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We find an exact time-dependent instanton solution on a vacuum Kerr-like warped spacetime in conformal dilaton gravity. Remarkably, the metric solution results from a first-order PDE, allowing the connection with self-duality. The antipodal boundary condition on the hypersurface of a Klein bottle $\sim \mathbb{C}^1\times\mathbb{C}^1$ is applied to describe the Hawking particles. We used the Hopf fibration to get $S^2$ as the black hole horizon, where the centrix is not in a torus but in the Klein bottle. The twist fits very well with the antipodal identification of the point on the horizon. No "cut and past" is necessary, so the Hawing particles remain pure without instantaneous information transport. A local observer passing the horizon will not notice a central singularity in suitable coordinates. The black hole paradoxes are also revisited in our new black hole model. A connection is made with the geomeric quantization of $\mathbb{C}^1\times\mathbb{C}^1\sim S^3$, by considering the symplectic 2-form. The model can be easily extended to the non-vacuum situation by including a scalar field. Both the dilaton and the scalar field can be treated as quantum fields when approaching the Planck area., Comment: 6 pages. 11 figures. Submitted to journal-- review V2: references corrected

We investigate on a Randall-Sundrum warped spacetime, a Kerr-like black hole in the conformal dilaton-Higgs $(\omega,\Phi)$ gravity model. We applied the antipodal boundary condition on the Klein surface using the $\mathds{Z}_2$-symmetry in the "large" (bulk) extra dimension. It turns out that the pseudo-Riemannian 5D manifold can be written as an effective 4D Riemannian brane spacetime, $\mathds{R}^2_+\times\mathds{R}^1\times S^1$, where $\mathds{R}^2_+$ is conformally flat. The solution in valid on both manifolds. So the solution can equally well described by an instanton solution. An advantage is that antipodicity can be maintained without a "cut-and-past" method or to rely on quantum cloning, when treating the scattering description of the evaporation process of the Hawking radiation. We need only the windingnumber as quantum number. Moreover, the equations are invariant under time reversal. The problem of finding the matching condition of the near-horizon approximation and the far-away Regge-Wheeler approximation, can possibly be solved by splitting the spacetime in a dilaton field times an "un-physical" spacetime, which is conformally flat. In the case of a constant gauge field, we find that the conform invariant mass term $\sim \Phi^2\omega^2$ in the Lagrangian follows directly from the superfluous dilaton equation by suitable choice of the scale of the extra dimension.Finally, we bring forward the relation between the embedded Klein surface in $\mathds{R}^4$ and the quantum mechanical information paradox., Comment: provisional version V4. minor correction.spellar corr. comment very welcome. cooperation also welcome. 10 figures

A throughout investigation is made of the exact black hole solution in five-dimensional warped conformal dilaton gravity, found in an earlier investigation. The singularities of the dynamical black hole spacetime are determined by the zeros of a meromorphic quintic polynomial, which has no essential singularities. The solutions of the polynomial are analyzed in the complex plane in relation to the icosahedron group and by the Hopf-fibrations of the Klein surface. 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 $\mathds{C}^2$, using the $\mathds{Z}_2$ symmetry on the two sides of the brane. If one writes $^{(5)}g_{\mu\nu}=\omega^{4/3}{^{(5)}}{\tilde g_{\mu\nu}}, {^{(5)}}{\tilde g_{\mu\nu}}={^{(4)}}{\tilde g_{\mu\nu}}+n_\mu n_\nu$, $ ^{(4)}\tilde g_{\mu\nu}=\bar\omega^2 {^{(4)}}\bar g_{\mu\nu}$, with $n_\mu$ the normal to the brane and $\omega$ the dilaton field, then ${^{(4)}}\bar g_{\mu\nu}$ is conformally flat. It is the contribution from the bulk which determines the real pole on the effective four-dimensional spacetime. 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., Comment: Version 2. Some minor changes. Comment welcome. 10 figures. 25 pages. To be presented at the 4-th Information Universe Conference, Groningen, The Netherlands. June 2022

A thorough investigation is presented of the exact black hole solution on a warped five-dimensional spacetime in conformal dilaton gravity (CDG), found in earlier work. Summarized, we will prove: The black hole solution in the CDG model on a warped 5D spacetime: 1. It is an exact solution for the metric components as well as for the dilaton field. 2.The quintic polynomial describing the zero's of the model, has no essential singularities. 3.If we write $^{(5)}g_{\mu\nu}=\omega^{4/3}{^{(5)}}{\tilde g_{\mu\nu}}, ^{(5)}\tilde g_{\mu\nu}=^{(4)}\tilde g_{\mu\nu}+n_\mu n_\nu, ^{(4)}\tilde g_{\mu\nu}=\bar\omega^2 {^{(4)}}\bar g{\mu\nu}$ then ${^{(4)}}\bar g{\mu\nu}$ is conformally flat and with $n_\mu$ the normal to the brane. 4. It fits the antipodal boundary condition, i.e., antipodal points in the projected space are identified using the embedding of a Klein surface in $\mathbb{C}^4$. 5. One can apply 't Hooft's back reaction method in constructing the unitary S-matrix and there is no "inside" of the black hole. 6. The contribution from the bulk determines the poles on the effective 4D spacetime. 7. The zeros of the quintic resolvent can analytically described by the icosahedral equation, i.e., in terms of hypergeometric functions and elliptic modular functions. 8. The Hopf fibration of the Klein bottle can be applied., Comment: V4 preliminary version. Some typos were corrected and the layout improved. Any comment is welcome! 19 pictures

