We study the geodesic equation in the space-time of an Abelian-Higgs string and discuss the motion of massless and massive test particles. The geodesics can be classified according to the particles energy, angular momentum and linear momentum along the string axis. We observe that bound orbits of massive particles are only possible if the Higgs boson mass is smaller than the gauge boson mass, while massless particles always move on escape orbits. Moreover, neither massive nor massless particles can ever reach the string axis for non-vanishing angular momentum. We also discuss the dependence of light deflection by a cosmic string as well as the perihelion shift of bound orbits of massive particles on the ratio between Higgs and gauge boson mass and the ratio between symmetry breaking scale and Planck mass, respectively.
We show that the extreme six-dimensional black string admits a conformal isometry under inversion. Duality relations between null geodesics of various brane geometries are demonstrated, some of which have a geometrical origin through an optical metric.
In this paper, we investigate the null geodesics of the static charged black hole in heterotic string theory. A detailed analysis of the geodesics are done in the Einstein frame as well as in the string frame. In the Einstein frame, the geodesics are solved exactly in terms of the Jacobi-elliptic integrals for all possible energy levels and angular momentum of the photons. In the string frame, the geodesics are presented for the circular orbits. As a physical application of the null geodesics, we have obtained the angle of deflection for the photons and the quasinormal modes of a massless scal…
We study the timelike geodesics and geodesic deviation for a two-dimensional stringy blackhole spacetime in Schwarzschild gauge. We have analyzed the properties of effective potential along with the structure of the possible orbits for test particles with different settings of blackhole parameters. The exactly solvable geodesic deviation equation is used to obtain corresponding deviation vector. The nature of deviation and tidal force is also examined in view of the behavior of corresponding deviation vector.The results are also compared with an another two-dimensional stringy blackhole spacet…
We study the geodesic equations in the space-time of a Schwarzschild black hole pierced by an infinitely thin cosmic string and give the complete set of analytical solutions of these equations for massive and massless particles, respectively. The solutions of the geodesic equations can be classified according to the particle's energy and angular momentum, the ratio between the component of the angular momentum aligned with the axis of the string and the total angular momentum, the deficit angle of the space-time and as well the horizon radius (or mass) of the black hole. For bound orbits of ma…
We find a class of solutions of Einstein's field equations representing spacetime outside a spinning cosmic string surrounded by a gas of non-spinning cosmic strings, and show that there exist closed timelike geodesics in this spacetime.
We analyze the null geodesic equations in five dimensional spherically symmetric spacetime with collapsing inhomogeneous dust cloud. By using a new method, we prove the existence and non-existence of solutions to null geodesic equation emanating from central singularity for smooth initial distribution of dust. Moreover, we also show that the null geodesics can extend to null infinity in a certain case, which imply the violation of cosmic censorship conjecture.
Recently, an analytical study of radial and circular orbits for null and time-like geodesics that propagate in the spacetime produced by a Schwarzschild black hole associated with cloud of strings, in a universe filled by quintessence, has been done in Ref. \cite{Mustafa:2021}. In this paper, we complete the aforementioned study by investigating possible analytical solutions to the equations of motion for other types of bound orbits, besides taking into account the cases of unbound orbits. This requires an extensive study of the corresponding effective potentials that categorize the test parti…
In this article we study the geodesic motion of test particles and light in the five-dimensional (rotating) black string spacetime. If a compact dimension is added to the four-dimensional Schwarzschild or Kerr spacetime, the new five-dimensional metric describes a (rotating) black string. The geodesics in the Schwarzschild and Kerr spacetime have been studied in great detail, however, when a compact dimension is added new behaviour occurs. We present the analytical solutions of the geodesic equations and discuss the possible orbits. The motion in the ordinary four-dimensional Schwarzschild and…
The existence and stability under linear perturbation of closed timelike curves in the spacetime associated to Schwarzschild black hole pierced by a spinning string are studied. Due to the superposition of the black hole, we find that the spinning string spacetime is deformed in such a way to allow the existence of closed timelike geodesics.
