Gravitational lensing by traversable Lorentzian wormholes is a new possibility which is analyzed here in the strong field limit. Wormhole solutions are considered in the Einstein minimally coupled theory and in the brane world model. The observables in both the theories show significant differences from those arising in the Schwarzschild black hole lensing. As a corollary, it follows that wormholes with zero Keplerian mass exhibit lensing properties which are qualitatively (though not quantitatively) the same as those of a Schwarzschild black hole. Some special features of the considered solutions are pointed out.

We examine the possibility of static wormhole solutions in the vacuum Brans-Dicke theory both in the original (Jordan) frame and in the conformally rescaled (Einstein) frame. It turns out that, in the former frame, wormholes exist only in a very narrow interval of the coupling parameter, viz., $-3/2<\mathrm{}\omega <-4/3.$ It is shown that these wormholes are not traversable in practice. In the latter frame, wormhole solutions do not exist at all unless energy conditions are violated by hand.

We propose a new model of a gravastar admitting conformal motion. While retaining the framework of the Mazur–Mottola model, the gravastar is assumed to be internally charged, with an exterior defined by a Reissner–Nordström instead of a Schwarzschild line element. The solutions, obtained by exploiting an assumed conformal Killing vector, involve (i) the interior region, (ii) the shell, and (iii) the exterior region of the sphere. Of these three cases the first one is of primary interest since the total gravitational mass here turns out to be an electromagnetic mass under some specific conditions. This suggests that the interior de Sitter vacuum of a charged gravastar is essentially an electromagnetic mass model that must generate gravitational mass which provides a stable configuration by balancing the repulsive pressure arising from charge with its attractive gravity to avert a singularity. Therefore the present model, like the Mazur–Mottola model, results in the construction of a compact astrophysical object, as an alternative to a black hole. We have also analyzed various other aspects such as the stress energy tensor in the thin shell and the entropy of the system

It is shown that three of the four Brans solutions of classes I–IV admit wormhole geometry. Two-way traversable wormholes in the Brans-Dicke theory are allowed not only for the negative values of the coupling parameter ω (ω<-2), as concluded earlier, but also for arbitrary positive values of ω (ω<∞). It also follows that the scalar field φ plays the role of exotic matter violating the weak energy condition.

It has been argued that the recently detected ring-down gravity waveforms could be indicative only of the presence of light rings in a horizonless object, such as a surgical Schwarzschild wormhole, with the frequencies differing drastically from those of the horizon quasinormal mode frequencies ${\omega }_{\mathrm{QNM}}$ at late times. While the possibility of such a horizonless alternative is novel by itself, we show by the example of the Ellis-Bronnikov wormhole that the differences in ${\omega }_{\mathrm{QNM}}$ in the eikonal limit (large $l$) need not be drastic. This result will be reached by exploiting the connection between ${\omega }_{\mathrm{QNM}}$ and the Bozza strong field lensing parameters. We shall also show that the lensing observables of the Ellis-Bronnikov wormhole can be very close to those of a black hole (say, $\text{Sgr}{\mathrm{A}}^{*}$ hosted by our galaxy) of the same mass. This situation indicates that the ring-down frequencies and lensing observables of the Ellis-Bronnikov wormhole can remarkably mimic those of a black hole. The constraint on wormhole parameter $\gamma$ imposed by experimental accuracy is briefly discussed. We also provide independent arguments supporting the stability of the Ellis-Bronnikov wormhole proven recently.

Taking the flat rotation curve as input and treating the matter content in the galactic halo region as perfect fluid, we obtain space time metric at the galactic halo region in the framework of general relativity. We find that the resultant metric is a non-relativistic-dark-matter-induced space-time embedded in a static Friedmann-Lema\^itre-Robertson-Walker universe. This means that the flat rotation curve not only leads to the existence of dark matter but also suggests the background geometry of the universe. The flat rotation curve and the demand that the dark matter be non-exotic together indicate a (nearly) flat universe as favored by the modern cosmological observations. We obtain the expressions for energy density and pressure of dark matter halo and consequently the equation of state of dark matter. Various other aspects of the solution are also analyzed.