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A promising method for understanding the geometric properties of a spacetime in the vicinity of the horizon of a Kerr-like black hole can be developed by applying the antipodal boundary condition on the two opposite regions in the extended Penrose diagram. By considering a conformally invariant Lagrangian on a Randall–Sundrum warped five-dimensional spacetime, an exact vacuum solution is found, which can be interpreted as an instanton solution on the Riemannian counterpart spacetime, R + 2 × R 1 × S 1 , where R + 2 is conformally flat. The antipodal identification, which comes with a CPT inversion, is par excellence, suitable when quantum mechanical effects, such as the evaporation of a black hole by Hawking radiation, are studied. Moreover, the black hole paradoxes could be solved. By applying the non-orientable Klein surface, embedded in R 4 , there is no need for instantaneous transport of information. Further, the gravitons become "hard" in the bulk, which means that the gravitational backreaction on the brane can be treated without the need for a firewall. By splitting the metric in a product ω 2 g ˜ μ ν , where ω represents a dilaton field and g ˜ μ ν the conformally flat "un-physical" spacetime, one can better construct an effective Lagrangian in a quantum mechanical setting when one approaches the small-scale area. When a scalar field is included in the Lagrangian, a numerical solution is presented, where the interaction between ω and Φ is manifest. An estimate of the extra dimension could be obtained by measuring the elapsed traversal time of the Hawking particles on the Klein surface in the extra dimension. Close to the Planck scale, both ω and Φ can be treated as ordinary quantum fields. From the dilaton field equation, we obtain a mass term for the potential term in the Lagrangian, dependent on the size of the extra dimension. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the exact time-dependent black hole solution on a warped five-dimensional Randall–Sundrum space–time in conformal dilaton gravity. The zeroes of the model are described by a meromorphic quintic polynomial, which has no essential singularities. The quintic equation can be reduced to the Brioschi form by means of the Weierstrass elliptic curve over ℚ. The model fits the antipodal boundary condition, i.e. antipodal points in the projected space are identified using the embedding of a Klein surface in ℂ 2 , using the ℤ 2 symmetry on the two sides of the brane. If one writes (5) g μ ν = ω 4 ∕ 3 (5) g ̃ μ ν , (5) g ̃ μ ν = (4) g ̃ μ ν + n μ n ν , (4) g ̃ μ ν = ω ̄ 2 (4) ḡ μ ν , with n μ the normal to the brane and ω the dilaton field, then (4) ḡ μ ν is conformally flat. It is the contribution from the bulk which determines the real pole on the effective four-dimensional space–time. There is no objection applying 't Hooft's back reaction method in constructing the unitary S-matrix for the Hawking radiation. Again, there is no "inside" of the black hole. The zeroes can also be analyzed by the icosahedron equation and by the Hopf-fibration of the Klein surface. [ABSTRACT FROM AUTHOR]

At first glance, it seems possible to construct in general relativity theory causality violating solutions. The most striking one is the Gott spacetime. Two cosmic strings, approaching each other with high velocity, could produce closed timelike curves. It was quickly recognized that this solution violates physical boundary conditions. The effective one particle generator becomes hyperbolic, so the center of mass is tachyonic. On a 5-dimensional warped spacetime, it seems possible to get an elliptic generator, so no obstruction is encountered and the velocity of the center of mass of the effective particle has an overlap with the Gott region. So a CTC could, in principle, be constructed. However, from the effective 4D field equations on the brane, which are influenced by the projection of the bulk Weyl tensor on the brane, it follows that no asymptotic conical space time is found, so no angle deficit as in the 4D counterpart model. This could also explain why we do not observe cosmic strings.

We investigate the space–time of a spinning cosmic string in conformal invariant gravity, where the interior consists of a gauged scalar field. We find exact solutions of the exterior of a stationary spinning cosmic string, where we write the metric as g μ ν = ω 2 g ̃ μ ν , with ω a dilaton field which contains all the scale dependences. The "unphysical" metric g ̃ μ ν is related to the (2 + 1) -dimensional Kerr space–time. The equation for the angular momentum J decouples, for the vacuum situation as well as for global strings, from the other field equations and delivers a kind of spin-mass relation. For the most realistic solution, J falls off as ∼ 1 r and ∂ r J → 0 close to the core. The space–time is Ricci flat. The formation of closed timelike curves can be pushed to space infinity for suitable values of the parameters and the violation of the weak energy condition can be avoided. For the interior, a numerical solution is found. This solution can easily be matched at the boundary on the exterior exact solution by special choice of the parameters of the string. This example shows the power of conformal invariance to bridge the gap between general relativity and quantum field theory. [ABSTRACT FROM AUTHOR]

