some exotic matter that violates the weak energy condition. The quantized fields are the natural candidates as their stress-energy tensor, in many cases, possesses desired properties. In this paper we construct and examine the stress-energy tensor of the quantized massive scalar, spinor and vector fields in six static wormhole spacetimes. We find that in all considered cases the quantum fields violate the Morris-Thorne conditions and do not have the form necessary to support the wormhole throat. This is in concord w…
We study gravitational lensing by a class of zero Ricci scalar wormholes which arise as solutions in a scalar-tensor theory of gravity. An attempt is made to find a possible link between lensing features, stable/unstable photon orbits and the energy conditions on the matter required to support these spacetimes. Our analysis shows (for this class of wormholes) that light rays always exhibit a positive deflection if the energy conditions are satisfied (nonexotic matter content). In contrast, if the energy conditions are violated (exotic matter), the net deflection of a light ray may be positive,…
We study a new approach for the wormhole construction in Einstein-Born-Infeld gravity, which does not require exotic matters in the Einstein equation. The Born-Infeld field equation is not modified from "coordinate independent" conditions of continuous metric tensor and its derivatives, even though the Born-Infeld fields have discontinuities in their derivatives at the throat in general. We study the relation of the newly introduced conditions with the usual continuity equation for the energy-momentum tensor and the gravitational Bianchi identity. We find that there is no violation of energy c…
In this paper, we develop an iterative approach to span the whole set of exotic matter models able to drive a traversable wormhole. The method, based on a Taylor expansion of metric and stress-energy tensor components in a neighbourhood of the wormhole throat, reduces the Einstein equations to an infinite set of algebraic conditions, which can be satisfied order by order. The approach easily allows the implementation of further conditions linking the stress-energy tensor components among each other, like symmetry conditions or equations of state. The method is then applied to some relevant exa…
A gravitational theory of a scalar field non-minimally coupled with torsion and boundary term is considered with the aim to construct Lorentzian wormholes. Geometrical parameters including shape and redshift functions are obtained for these solutions. We adopt the formalism of Noether Gauge Symmetry Approach in order to find symmetries, Lie brackets and invariants (conserved quantities). Furthermore by imposing specific forms of potential function, we are able to calculate metric coefficients and discuss their geometrical behavior.
The SYK model has a wormhole-like solution after averaging over the fermionic couplings in the nearly $AdS_2$ space. Even when the couplings are fixed the contribution of these wormholes continues to exist and new saddle points appear which are interpreted as "half-wormholes". In this paper, we will study the fate of these wormholes in a model without quenched disorder namely a tensor model with $O(N)^{q-1}$ gauge symmetry whose correlation function and thermodynamics in the large $N$ limit are the same as that of the SYK model. We will restate the factorization problem linked with the wormhol…
In this study, we reach the equations of motion of Morris-Thorne wormhole geometry by means of the Einstein Field Equations and Klein-Gordon Equation of Scalar-Tensor theory by direct calculation. We discuss the anisotropic matter energy distribution. We determine a relation between the radial and the transverse pressures. Hence, we express the anisotropic energy momentum tensor in terms of one pressure class, by means of that relation. Besides that, we check the isotropic case and show that there is no traversable wormhole, in the zero redshift function situation, if the space is fulfilled wi…
We present a new class of solutions for static spherically symmetric wormhole spacetimes in conformal gravity and outline a detailed method for their construction. As an explicit example, we construct a class of traversable and non-traversable wormholes that are locally conformal to Schwarzschild-(anti) de Sitter spacetimes. These wormhole spacetimes are exact vacuum solutions in, but not being limited to, Weyl gravity and conformal scalar-tensor theories. Importantly, the method implies that every conformal theory of gravity with static spherically symmetric solutions will trivially contain w…
We obtain a static spherically symmetric wormhole solution due to the vacuum expectation value (VEV) of a Kalb-Ramond field. The Kalb-Ramond VEV is a background tensor field which produces a local Lorentz symmetry breaking (LSB) of spacetime. Considering a non-minimal coupling between the Kalb-Ramond (VEV) and the Ricci tensor, we found an exact traversable wormhole solution sustained by matter sources with a negative isotropic pressure. The matter source satisfies the energy conditions at the throat for particular choices of the LSB parameter. Moreover, we employ the Gauss-Bonnet method to an…
The so-called hybrid metric-Palatini theory of gravity (HMPG), proposed in 2012 by T. Harko et al., is known to successfully describe both local (solar-system) and cosmological observations. This paper gives a complete description of static, spherically vacuum solutions of HMPG in the simplest case where its scalar-tensor representation has a zero scalar field potential $V(ϕ)$, and both Riemannian ($R$) and Palatini ($\cal R$) Ricci scalars are zero. Such a scalar-tensor theory coincides with general relativity with a phantom conformally coupled scalar field as a source of gravity. Generic asy…
We discuss how the assumption of variable equation of state (EoS) allows the elimination of the instability at equilibrium throat radius $a_0=3M$ featured by previous Schwarzschild thin-shell wormhole models. Unobstructed stability regions are found for three choices of variable EoS. Two of these EoS entail linear stability at every equilibrium radius. Particularly, the thin-shell remains stable as $a_0$ approaches the Schwarzschild radius $2M$. A perturbative analysis of the wormhole equation of motion is carried out in the case of variable Chaplygin EoS. The squared proper angular frequency …
We construct a large class of explicit, asymptotically flat and regular wormhole solutions in higher order scalar tensor theories. The solutions are vacuum solutions of scalar tensor theory and no matter (exotic or regular) is introduced in order to support them. They are constructed via a general disformal transformation of a seed black hole solution. The seed solutions belong to a particular Horndeski theory which requires the presence of all extended Galileons and has a higher dimensional Lovelock origin. As a result, the resulting wormholes are always solutions of general beyond Horndeski …