There is observational evidence that the spin axes of quasars in large quasar groups are correlated over hundreds of Mpc. This is found in the radio sector 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 by 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 3 large quasar groups in order 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 Clowes2013. 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., Comment: Second version. No major changes. Feedback welcome. 3 figures 3 pages

We find evidence of the alignment of the azimuthal angle of the spin vectors of quasars in large quasar groups of different redshift. This effect is probably of cosmological origin and could be explained by symmetry breaking of the scalar-gauge field of cosmic strings in the early universe. It is expected that this effect will be more profound for higher redshift., Comment: Final version 8 figures. Accepted for MNRAS

We review the (2+1)-dimensional Ba\u{n}ados-Teitelboim-Zanelli black hole solution in conformally invariant gravity, uplifted to (3+1)-dimensional spacetime. As matter content we use a scalar-gauge field. The metric is written as $g_{\mu\nu}=\omega^2\tilde g_{\mu\nu}$, where the {\it dilaton field} $\omega$ contains all the scale dependencies and where $\tilde g_{\mu\nu}$ represents the "un-physical" spacetime. A numerical solution is presented and shows how the dilaton can be treated on equal footing with the scalar field. The location of the apparent horizon and ergo-surface depends critically on the parameters and initial values of the model. It is not a hard task to find suitable initial parameters in order to obtain a regular and {\it singular free} $g_{\mu\nu}$ out of a BTZ-type solution for $\tilde g_{\mu\nu}$. In the vacuum situation, an {\it exact} time-dependent solution in the Eddington-Finkelstein coordinates is found, which is valid for the (2+1)-dimensional BTZ spacetime as well as for the uplifted (3+1)-dimensional BTZ spacetime. While $\tilde g_{\mu\nu}$ resembles the standard BTZ solution with its horizons, $g_{\mu\nu}$ is {\it flat}. The dilaton field becomes an infinitesimal renormalizable quantum field, which switches on and off Hawking radiation. This solution can be used to investigate the small distance scale of the model and the black hole complementarity issues. It can also be used to describe the problem how to map the quantum states of the outgoing radiation as seen by a distant observer and the ingoing by a local observer in a one-to-one way. The two observers will use a different conformal gauge. A possible connection is made with the antipodal identification and unitarity issues., Comment: Version V4; some minor correction. 3 more figures added. Comment very welcome! 26 figures. 16 pages

We investigate the spacetime 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_{\mu\nu}=\omega^2\tilde g_{\mu\nu}$, with $\omega$ a dilaton field which contains all the scale dependences. The "unphysical" metric $\tilde g_{\mu\nu}$ is related to the $(2+1)$-dimensional Kerr spacetime. 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 $\sim\frac{1}{r}$ and $\partial_r J \rightarrow 0$ close to the core. The spacetime 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. It turns out, as expected from the "holographic" principle, that the exact solution of the exterior is equivalent with the warped five-dimensional brane world model, with only a cosmological constant in the bulk. This example shows the power of conformal invariance to bridge the gap between general relativity and quantum field theory., Comment: Final version. To present at TMF conference 2019 Torino. arXiv admin note: text overlap with arXiv:1511.08652

We investigate the conformal invariant Lagrangian of the self-gravitating U(1) scalar-gauge field and find new features of the model on the time-dependent axially symmetric Bondi-Marder 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 $g_{\mu\nu}=\omega^2 \bar g_{\mu\nu}$, where $\omega$ is the conformal factor and $\bar g_{\mu\nu}$ the `un-physical` spacetime. If we try to match this vacuum solution onto 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 5D dilaton field act as a warp factor. Moreover, the tracelessness of the energy-momentum tensor could then be maintained by a contribution from the bulk., Comment: version 2. Layout improved and minor corrections. 15 pages; 7 figures. To present at the XI Black Hole workshop Lisbon, dec. 2018