The recently found alignment of the polarization axes (PA) of quasars in large quasar groups (LQGs) on Mpc scales can be explained by general relativistic cosmic string networks. By considering the cosmic string as a result of spontaneous symmetry breaking of the gauged U(1) abelian Higgs model with topological charge , many stability features of -vortex solutions of superconductivity can be taken over. Decay of the high multiplicity () super-conducting vortex into a lattice of vortices of unit magnetic flux is energetically favorable. The temporarily broken axial symmetry will leave an imprint of a preferred azimuthal-angle on the lattice. The stability of the lattice depends critically on the parameters of the model, especially when gravity comes into play. In order to handle the strong nonlinear behavior of the time-dependent coupled field equations of gravity and the scalar-gauge field, we will use a high-frequency approximation scheme to second order on a warped 5D axially symmetric spacetime with the scalar-gauge field residing on the brane. We consider different winding numbers for the subsequent orders of perturbations of the scalar field. A profound contribution to the energy-momentum tensor comes from the bulk spacetime and can be understood as 'dark'-energy. The cosmic string becomes super-massive by the contribution of the 5D Weyl tensor on the brane and the stored azimuthal preferences will not fade away. During the recovery to axial symmetry, gravitational and electro-magnetic radiation will be released. The perturbative appearance of a nonzero energy-momentum component can be compared with the phenomenon of bifurcation along the Maclaurin-Jacobi sequence of equilibrium ellipsoids of self-gravitating compact objects, signaling the onset of secular instabilities. There is a kind of similarity with the Goldstone-boson modes of spontaneously broken symmetries of continuous groups. The recovery of the SO(2) symmetry from the equatorial eccentricity takes place on a time-scale comparable with the emission of gravitational waves. The emergent azimuthal-angle dependency in our model can be used to explain the aligned PA in LQGs on Mpc scales. Spin axis direction perpendicular to the major axes of LQGs when the richness decreases can be explained as a second-order effect in our approximation scheme by the higher multiplicity terms. The preferred directions are modulo , with being an integer dependent on the th order of approximation. When more data of quasars of high redshift becomes available, one could prove that the alignment emerged after the symmetry breaking scale and must have a cosmological origin. The effect of the warp factor on the second-order perturbations could also be an indication of the existence of extra large dimensions. [ABSTRACT FROM AUTHOR]

There has been observational evidence about spin axes of quasars in large quasar groups correlated over hundreds of Mpc. This is seen in the radio spectrum as well as in the optical range. There is not yet a satisfactory explanation of this "spooky" alignment. This alignment cannot be explained by mutual interaction at the time that quasars manifest themselves optically. A cosmological explanation could be possible in the formation of superconducting vortices (cosmic strings) in the early universe, just after the symmetry-breaking phase of the universe. We gathered from the NASA/IPAC and SIMBAD extragalactic databases the right ascension, declination, inclination, position angle and eccentricity of the host galaxies of three large quasar groups to obtain the azimuthal and polar angle of the spin vectors. The alignment of the azimuthal angle of the spin vectors of quasars in their host galaxy is confirmed in the large quasar group U1.27 and compared with two other groups in the vicinity, i.e., U1.11 and U1.28, investigated by Clowes (2013). It is well possible that the azimuthal angle alignment fits the predicted azimuthal angle dependency in the theoretical model of the formation of general relativistic superconducting vortices, where the initial axial symmetry is broken just after the symmetry breaking of the scalar-gauge field. [ABSTRACT FROM AUTHOR]

The time evolution of a self-gravitating U(l) cosmic string on a warped five-dimensional (5D) axially symmetric spacetime is numerically investigated. Although cosmic strings are theoretically predicted in four-dimensional (4D) general relativistic models, there is still no observational evidence of their existence. From recent observations of the cosmic microwave background (CMB), it is concluded that these cosmic strings cannot provide a satisfactory explanation for the bulk of density perturbations. They even could not survive inflation. It is conjectured that only in a 5D warped braneworld model there will be observable imprint of these so-called cosmic superstrings on the induced effective 4D brane metric for values of the symmetry breaking scale larger than the grand unified theory (GUT) values. The warp factor makes these strings consistent with the predicted mass per unit length on the brane. However, in a time-dependent setting, it seems that there is a wavelike energy-momentum transfer to infinity on the brane, a high-energy braneworld behavior. This in contrast to earlier results in approximation models. Evidence of this information from the bulk geometry could be found in the gravitational cosmic background radiation via gravitational wave energy-momentum affecting the brane evolution. Fluctuations of the brane when there is a U(l) gauge field present, are comparable with the proposed brane tension fluctuations, or branons, whose relic abundance can be a dark matter candidate. We briefly made a connection with the critical behavior at the threshold of black hole formation found by Choptuik several decades ago in self-gravitating time-dependent scalar field models. The critical distinction between dispersion of the scalar waves and singular behavior fade away when a time-dependent warp factor is present. [ABSTRACT FROM AUTHOR]

