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Bouncing non-singular isotropic cosmological solutions are investigated in a simple model of scalar-tensor gravity. New families of such solutions are found and their properties are presented and analyzed using an effective potential as the main tool. Bouncing solutions are shown to exist for a Higgs-like self-interaction potential which is bounded from below, in contrast to previous solutions that appeared in the literature based on potentials which were unbounded from below. In the simplest version of a scalar field with the quartic potential and conformal coupling to gravity, bouncing spatially flat solutions either have the Hubble function diverging in the past before the bounce, but with a well-behaved future, or are globally regular but unstable with respect to anisotropic or inhomogeneous perturbations at some finite values of the scalar field and curvature. Regular solutions can only exist in the part of the parameter space where the maximum of the effective potential is larger than the first zero of the potential, and gravity becomes repulsive at the bounce., Comment: 22 pages; few misprints corrected, accepted for publication in JCAP

The vector-tensor Horndeski theory is supplemented by a real, massless scalar field non-minimally coupled to the Horndeski interaction term. The generic dyonic Reissner-Nordstrom solutions characterized by electric and magnetic charges, acquire an instability and bifurcate into electromagnetically charged solutions presenting an horizon and a cloud of scalar hairs at specific values of the non-minimal coupling constant. These hairy black holes are studied in terms of the physical parameters of the model and the critical phenomena limiting their domain of existence are discussed., Comment: 14 pages; Clarifications added in few places as well as some remarks about negative alpha solutions. To be published in Phys Rev D

Bouncing non-singular isotropic cosmological solutions are investigated in a simple model of scalar-tensor gravity. New families of such solutions are found and their properties are presented and analyzed using an effective potential as the main tool. Bouncing solutions are shown to exist for a Higgs-like self-interaction potential which is bounded from below, in contrast to previous solutions that appeared in the literature based on potentials which were unbounded from below. In the simplest version of a scalar field with the quartic potential and conformal coupling to gravity, bouncing spatially flat solutions either have the Hubble function diverging in the past before the bounce, but with a well-behaved future, or are globally regular but unstable with respect to anisotropic or inhomogeneous perturbations at some finite values of the scalar field and curvature. Regular solutions can only exist in the part of the parameter space where the maximum of the effective potential is larger than the first zero of the potential, and gravity becomes repulsive at the bounce., Comment: 22 pages; few misprints corrected, accepted for publication in JCAP

Bouncing non-singular isotropic cosmological solutions are investigated in a simple model of scalar-tensor gravity. New families of such solutions are found and their properties are presented and analyzed using an effective potential as the main tool. Bouncing solutions are shown to exist for a Higgs-like self-interaction potential which is bounded from below, in contrast to previous solutions that appeared in the literature based on potentials which were unbounded from below. In the simplest version of a scalar field with the quartic potential and conformal coupling to gravity, bouncing spatially flat solutions either have the Hubble function diverging in the past before the bounce, but with a well-behaved future, or are globally regular but unstable with respect to anisotropic or inhomogeneous perturbations at some finite values of the scalar field and curvature. Regular solutions can only exist in the part of the parameter space where the maximum of the effective potential is larger than the first zero of the potential, and gravity becomes repulsive at the bounce., Comment: 22 pages; few misprints corrected, accepted for publication in JCAP

The vector-tensor Horndeski theory is supplemented by a real, massless scalar field non-minimally coupled to the Horndeski interaction term. The generic dyonic Reissner-Nordstrom solutions characterized by electric and magnetic charges, acquire an instability and bifurcate into electromagnetically charged solutions presenting an horizon and a cloud of scalar hairs at specific values of the non-minimal coupling constant. These hairy black holes are studied in terms of the physical parameters of the model and the critical phenomena limiting their domain of existence are discussed., Comment: 14 pages; Clarifications added in few places as well as some remarks about negative alpha solutions. To be published in Phys Rev D

Bouncing non-singular isotropic cosmological solutions are investigated in a simple model of scalar-tensor gravity. New families of such solutions are found and their properties are presented and analyzed using an effective potential as the main tool. Bouncing solutions are shown to exist for a Higgs-like self-interaction potential which is bounded from below, in contrast to previous solutions that appeared in the literature based on potentials which were unbounded from below. In the simplest version of a scalar field with the quartic potential and conformal coupling to gravity, bouncing spatially flat solutions either have the Hubble function diverging in the past before the bounce, but with a well-behaved future, or are globally regular but unstable with respect to anisotropic or inhomogeneous perturbations at some finite values of the scalar field and curvature. Regular solutions can only exist in the part of the parameter space where the maximum of the effective potential is larger than the first zero of the potential, and gravity becomes repulsive at the bounce., Comment: 22 pages; few misprints corrected, accepted for publication in JCAP