We study the geodesic motion of test particles in the space-time of two Abelian-Higgs strings interacting via their magnetic fields. These bound states of cosmic strings constitute a field theoretical realization of p-q-strings which are predicted by inflationary models rooted in String Theory, e.g. brane inflation. In contrast to previously studied models describing p-q-strings our model possesses a Bogomolnyi-Prasad-Sommerfield (BPS) limit. If cosmic strings exist it would be exciting to detect them by direct observation. We propose that this can be done by the observation of test particle m…
The causal geodesics in the equatorial plane of a static extremal charged black holes in heterotic string theory are examined with regard to their geodesic stability, and compared with similar geodesics in the non-extremal situation. Extremization of the effective potential for time-like and null circular geodesics implies that in the extremal limit, the radius of ISCO(Inner-most Stable Circular Orbit) $(r_{ISCO})$, circular photon orbit (CPO) $(r_{ph})$ and marginally bound circular orbit (MBCO) $(r_{mb})$ are coincident with the event horizon $(r_{hor})$ i.e. $r_{ISCO}=r_{ph}=r_{mb}=r_{hor}=…
We study the integrability of the equations of motion for the Nambu-Goto strings with a cohomogeneity-one symmetry in Minkowski spacetime. A cohomogeneity-one string has a world surface which is tangent to a Killing vector field. By virtue of the Killing vector, the equations of motion can be reduced to the geodesic equation in the orbit space. Cohomogeneity-one strings are classified into seven classes (Types I to VII). We investigate the integrability of the geodesic equations for all the classes and find that the geodesic equations are integrable. For Types I to VI, the integrability comes …
Here we consider isofrequency pairing of geodesic orbits that share the same three orbital frequencies associated with $Ω^{\hat{r}}$, $Ω^{\hatφ}$, and $Ω^{\hatω}$ in a particular region of parameter space around black string spacetime geometry. We study the effect arising from the extra compact spatial dimension on the isofrequency pairing of geodesic orbits and show that such orbits would occur and become in a cylindrical manner in the allowed region as particles move along the black string. We find that the effect due to the extra dimension leads to an increase in the number of the isofreque…
Special multi-cosmic string metrics are analytically extended to describe configurations of Wheeler-Misner wormholes and ordinary cosmic strings. I investigate in detail the case of flat, asymptotically Minkowskian, Wheeler-Misner wormhole spacetimes generated by two cosmic strings, each with tension $-1/4G$.
Global U(1) strings with cylindrical symmetry are studied in anti-de Sitter spacetime. According as the magnitude of negative cosmological constant, they form regular global cosmic strings, extremal black cosmic strings and charged black cosmic strings, but no curvature singularity is involved. The relationship between the topological charge of a neutral global string and the black hole charge is clarified by duality transformation. Physical relevance as straight string is briefly discussed.
There are two disjointed problems in cosmology within General Relativity (GR), which can be addressed simultaneously by studying the nature of geodesics around $t\rightarrow 0$, where $t$ is the physical time. One is related to the past geodesic completeness of the inflationary trajectory due to the presence of a cosmological singularity, and the other one is related to the homogeneity condition required to inflate a local space-time patch of the universe. We will show that both the problems have a common origin, arising from how the causal structure of null and timelike geodesics are structur…
We make a systematic investigation of stationary cylindrically symmetric solutions to the five-dimensional Einstein and Einstein-Gauss-Bonnet equations. Apart from the five-dimensional neutral cosmic string metric, we find two new exact solutions which qualify as cosmic strings, one corresponding to an electrically charged cosmic string, the other to an extended superconducting cosmic string surrounding a charged core. In both cases, test particles are deflected away from the singular line source. We extend both kinds of solutions to exact multi-cosmic string solutions.
