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The accretion disks around black holes consist of infalling matter boosted almost to the speed of light making collisions with opposite counterpart. This is the rough picture occurring near black holes or other strongly gravitating centers that produce observed phenomena such as astrophysical jets. A toy model that can be considered imitating such a process is colliding null sources in general relativity. We present such a simple model projected into the plane of null coordinates that takes into account only neutral sources. We show that even at such a simplified model, uncharged and non-rotating, it is possible to obtain jet-like ejections albeit they lie below the horizon. In the present study the spacetime consists of either one of i) a cloud of strings, ii) a global monopole, iii) a particular model of bumblebee gravity, all described by a similar class of stress-energy tensor. There are gravitational waves accompanying the null sources and naturally collision of gravitational waves is also taken into account. After the collision, the spacetime contains both null and non-null sources, followed by trailing gravitational radiations. Locally the interaction region of the colliding null-sources and gravitational waves is isometric to the static background spacetime., Comment: Accepted by Physica Scripta

At certain time the Nariai spacetime is split into two parts. The resulting cosmology consists of the original Nariai and a new component with topology $(flat)_2\times S^2$, that is equivalent to a cloud of strings. We explore the properties of our hybrid cosmological model.

Comformally flat spacetime converts the Anti-de Sitter (AdS) spacetime into a z-dependent metric. We take advantage of this metric to solve Dirac equations in the AdS geometry analytically, including Dirac, Majorana, Dirac tachyon and Majorana tachyon. Constraints on Majorana wavefunctions limit the mass. Besides, there gives rise flatlands and Majorana particles hop in between, just mimicking the D-brane stack and open strings. Furthermore, a plausible way of ion-trapped experiment is suggested., Comment: 6 pages, 2 figures

As an extension of a thin-shell, we adopt a single parametric plane-symmetric Kasner-type spacetime to represent an exact thick-plate. This naturally extends the domain wall spacetime to a domain thick-wall case. Physical properties of such a plate with symmetry axis $z$ and thickness $0\leq z\leq z_{0}$ are investigated. Geodesic analysis determines the possibility of a Newtonian-like fall, namely with constant negative acceleration as it is near the Earth's surface. This restricts the Kasner-like exponents to a finely-tuned set, which together with the thickness and energy parameter determine the G-force of the plate. In contrast to the inverse square law, the escape velocity of the thick-shell is unbounded. The metric is regular everywhere but expectedly the energy-momentum of the thick-plate remains problematic., Comment: 11 pages, 1 figure

The non-trivial naked singularities that possess directional behavior in the charged and uncharged Zipoy-Voorhees (ZV) spacetimes, known as {\gamma} - metrics are investigated within the context of quantum mechanics. Classically singular spacetime is understood as a geodesic incompleteness with respect to a particle probe, while quantum singularity is understood as a non-unique evolution of test quantum wave packets. In this study, quantum wave packets obeying Klein - Gordon equation are used to probe timelike naked singularities. It is shown by rigorous mathematical calculations that the outermost singularity developed in the charged and uncharged Zipoy-Voorhees spacetime on the equatorial plane is quantum mechanically singular for all values of the deformation parameter {\gamma}. However, directional singularities that develop on the symmetry axis is shown to be healed partially for specific range of the parameter {\gamma}, if the analysis is restricted purposely to only specific mode (s-wave mode). Allowing arbitrary modes, classical directional singularities remains quantum singular., Comment: Slightly detailed version

Through the Ernst formalism we provide expression for a class of colliding Einstein-Maxwell (EM) metrics with cross polarization. Local isometry is imposed as a means to transform interaction region of the spacetime into stationary, charged Zipoy-Voorhees (ZV) metric in Schwarzschild coordinates. The ZV-metric is known to describe planetary/stellar objects with arbitrary topology. "The world may be seen in a grain of sand" - William Blake., Comment: A section has been added

In the 1+1-dimensional dilatonic background of Callan et al. \cite{Callan1992}, we collide fields. Real and ghost fields are considered separately. The colliding ghost fields in the lineland creates particle-like wormholes. These structures, however, collapse to a black hole whenever the supporting ghosts are removed.

Sandwich gravitational waves are given globally in terms of step functions at the boundaries. Linearized Einstein-Weyl equations are solved exactly in this background in Rosen coordinates. Depending on the geometry and composition of the sandwich wave, the neutrino's energy-momentum redistributes itself. At the test field level, since the background will not change, the neutrino's energy density in particular will show variations between positive and negative extrema when crossing the sandwich wave. This may reveal facts about the weakly interacting neutrinos in cosmology., Comment: Accepted Version to appear in Class.Quant.Grav