We construct exact solutions of magnetically charged black holes in the vector-tensor Horndeski gravity and discuss their main features. Unlike the analogous electric case, the field equations are linear in a simple (quite standard) parametrization of the metric tensor and they can be solved analytically even when a cosmological constant is added. The solutions are presented in terms of hypergeometric functions which makes the analysis of the black hole properties relatively straightforward. Some of the aspects of these black holes are quite ordinary like the existence of extremal configurations with maximal magnetic charge for a given mass, or the existence of a mass with maximal temperature for a given charge, but others are somewhat unexpected, like the existence of black holes with a repulsive gravitational field. We perform our analysis for both signs of the non-minimal coupling constant and find black hole solutions in both cases but with significant differences between them. The most prominent difference is the fact that the black holes for the negative coupling constant have a spherical surface of curvature singularity rather than a single point. On the other hand, the gravitational field produced around this kind of black holes is always attractive. Also, for small enough magnetic charge and negative coupling constant, extremal black holes do not exist and all magnetic black holes have a single horizon. In addition we study the trajectories around these magnetic black holes for light as well as massive particles either neutral or electrically charged. Finally, we compare the main features of these black holes with their electric counterparts, adding some aspects that have not been discussed before, like temperature, particle trajectories and light deflection by electrically charged Horndesky black holes., Comment: 30 pages, significantly expanded version + title change. Accepted for publication in PRD

We have discovered a new type of scalarized charged black holes in a surprisingly simple system: an Einstein-Maxwell-Klein-Gordon field theory where the three fields couple non-minimally through a Horndeski vector-tensor term. In addition to hairy charged black holes, this system exhibits Horndeski-Reissner-Nordstrom solutions and ordinary Reissner-Nordstrom ones which bifurcate to the scalarized solutions. There exist also vector-tensor black hole solutions which possess central curvature singularities although their metric components are finite there, and also solutions with naked singularities producing regular metric components everywhere around them. We analyze the solutions and present their main features., Comment: 13 pages, 7 figures; some clarifications added, figures 1-2 modified, few references added; accepted for publication in PRD

We have discovered a new type of scalarized charged black holes in a surprisingly simple system: an Einstein-Maxwell-Klein-Gordon field theory where the three fields couple non-minimally through a Horndeski vector-tensor term. In addition to hairy charged black holes, this system exhibits Horndeski-Reissner-Nordstrom solutions and ordinary Reissner-Nordstrom ones which bifurcate to the scalarized solutions. There exist also vector-tensor black hole solutions which possess central curvature singularities although their metric components are finite there, and also solutions with naked singularities producing regular metric components everywhere around them. We analyze the solutions and present their main features., Comment: 13 pages, 7 figures; some clarifications added, figures 1-2 modified, few references added; accepted for publication in PRD

The grand challenges of contemporary fundamental physics—dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem—all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress. This write-up is an initiative taken within the framework of the European Action on 'Black holes, Gravitational waves and Fundamental Physics'.

The grand challenges of contemporary fundamental physics—dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem—all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress. This write-up is an initiative taken within the framework of the European Action on 'Black holes, Gravitational waves and Fundamental Physics'.

The grand challenges of contemporary fundamental physics-dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem-all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress. This write-up is an initiative taken within the framework of the European Action on 'Black holes, Gravitational waves and Fundamental Physics'.