We show that the Einstein field equations for a five-dimensional warped spacetime, where only gravity can propagate into the bulk, determine the dynamical evolution of the warp factor of the four-dimensional brane spacetime. This can be explained as a holographic manifestation. The warped 5D model can be reformulated by considering the warp factor as a dilaton field ($\omega$) conformally coupled to gravity and embedded in a smooth $M_4 \otimes R$ manifold. On the brane, where the U(1) scalar gauge fields live, the dilaton field manifests itself classically as a warp factor and enters the evolution equations for the metric components and matter fields. We write the Lagrangian for the Einstein-scalar gauge fields in a conformal invariant setting. 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 in the projected Einstein tensor. These terms can be interpreted as a constraint in order to maintain conformal invariance. By considering the dilaton field and Higgs field on equal footing on small scales, there will be no singular behavior, when $\omega\rightarrow 0$ and one can deduce constraints to maintain regularity of the action. Our conjecture is that $\omega$, alias warp factor, has a dual meaning. At very early times, when $\omega \rightarrow 0$, it describes the small-distance limit, while at later times it is a warp (or scale) factor that determines the dynamical evolution of the universe. We also present a numerical solution of the model and calculate the (time-dependent) trace-anomaly. The solution depends on the mass ratio of the scalar and gauge fields, the parameters of the model and the vortex charge $n$., Comment: Final version-6. Layout improved and a numerical solution added. 20 pictures. Comment welcome. Presented at "X Black Holes Workshop", Aveiro, Dec. 2017

We find a emergent azimuthal-angle dependency of the Nielsen-Olesen vortices in the general relativistic situation just after the symmetry breaking at GUT-scale. Using a high-frequency perturbation method, we obtain in the first and second order perturbation equations $\varphi$-dependent terms left over after the phase transition of the Higgs field. Vortices with high multiplicity decay into a lattice with entangled Abrikosov vortices. The stability of this lattice of correlated flux $n=1$ vortices with preferred azimuthal-angle is guaranteed by the contribution from the bulk spacetime by means of the warp factor: the cosmic string becomes super-massive for some time during the evolution and initiates the excitations of the vortices to high multiplicity. The correlation will not fade away during the expansion by the warp factor. We used this azimuthal-angle correlation for the explanation of the recently observed alignment of polarization axes of quasars in large quasar groups. The detailed behavior of this alignment can be explained with our model. The two different orientations perpendicular to each other in quasars groups of less richness could be a second order effect in our model. There is a striking similarity between this phase transition of the gauged Higgs field and the temporarily breaking of the axially symmetry of self-gravitating cosmic string, by the appearance of non-diagonal energy-momentum tensor components. The eccentricity of the ellipsoid can be seen as order parameter. Recovery to SO(2) symmetry induces emission of gravitational and electro-magnetic radiation. More data of high-redshift quasars will be needed in order to test the second order effect predicted in our model., Comment: This is an improved version of gr-qc/1609.05068 Presented at the "First Hermann Minkowski Meeting", Varna 2017

The recently discovered alignment of quasar polarizations on very large scales could possibly explained by considering cosmic strings on a warped five dimensional spacetime. Compact objects, such as cosmic strings, could have tremendous mass in the bulk, while their warped manifestations in the brane can be consistent with general relativity in 4D. The self-gravitating cosmic string induces gravitational wavelike disturbances which could have effects felt on the brane, i.e., the massive effective 4D modes (Kaluza-Klein modes) of the perturbative 5D graviton. This effect is amplified by the time dependent part of the warp factor. Due to this warp factor, disturbances don't fade away during the expansion of the universe. From a non-linear perturbation analysis it is found that the effective Einstein 4D equations on an axially symmetric spacetime, contain a "back-reaction" term on the righthand side caused by the projected 5D Weyl tensor and can act as a dark energy term. The propagation equations to first order for the metric components and scalar-gauge fields contain $\varphi$-dependent terms, so the approximate wave solutions are no longer axially symmetric. The disturbances, amplified by the warp factor, can possess extremal values for fixed polar angles. This could explain the two preferred polarization vectors mod $(\varphi, 90^o)$., Comment: Revised version1 -- some minor corrections 7 pages-- no figures -- to appear in JMP -- will be presented at "Hot topics in Modern Cosmology" Spontaneous Workshop 10; May 2016 Carg\`ese. arXiv admin note: text overlap with arXiv:1407.7505

In a flat Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) geometry, we consider the expansion of the universe powered by the gravitationally induced `adiabatic' matter creation. To demonstrate how matter creation works well with the expanding universe, we have considered a general creation rate and analyzed this rate in the framework of dynamical analysis. The dynamical analysis hints the presence of a non-singular universe (without the big bang singularity) with two successive accelerated phases, one at the very early phase of the universe (i.e. inflation), and the other one describes the current accelerating universe, where this early, late accelerated phases are associated with an unstable fixed point (i.e. repeller) and a stable fixed (attractor) points, respectively. We have described this phenomena by analytic solutions of the Hubble function and the scale factor of the FLRW universe. Using Jacobi Last multiplier method, we have found a Lagrangian for this matter creation rate describing this scenario of the universe. To match with our early physics results, we introduce an equivalent dynamics driven by a single scalar field and discussed the associated observable parameters compared them with the latest PLANCK data sets. Finally, introducing the teleparallel modified gravity, we have established an equivalent gravitational theory in the framework of matter creation., Comment: 15 pages (two column format), 3 figures, Some typos corrected, Published version in MNRAS