Starting from an integral of the interaction region of colliding Einstein-Maxwell waves and by applying a coordinate transformation, we obtain the charged version of the static Zipoy-Voorhees (ZV) metric valid for all values of the distortion parameter $\gamma$. In Schwarzschild coordinates, we investigate the effect of the charge in the newly found spacetime, stress the analogy with Reissner - Nordstrom metric and discuss some of its features. It is shown that from the expression of Weyl curvature, directional singularities become manifest. For astrophysical importance, we find lensing of null geodesics from the Gauss - Bonnet theorem in such non - spherically charged objects. To prepare the ground for our null, circular geodesics we consider the angular equation linearized about the symmetry plane $\theta=\pi/2$. This, in turn, suggests the distortion parameter (the $ZV$ parameter) must be in the interval $1/2<\gamma<1$. It is found that the lensing angle is highly dependent on the distortion parameter, and becomes decisive on the effect of the charge. For a class of charged compact stars, we plot the deflection angle versus the ratio of impact parameter to the radius of the star. Plots have revealed that for perfectly spherical compact stars, it is hard to identify the effect of electric/magnetic charge, but for non-spherical compact stars the effect of electric charge becomes apparent. For comparison, the same lensing angle has also been found for the stationary ZV metric in the equatorial plane. Our analysis indicates that depending on the value of $\gamma$, the stationary state induces counter effect on the bending angle and thus, when compared with the uncharged static ZV case, the bending angle decreases. The influence of the parameter $\gamma$ on the gravitational redshift is also displayed., Comment: New sections are added and supported with new graphs. Typos are corrected. Matched with published version

In this paper, based on the thin-shell formalism, we introduce a classical model for particles in the framework of $n+1-$dimensional $\left[\frac{n}{2}\right]$-order pure Lovelock gravity. In particular, we construct a spherically symmetric particle of radius $a$ whose inside is a flat Minkowski spacetime while its outside is charged pLG solution. Knowing that in $n+1-$dimensional spherically symmetric Einstein gravity ($R$-gravity) such a particle model cannot be constructed, as we have discussed first, provides the main motivation for this study. In fact, it is the richness of Lovelock parameters that provides such a particle construction possible. On the thin-shell, the energy-momentum components are chosen to vanish, yet their normal derivatives are non-zero., Comment: 9 pages, No figures

The quartic self-interacting conformal scalar field is used to construct a thin-shell wormhole satisfying all energy conditions. Accompanying the scalar field is the extremal Reissner-Nordstr\"om black hole with a positive cosmological constant. New junction conditions apt for the higher-order terms are introduced in the Gaussian normal coordinates. Our approach may provide a guideline towards getting rid of exotic matter in TSWs., Comment: 5 pages, 1 figure (including 6 subfigures)

By using the formalism of thin-shells, we construct a geometrical model of a particle in third-order Lovelock gravity. This particular theory which is valid at least in 7 dimensions, provides enough degrees of freedom and grounds towards such a construction. The particle consists of a flat interior and a non-black hole exterior spacetimes whose mass, charge, and radius are determined from the junction conditions, in terms of the parameters of the theory., Comment: 7 pages, 1 figure (7 subfigures)

We investigate the infinite discontinuity points of stability diagram in thin-shell wormholes. The square of the speed of sound $\beta _{0}^{2}$,\ which is expressed in terms of pressure and energy density at equilibrium on the throat, arises with a divergent amplitude. As this is physically non-acceptable, \ we revise the equation of state, such that by fine-tuning of the pressure at static equilibrium, which is at our disposal, eliminates such a singularity. The efficacy of the method is shown in Schwarzschild, extremal Reissner-Nordstr\"{o}m, and dilaton thin-shell wormholes., Comment: 10 pages, 6 figures

Recently, ultra diffuse galaxy (UDG) of Dragonfly 44 in the Coma Cluster was observed and observations of the rotational speed suggest that its mass is almost same as the mass of the Milky Way. On the other hand, interestingly, the galaxy emits only 1 \% of the light emitted by the Milky Way. Then, astronomers reported that Dragonfly 44 may be made almost entirely of dark matter. In this study we try to show that the dark matter that constitutes Dragonfly 44 can form the wormhole or not. Two possible dark matter profiles are used, namely, ultra diffuse galaxy King's model and generalized Navarro-Frenk-White (NFW) dark matter profile. We have shown that King's model dark matter profile does not manage to provide wormhole whereas generalized Navarro-Frenk-White (NFW) dark matter profile is managed to find wormholes., Comment: 8 pages, two columns. Accepted for publication in Canadian Journal of Physics

A regular class of static, cylindrically symmetric pure magnetic field metrics is rederived in a different metric ansatz in all dimensions. Radial, time dependent perturbations show that for dimensions d>3 such spacetimes are stable at both near r\approx0 and large radius r\rightarrow\infty. In a different gauge these stability analysis and similar results were known beforehand. For d=3, however, simultaneous stability requirement at both, near and far radial distances can not be reconciled for time - dependent perturbations. Restricted, numerical geodesics for neutral particles reveal a confinement around the center in the polar plane. Charged, time-like geodesics for d=4 on the other hand are shown numerically to run toward infinity., Comment: 11 pages, 3figures