In the stringy cosmology, we investigate singularities in geodesic surface congruences for the time-like and null strings to yield the Raychaudhuri type equations possessing correction terms associated with the novel features owing to the strings. Assuming the stringy strong energy condition, we have a Hawking-Penrose type inequality equation. If the initial expansion is negative so that the congruence is converging, we show that the expansion must pass through the singularity within a proper time. We observe that the stringy strong energy conditions of both the time-like and null string congr…
In this paper we add a compact dimension to Schwarzschild-(anti-) de sitter and Kerr-(anti-) de sitter spacetimes, which describes (rotating) black string-(anti-) de sitter spacetime. We study the geodesic motion of test particles and light rays in this spacetime. We present the analytical solutions of the geodesic equations in terms of Weierstrass elliptic and Kleinian sigma hyperelliptical functions. We also discuss the possible orbits and classify them according to particle's energy and angular momentum. Moreover, the obtained results, are compared to Schwarzschild-(anti-) de sitter and Ker…
(p,q)-strings are bound states of p F-strings and q D-strings and are predicted to form at the end of brane inflation. As such these cosmic superstrings should be detectable in the universe. In this paper we argue that they can be detected by the way that massive and massless test particles move in the space-time of these cosmic superstrings, in particular we study solutions to the geodesic equation in the space-time of field theoretical (p,q)-strings. The geodesics can be classified according to the test particle's energy, angular momentum and momentum in the direction of the string axis. We …
We present a cosmic string on a warped five dimensional space time in Einstein-Yang-Mills theory. Four-dimensional cosmic strings show some serious problems concerning the mechanism of string smoothing related to the string mass per unit length, $Gμ\approx 10^{-6}$. A warped cosmic string could overcome this problem and also the superstring requirement that $Gμ$ must be of order 1, which is far above observational bounds. Also the absence of observational evidence of axially symmetric lensing effect caused by cosmic strings could be explained by the warped cosmic string model we present: the a…
We study the geometry generated by a massless cosmic string. We find that this is given by a Riemann flat spacetime with a conical singularity along the worldsheet of the string. The geometry of such a spacetime is completely fixed by the holonomy of a simple loop wrapping the conical singularity. In the case of a massless cosmic string, this holonomy is a null-rotation/parabolic Lorentz transformation with a parabolic angle given by the linear energy density of the cosmic string. This description explicitly shows that there is no gravitational shockwave accompanying the massless cosmic string…
We study cosmic Nielsen-Olesen strings in space-times with a positive cosmological constant. For the free cosmic string in a cylindrically symmetric space-time, we calculate the contribution of the cosmological constant to the angle deficit, and to the bending of null geodesics. For a cosmic string in a Schwarzschild-de Sitter space-time, we use Kruskal patches around the inner and outer horizons to show that a thin string can pierce them.
We examine the Einstein equation with the energy-momentum tensors which correspond to an infinite line string of finite radius plus an outgoing radiation field. It is used to see the effect of the radiation field on the spacetime of a cosmic string. We make some assumptions about the metric coefficients and find a class of exact solution. The result can be applied to study the back reaction on a radiating cosmic string.
In this work we deal with the spacetime shaped by a straight cosmic string, emerging from local gauge theories, in the braneworld gravity context. We search for physical consequences of string features due to the modified gravitational scenario encoded in the projected gravitational equations. It is shown that cosmic strings in braneworld gravity may present significant differences when compared to the general relativity predictions since its linear density is modified and the deficit angle produced by the cosmic string is attenuated. Furthermore, the existence of cosmic strings in that scenar…
The dynamics of closed cosmic strings in Peres background, using finite-difference method, has been considered. It is shown that motion of the strings is very complicated and its perform complex oscillations and deformed to form loops and cusps.
Chiral cosmic strings are naturally produced at the end of D-term inflation and they present very interesting cosmological consequences. In this work, we investigate the formation and evolution of wakes by a chiral string. We show that, for cold dark matter, the mechanism of forming wakes by a chiral string is similar to the mechanism by an ordinary string.
We study the geodesic motion of massless test particles in the background of a magnetic charged black hole spacetime in four dimensions in dilaton-Maxwell gravity. The behaviour of effective potential in view of the different values of black hole parameters is analysed in the equatorial plane. The possible orbits for null geodesics are also discussed in detail in view of the different values of the impact parameter. We have also calculated the frequency shift of photons in this spacetime. The results obtained are then compared with those for the electrically charged stringy black hole spacetim…
While considering the chameleon scalar field model with the spatially flat FLRW background, we investigate the late-time acceleration phase of the universe, wherein we apply the typical potential usually used in this model. Through setting some constraints on the free parameters of the model, we indicate that the non-minimal coupling between the matter and the scalar field in such a model should be strongly coupled in order to have an accelerated expansion of the universe at the late-time. We also investigate the relative acceleration of the parallel geodesics by obtaining the geodesic deviati…
We studied the singularity of the geodesic surface congruence for timelike and null strings using the expansion of the universe in the string theory. We had Raychaudhuri type equation for the expansion. Assuming the stringy strong energy condition and initial convergence, we induced the existence of singularity and got the same inequality equation of the string strong energy condition for both timelike and null stringy congruence. In this paper we want to study the twist and shear aspects of the stingy geodesic surface congruence. Under some natural conditions we derive the equations of the tw…
In this paper, we introduce a new approach to a treatment of the gravitational effects (redshift, time delay and lensing) on the observed cosmic microwave background (CMB) anisotropies based on the Boltzmann equation. From the Liouville's theorem in curved spacetime, the intensity of photons is conserved along a photon geodesic when non-gravitational scatterings are absent. Motivated by this fact, we derive a second-order line-of-sight formula by integrating the Boltzmann equation along a perturbed geodesic (curve) instead of a background geodesic (line). In this approach, the separation of th…
The unique, conical spacetime created by cosmic strings brings about distinctive gravitational lensing phenomena. The variety of these distinctive phenomena is increased when the strings have non-trivial mutual interactions. In particular, when strings bind and create junctions, rather than intercommute, the resulting configurations can lead to novel gravitational lensing patterns. In this brief note, we use exact solutions to characterize these phenomena, the detection of which would be strong evidence for the existence of complex cosmic string networks of the kind predicted by string theory-…
Distributional sources of cosmic walls crossed by cosmic strings from Riemann-Cartan (RC) Geometry. The matter density of the planar wall is maximum at the point where the cosmic string crosses the cosmic wall. Cartan torsion is has a support on the cosmic string given by the Dirac $ δ$-function. Off the sources are left with a torsionless vacuum.