We present the "classical" Nielsen-Olesen vortex solution on a warped 5-dimensional spacetime, where we solved the effective 4-dimensional equations from the 5-dimensional equations together with the junction and boundary conditions. 4-dimensional cosmic strings show some serious problems concerning the mechanism of string smoothing related to the string mass per unit length, Gμ ≤ 10-6. Moreover, there is no observational evidence of axially symmetric lensing effect caused by cosmic strings. Also super-massive cosmic strings (Gμ ≳ 1), predicted by superstring theory, possess some problems. They are studied because the universe may have undergone phase transitions at scales much higher than the GUT scale. But Gμ ≳ 1 is far above observational bounds, so one needs an inflationary scenario to smooth them out. Further, it is believed that these super-massive strings never extended to macroscopic size. Brane world models could overcome these problems. Gμ could be warped down to GUT scale, even if its value was at the Planck scale. In our warped cosmic string model, where the string mass per unit length in the bulk can be of order of the Planck scale, we find that the 4-dimensional brane spacetime is exponential warped down. Moreover, asymptotically the induced 4-dimensional spacetime does not show conical behavior. So there is no angle deficit compared to its value in the bulk and the spacetime seems to be unphysical, at least under fairly weak assumptions on the stress-energy tensor and without a positive brane tension. The results are confirmed by numerical solutions of the field equations. [ABSTRACT FROM AUTHOR]

We investigated the SU(2) Einstein-Yang-Mills system on a stationary axially symmetric nondiagonal spacetime. The equations are numerically solved. There is evidence for the existence of a regular solution with nonvanishing angular momentum, and finite energy density for all r. The behavior of the solution depends critical on the ratio of the Planck scale M[sub p1] and Yang-Mills couplings constant g, i.e., α = M[sub p1]/g = ... the asymptotic behavior of the solution is strongly affected by the boundary conditions of one of the YM components at z = 0. It is conjectured that the singular behavior of the metric components at finite distance of the core is related to the gravitational instability found in the self-gravitating fiat-space non-Abelian monopole, the EinsteinSkyrme model and Einstein-Yang-Mills-Higgs model. [ABSTRACT FROM AUTHOR]

Abstract We investigate the conformal invariant Lagrangian of the self-gravitating U(1) scalar-gauge field on the time-dependent Bondi–Marder axially symmetric spacetime. By considering the conformal symmetry as exact at the level of the Lagrangian and broken in the vacuum, a consistent model is found with an exact solution of the vacuum Bondi–Marder spacetime, written as g μ ν = ω 2 g ̄ μ ν , where ω is the conformal factor and g ̄ μ ν the 'un-physical' spacetime. Curvature could then be generated from Ricci-flat g ̄ μ ν by suitable dilaton fields and additional gauge freedom. If we try to match this vacuum solution on the interior vortex solution of the coupled Einstein-scalar-gauge field, we need, besides the matching conditions, constraint equations in order to obtain a topological regular description of the small-scale behaviour of the model. Probably, one needs the five-dimensional warped counterpart model, where the warp factor determines the large-scale behaviour of the model. The warped five-dimensional model can be reformulated by considering the warp factor as a dilaton field conformally coupled to gravity and embedded in a smooth M 4 ⊗ R manifold. Dark energy and the cosmological constant could then be emergent in this model. The dilaton field has a dual meaning. At very early times, when ω → 0 , it describes the small-distance limit, while at later times it manifests itself as a warp (or scale) factor that determines the dynamical evolution of the universe. However, as expected, the conformal invariance is broken (trace-anomaly) by the appearance of a mass term and a quadratic term in the energy–momentum tensor of the scalar-gauge field, arising from the extrinsic curvature terms of the projected Einstein tensor. By considering the dilaton field and Higgs field on equal footing on small scales, there will be no singular behaviour, when ω → 0 and one can deduce constraints to maintain regularity of the action. [ABSTRACT FROM AUTHOR]