A method is given to generate the non-linear interaction (collision) of linearly polarized gravity coupled torsion waves in a non-metric theory. Explicit examples are given in which strong mutual focussing of gravitational waves containing impulsive and shock components coupled with torsion waves does not result in a curvature singularity. However, the collision of purely torsion waves displays a curvature singularity in the region of interaction., Comment: 16 pages, 1 ps figure, It will appear in Int. Jour. of Theor. Physics

By gauging an Abelian electromagnetic (em) solution through a non-Abelian transformation and in accordance with a theorem proved long time ago, we construct a simple class of colliding Einstein-Yang-Mills (EYM) plane waves. The solution is isometric to the Wu-Yang charged Kerr-Newman (KN) black hole and shares much of the properties satisfied by colliding Einstein-Maxwell (EM) plane waves. In the linear polarization limit with unit degenerate charge it reduces to the Bell-Szekeres (BS) solution for colliding em shock waves., Comment: 9 pages, no figures, To appear in IJMPA

The Cauchy horizon forming colliding wave solution due to Chandrasekhar and Xanthopoulos (CX) has been generalized by inclusion of the NUT (Newman - Unti - Tamburino) parameter. This is done by transforming the part of the inner horizon region of a Kerr-Newman-NUT black hole into the space of colliding waves. By taking appropriate combination of Killing vectors and analytically extending beyond the Cauchy horizon the time-like hyperbolic sigularities are resolved as well. This provides another example of its kind among the type - D metrics with special emphasis on the role of the NUT parameter. Finally, it is shown that horizons of colliding higher dimensional plane waves obtained from the black p-branes undergoes a similar procedure of analytic extension., Comment: 26 pages. 3 ps figures

A method is given which renders indirect detection of strong gravitational waves possible. This is based on the reflection (collision) of a linearly polarized electromagnetic shock wave from (with) a cross polarized impulsive and shock gravitational waves in accordance with the general theory of relativity. This highly non-linear process induces a detectable Faraday rotation in the polarization vector of the electromagnetic field., Comment: Final version. Minor revision, new figures and references are added. To appear in Physical Review D

We consider colliding wave packets consisting of hybrid mixtures of electromagnetic, gravitational and scalar waves. Irrespective of the scalar field, the electromagnetic wave still reflects from the gravitational wave. Some reflection processes are given for different choice of packets in which the Coulomb-like component $\Psi_2$ vanishes. Exact solution for multiple reflection of an electromagnetic wave from successive impulsive gravitational waves is obtained in a closed form. It is shown that a succesive sign flip in the Maxwell spinor arises as a result of encountering with an impulsive train (i.e. the Dirac's comb curvature) of gravitational waves. Such an observable effect may be helpful in the detection of gravitational wave bursts., Comment: 20 pages, 3 ps figures, small typos corrected, published version

The correspondence between black holes and colliding waves extends to cover the near horizon geometry of rotating black holes and colliding waves with cross polarization. Extreme Kerr and Kerr-Newman geometries are given as examples., Comment: 6 pages

It was believed that when gravitational, electromagnetic and scalar waves interact, a spacelike curvature singularity or Cauchy horizon develops because of mutual focusing. We show with an exact solution that the collision of Einstein-Maxwell-Scalar fields, in contrast to previous studies, predicts singularities on null surfaces and that this is a transition phase between spacelike singularities and regular horizons. Divergences of tidal forces in the null singularities is shown to be weaker relative to the spacelike ones. Using the local isometry between colliding plane waves and black holes, we show that the inner horizon of Reissner-Nordstrom black hole transforms into a null singularity when a particular scalar field is coupled to it. We also present an analytic exact solution, which represents a Reissner-Nordstrom black hole with scalar hair in between the ergosphere., Comment: 21 pages, 2 ps figures, submitted for publication

Colliding Einstein-Maxwell-Scalar fields need not necessarily doomed to become in a spacelike singularity. Examples are given in which null singularities emerge as intermediate stages between a spacelike singularity and a regular horizon., Comment: 6 pages, no figures

Single pulse of null dust and colliding null dusts both transform a regular horizon into a space-like singularity in the space of colliding waves. The local isometry between such space-times and black holes extrapolates these results to the realm of black holes. However, inclusion of particular scalar fields instead of null dusts creates null singularities rather than space-like ones on the inner horizons of black holes., Comment: Final version to appear in PRD

The quasiregular singularities (horizons) that form in the collision of cross polarized electromagnetic waves are, as in the linear polarized case unstable. The validity of the Helliwell-Konkowski stability conjecture is tested for a number of exact back-reaction cases. In the test electromagnetic case the conjecture fails to predict the correct nature of the singularity while in the scalar field and in the null dust cases the aggrement is justified., Comment: Latex file, 26 pages, 1 ps figure