We investigate the effect of the stochastic gravitational wave (GW) background produced by kinks on infinite cosmic strings, whose spectrum was derived in our previous work, on the B-mode power spectrum of the cosmic microwave background (CMB) anisotropy. We find that the B-mode polarization due to kinks is comparable to that induced by the motion of the string network and hence the contribution of GWs from kinks is important for estimating the B-mode power spectrum originating from cosmic strings. If the tension of cosmic strings μis large enough i.e., Gμ>~ 10^{-8}, B-mode polarization induce…
We examine a Nambu-Goto string trajectory in the neighbourhood of a cusp and determine the extrinsic curvature invariants. These are demonstrated to be finite, in contradiction with naive expectation. Thus the Nambu action is a valid approximation for the motion of a cosmic string vortex even at cusps. This suggests that cusp annihilation is not a feasible mechanism for particle radiation from cosmic strings.
In these lectures, I review the current status of cosmic strings and cosmic superstrings. I first discuss topological defects in the context of Grand Unified Theories, focusing in particular in cosmic strings arising as gauge theory solitons. I discuss the reconciliation between cosmic strings and cosmological inflation, I review cosmic string dynamics, cosmic string thermodynamics and cosmic string gravity, which leads to a number of interesting observational signatures. I then proceed with the notion of cosmic superstrings arising at the end of brane inflation, within the context of brane-wo…
We point out that the results by Brandenberger et al. in Phys.Rev.D77:083502(2008) that the geometry around the straight cosmic strings with stationary junctions is flat to linear order in the string tension can be immediately extended to any order.
Cosmic string wakes lead to a large signal in 21 cm redshift maps at redshifts larger than that corresponding to reionization. Here, we compute the angular power spectrum of 21 cm radiation as predicted by a scaling distribution of cosmic strings whose wakes have undergone shock heating.
We consider the femto-lensing due to a cosmic string. If a cosmic string with the deficit angle $Δ\sim 100$ [femto-arcsec] $\sim10^{-18}$ [rad] exists around the line of sight to a gamma-ray burst, we may observe characteristic interference patterns caused by gravitational lensing in the energy spectrum of the gamma-ray burst. This "femto-lensing" event was first proposed as a tool to probe small mass primordial black holes. In this paper, we propose use of the femto-lensing to probe cosmic strings with extremely small tension. Observability conditions and the event rate are discussed. Differe…
Understanding of the signatures of cosmic string networks is limited by a large uncertainty in the sizes at which cosmic string loops form. We review cosmic string network evolution, and the gravitational signatures, with emphasis on this uncertainty. We then review a recent analytic model of cosmic string networks. In combination with recent simulations, this suggests that 90% of the string goes into very small loops, at the gravitational radiation scale, and 10% into loops near the Hubble scale. We discuss cosmic string signatures in such a scenario, and the `inverse problem' of determining …
Cosmic strings produce charged particles which, by emitting electromagnetic radiation, partially ionize neutral hydrogen during the dark ages. Corrections to the ionization fraction of neutral hydrogen induced by cosmic strings could lead to new observational effects and/or new constraints on the string tension around $Gμ\sim 10^{-16} - 10^{-22}$ for values of the primordial magnetic field in the range $B_0 \sim 10^{-11}-10^{-9}$ Gauss.