Noether symmetry has been invoked to explore the forms of a couple of coupling parameters and the potential appearing in a general scalar-tensor theory of gravity in the background of Robertson-Walker space-time. Exact solutions of Einstein's field equations in the familiar Brans-Dicke, Induced gravity and a General non-minimally coupled scalar-tensor theories of gravity have been found using the conserved current and the energy equation, after being expressed in a set of new variables. Noticeably, the form of the scale factors remains unaltered in all the three cases and represents cosmologic…
We construct an asymptotically flat Morris-Thorne wormhole solution supported by anisotropic matter fluid and a vector field which is coupled to gravity in a non-minimal way with broken Abelian gauge symmetry. In this paper, a specific shape function is considered. We find that the ansatz of vector field plays a significant role in determining the spacetime geometry of the wormhole. If there exists the electrostatic potential only, the redshift function could be considered as a constant value, implying the vanishing tidal force. However, when the vector potential in radial-direction is involve…
Recently, it has been shown by Lobo, Parsaei and Riazi (LPR) that phantom energy with $ω=p_{r}/ρ<-1$ could support phantom wormholes. Several classes of such solutions have been derived by them. While the inner spacetime is represented by asymptotically flat phantom wormhole that have repulsive gravity, it is most likely to be unstable to perturbations. Hence, we consider a situation, where a phantom wormhole is somehow trapped inside a Schwarzschild sphere across a thin shell. Applying the method developed by Garcia, Lobo and Visser (GLV), we shall exemplify that the shell can possess zones o…
Stress-energy tensor of quantized scalar fields in a zero-tidal wormhole
School of Physics and Optoelectronics, South China University of Technology（华南理工大学物理与光电工程学院）；Faculty of Arts and Sciences, Beijing Normal University, Zhuhai（北京师范大学珠海校区文理学院）
In this essay I argue that the Hilbert space of states dual to a traversable wormhole is smaller than the tensor product of the independent Hilbert spaces of the boundary field theories. From the point of view of semiclassical physics, the decrease in the number of states is perceived as an emergent, non-local interaction stabilizing the wormhole. This presents new possibilities for models of radiating black holes and raises questions about results established under the spell of the tensor product.
In this work, we analyse the evolution of time-dependent traversable wormhole geometries in a Friedmann-Lemaître-Robertson-Walker background in the context of the scalar-tensor representation of hybrid metric-Palatini gravity. We deduce the energy-momentum profile of the matter threading the wormhole spacetime in terms of the background quantities, the scalar field, the scale factor and the shape function, and find specific wormhole solutions by considering a barotropic equation of state for the background matter. We find that particular cases satisfy the null and weak energy conditions for al…
An interesting class of scalar-tensor models, denoted by kinetic gravity braiding (KGB), has recently been proposed. These models contain interactions of the second derivatives of the scalar field that do not lead to additional degrees of freedom and exhibit peculiar features, such as an essential mixing of the scalar $ϕ$ and tensor kinetic $X$ terms. In this work, we consider the possibility that wormhole geometries are sustained by the KGB theory. More specifically, we present the full gravitational field equations in a static and spherically symmetric traversable wormhole background, and ou…
Quasinormal modes of a two-parameter family of Lorentzian wormhole spacetimes, which arise as solutions in a specific scalar-tensor theory associated with braneworld gravity, are obtained using standard numerical methods. Being solutions in a scalar-tensor theory, these wormholes can exist with matter satisfying the Weak Energy Condition. If one posits that the end-state of stellar-mass binary black hole mergers, of the type observed in GW150914, can be these wormholes, then we show how their properties can be measured from their distinct signatures in the gravitational waves emitted by them a…
When Morris and Thorne first proposed the possible existence of traversable wormholes, they adopted the following strategy: maintain complete control over the geometry, thereby leaving open the determination of the stress-energy tensor. In this paper we determine this tensor by starting with a noncommutative-geometry background and assuming that the static and spherically symmetric spacetime admits conformal motions. This had been established in a previous collaboration with Rahaman et al. using a slightly different approach. Accordingly, the main purpose of this paper is to show that the worm…
In this paper we have examined the validity of some proposed definitions of gravitational entropy (GE) in the context of traversable wormhole solutions of the Einstein field equations. Here we have adopted two different proposals of GE and checked for their applicability in the case of these wormholes. The first one is the phenomenological approach proposed by Rudjord et al \cite{entropy1} and expanded by Romero et al in \cite{entropy2}, which is a purely geometric method of measuring gravitational entropy. The latter one is the Clifton-Ellis-Tavakol (CET) proposal \cite{CET} for the gravitati…
The presented thesis is devoted to the study of instabilities of compact objects within the Einstein-Gauss-Bonnet theory. This theory includes higher-order corrections in curvature, which are inspired by the low energy limit of string theory. We study linear instability of higher-dimensional black holes in the de Sitter universe. The time-domain picture allows us to obtain the parametric region of stability for the gravitational perturbations in all three channels, i.e., for scalar-type, vector-type, and tensor-type perturbations. We observed that while the scalar and tensor channels show inst…
We introduce a new coupling between stress tensors of the CFTs living on the two boundaries of the BTZ black hole. Similar to the $T \bar{T}$-deformation, the system exhibits universal properties and is solvable. The resulting geometry is an extreme case of a wormhole with the right and left BTZ wedges glued together along the horizons. We show that the geometry is realized by uniform shock waves emanating from both asymptotic boundaries. The construction has profound implications for the structure of the Hilbert space of states of the dual QFT.