It is known for a long time that the space time around a spinning cylindrical symmetric compact object such as the cosmic string, show un-physical behavior, i.e., they would possess closed time like curves (CTC). This controversy with Hawking's chronology protection conjecture is unpleasant but can be understood if one solves the coupled scalar-gauge field equations and the matching conditions at the core of the string. A new interior numerical solution is found of a self gravitating spinning cosmic string with a U(1) scalar gauge field and the matching on the exterior space time is revealed. It is conjectured that the experience of CTC's close to the core of the string is exceedingly unlikely. It occurs when the causality breaking boundary, $r_\mu$, approaches the boundary of the cosmic string, $r_{CS}$. Then the metric components become singular and the proper time on the core of the string stops flowing. Further, we expect that the angular momentum $J$ will decrease due to the emission of gravitational energy triggered by the scalar perturbations. When a complete loop is taken around the string, the interior time jumps by a factor $2\pi J$. The proper time it takes to make a complete loop becomes infinite and will be equal to the period that $g_{\varphi\varphi}$ remains positive. In this time interval the angular momentum will be reduced to zero by emission of wave energy. The physical situation of an observer who experience $r_{\mu}\rightarrow r_{CS}$ is very unpleasant: the energy-momentum tensor components diverge., Comment: preliminary version. 12 figures. A short version was presented at the second Time Machine Factory conference in Turin, 25-28 oct 2015

If we live on the weak brane with zero effective cosmological constant in a warped 5D bulk spacetime, gravitational waves and brane fluctuations can be generated by a part of the 5D Weyl tensor and carries information of the gravitational field outside the brane. We consider on a cylindrical symmetric warped FRW background the U(1) self-gravitating scalar-gauge field without bulk matter. It turns out that "branons" can be formed dynamically, due to the modified energy-momentum tensor components of the cosmic string. As a result, we find that the late-time behavior could be significant deviate from the standard evolution of the universe. The effect is triggered by the time-dependent warp factor, of the form $\sqrt{ae^{\tau t}+be^{-\tau t}}$ and the modified brane equations, comparable with a dark energy effect. This is a brane-world mechanism, not present is standard 4D FRW, where the large disturbances are rapidly damped as the expansion proceed. Because gravity can propagate in the bulk, the cosmic string can build up a huge angle deficit (or mass per unit length) by the warp factor. Disturbances in the spatial components of the stress-energy tensor cause cylindrical symmetric waves, amplified due to the presence of the bulk space and warpfactor. This long range effect could also explain the recently found spooky alignment of quasars in vast structures in the cosmic web., Comment: Final version; 10 pages and 14 figures; to appear in Found. of Phys

On a warped five-dimensional Friedmann-Lema\^{\i}tre-Robertson-Walker(FLRW) spacetime, dark energy can be induced by a U(1) scalar-gauge field on the brane. We consider a zero effective cosmological constant, i.e., the Randall-Sundrum(RS) fine-tuning and no bulk matter fields. The standard model fields interact via the bulk Weyl tensor and cause brane fluctuations. Due to the warp factor, disturbances don't fade away during the expansion of the universe. The late-time behavior could be significant deviate from the standard evolution of the universe. The effect is triggered by the time-dependent part of the warp factor. The self-gravitating cosmic string builds up a huge mass per unit length in the bulk and can induce massive KK-modes felt on the brane. From a nonlinear perturbation analysis it is found that the effective Einstein equations contain a "back-reaction" term on the righthand side caused by the projected 5D Weyl tensor and can act as a dark energy term. The propagation equations to first order for the metric components and scalar-gauge fields show explicit $\varphi$-dependency., Comment: Revised version of "Dark energy generated by warped cosmic strings". Talk at MG14, DE1, Rome july 2015

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., Comment: Presented at the conference "TimeMachineFactory" TM2012, Torino 2012

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, $G\mu \approx 10^{-6}$. A warped cosmic string could overcome this problem and also the superstring requirement that $G\mu$ 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 angle deficit of the string is warped down to unobservable value in the brane, compared to its value in the bulk. It turns out that only for negative cosmological constant, a consistent numerical solution of the model is possible., Comment: 6 pages, 6 figures; plus-minus sign added in solution Eq.40; correction of numbering of equations