Supplementing earlier literature by e.g. Tipler, Clarke, & Ellis (1980), Israel (1987), Thorne, (1994), Earman (1999), Senovilla & Garfinkle (2015), Curiel (2019ab), and Landsman (2021ab), I provide a historical and conceptual analysis of Penrose's path-breaking 1965 singularity (or incompleteness) theorem. The emphasis is on the nature and historical origin of the assumptions and definitions used in-or otherwise relevant to-the theorem, as well as on the discrepancy between the (astro)physical goals of the theorem and its actual content: even if its assumptions are met, the theorem fails to p…
We consider a local cosmic string described by the Abelian-Higgs model in the framework of scalar-tensor gravities. We find the metric of the cosmic string in the weak-field approximation. The propagation of particles and light is analysed in this background. This analysis shows that the (unperturbed) cosmic string in scalar-tensor theories presents some analogous features to the wiggly cosmic string in General Relativity.
The exact metric around a wiggly cosmic string is found by modifying the energy momentum-tensor of a straight infinitely thin cosmic string to include an electric current along the symmetry axis.
Towards the end of the brane inflationary epoch in the brane world, cosmic strings (but not texture, domain walls or monopoles) are copiously produced during brane collision. These cosmic strings are D$p$-branes with $(p-1)$ dimensions compactified. We elaborate on this prediction of the superstring theory description of the brane world. Using the data on the temperature anisotropy in the cosmic microwave background, we estimate the cosmic string tension $μ$ to be around $G μ\simeq 10^{-7}$. This in turn implies that the anisotropy in the cosmic microwave background comes mostly from inflation…
The spontaneous loss of angular momentum of a spinning cosmic string due to particle emission is discussed. The rate of particle production between two assymptotic spacetimes: the spinning cosmic string spacetime in the infinite past and a non-spinning cosmic string spacetime in the infinite future is calculated.
We extend the work done for cosmic strings and show that for a more general class of locally flat metrics the one loop calculation do not introduce any new divergences to the VEV of the energy of a scalar particle. We explicitly perform the calculation for the configuration where we have one cosmic string in the presence of a dipole made out of cosmic strings.
Topological defects experimentally induced by rotational dynamics in a continuous media replicate the coherent structure features of cosmic strings as well as hadrons.
Brane inflation in superstring theory predicts that cosmic strings (but not domain walls or monopoles) are produced towards the end of the inflationary epoch. Here, we discuss the production, the spectrum and the evolution of such cosmic strings, properties that differentiate them from those coming from an abelian Higgs model. As D-branes in extra dimensions, some type of cosmic strings will dissolve rapidly in spacetime, while the stable ones appear with a spectrum of cosmic string tensions. Moreover, the presence of the extra dimensions reduces the interaction rate of the cosmic strings in s…
We study massless cosmic strings which are one-dimensional objects moving with the speed of light. Perturbations of velocities of test bodies and anisotropy of cosmic microwave background generated by massless cosmic strings are analysed. These phenomena are analogous to the string wake effect and the Kaiser-Stebbins effect for standard (massive) cosmic strings. There are two regimes depending on the energy $E$ of a massless string per unit length. At low energies, $EG/c^4\ll 1$, massless and massive strings act similarly. At high energies, $EG/c^4 \sim 1$, massless string effects are quite di…
We use our model of the small scale structure on cosmic strings to develop further the result of Siemens, Olum, and Vilenkin that the gravitational radiation length scale on cosmic strings is smaller than the previously assumed $ΓGμt$. We discuss some of the properties of cosmic string loops at this cutoff scale, and we argue that recent network simulations point to two populations of cosmic string loops, one near the horizon scale and one near the gravitational radiation cutoff.
In the context of SUSY GUTs, GUT scale cosmic strings formed at the end of hybrid inflation are compatible with currently available CMB measurements. The maximum allowed cosmic strings contribution to the CMB data constrains the free parameters (mass scales, couplings) of inflationary models. For F-term inflation either the superpotential coupling must be fine tuned or one has to invoke the curvaton mechanism. D-term inflation should be addressed in the framework of SUGRA. We find that the cosmic strings contribution is not constant, contrary to some previous results. Using CMB measurements we…