We find new spherically symmetric charged boson star solutions of a complex scalar field coupled non-minimally to gravity by a "John-type" term of Horndeski theory, that is a coupling between the kinetic scalar term and Einstein tensor. We study the parameter space of the solutions and find two distinct families according to their position in parameter space. More widespread is the family of solutions (which we call branch 1) existing for a finite interval of the central value of the scalar field starting from zero and ending at some finite maximal value. This branch contains as a special case the charged boson stars of the minimally coupled theory. In some regions of parameter space we find a new second branch ("branch 2") of solutions which are more massive and more stable than those of branch 1. This second branch exists also in a finite interval of the central value of the scalar field, but its end points (either both or in some cases only one) are extremal Reissner-Nordstrom black hole solutions., Comment: Revised version. Accepted for publication in Phys Rev D

We find new spherically symmetric charged boson star solutions of a complex scalar field coupled non-minimally to gravity by a "John-type" term of Horndeski theory, that is a coupling between the kinetic scalar term and Einstein tensor. We study the parameter space of the solutions and find two distinct families according to their position in parameter space. More widespread is the family of solutions (which we call branch 1) existing for a finite interval of the central value of the scalar field starting from zero and ending at some finite maximal value. This branch contains as a special case the charged boson stars of the minimally coupled theory. In some regions of parameter space we find a new second branch ("branch 2") of solutions which are more massive and more stable than those of branch 1. This second branch exists also in a finite interval of the central value of the scalar field, but its end points (either both or in some cases only one) are extremal Reissner-Nordstrom black hole solutions., Comment: Revised version. Accepted for publication in Phys Rev D

The Einstein-Proca system is studied in the case of a complex vector-field self-interacting through an appropriate potential with a global U(1) symmetry. The corresponding equations for a static, cylindrically symmetric metric and matter fields are then constructed and solved. In the probe limit (no gravity), it is shown that the equations admit at least two classes of regular solutions distinguished by the asymptotic behavior of the matter fields. One of these classes corresponds to lumps of vector fields localized in a cylindrical region, we naturally call these solutions "Proca-Q-tubes". They constitute the cylindrical counterparts of spherical Proca-Q-balls constructed recently, they can be characterized by finite mass and charge per unit-length of the tube. The domain of existence of these Proca-Q-tubes with respect to the coupling constants determining the potential is studied in detail. Finally, the gravitating Proca-Q-tubes are constructed and studied., Comment: Revised version: discussions expanded and references added. Note also some sign changes wrt previous version; to appear on Phys. Rev. D; 15 pages

The Einstein-Proca system is studied in the case of a complex vector-field self-interacting through an appropriate potential with a global U(1) symmetry. The corresponding equations for a static, cylindrically symmetric metric and matter fields are then constructed and solved. In the probe limit (no gravity), it is shown that the equations admit at least two classes of regular solutions distinguished by the asymptotic behavior of the matter fields. One of these classes corresponds to lumps of vector fields localized in a cylindrical region, we naturally call these solutions "Proca-Q-tubes". They constitute the cylindrical counterparts of spherical Proca-Q-balls constructed recently, they can be characterized by finite mass and charge per unit-length of the tube. The domain of existence of these Proca-Q-tubes with respect to the coupling constants determining the potential is studied in detail. Finally, the gravitating Proca-Q-tubes are constructed and studied., Comment: Revised version: discussions expanded and references added. Note also some sign changes wrt previous version; to appear on Phys. Rev. D; 15 pages

Motivated by the Higgs Inflation scenario, we study static spherically-symmetric solutions of the non-Abelian Higgs model coupled non-minimally to Gravity. We find solutions for the self-gravitating sphaleron as well as monopole-like solutions and study the impact of the non-minimal coupling on their properties. Finally we discuss shortly the possibility that these solutions interact gravitationally with star-like objects like boson stars.

Motivated by the Higgs Inflation scenario, we study static spherically-symmetric solutions of the non-Abelian Higgs model coupled non-minimally to Gravity. We find solutions for the self-gravitating sphaleron as well as monopole-like solutions and study the impact of the non-minimal coupling on their properties. Finally we discuss shortly the possibility that these solutions interact gravitationally with star-like objects like boson stars.

We study spherically-symmetric solutions in Massive Gravity generated by matter sources with polytropic equation of state. We concentrate in the non-perturbative regime where the mass term non-linearities are important, and present the main features of the solutions., Comment: Revised version. To be published in Phys Rev D

We study spherically-symmetric solutions in Massive Gravity generated by matter sources with polytropic equation of state. We concentrate in the non-perturbative regime where the mass term non-linearities are important, and present the main features of the solutions., Comment: Revised version. To be published in Phys Rev D

The cylindrically-symmetric static vacuum equations of Conformal Gravity are solved for the case of additional boost symmetry along the axis. We present the complete family of solutions which describe the exterior gravitational field of line sources in Conformal Gravity. We also analyze the null geodesics in these spaces., Comment: Revised version. To be published in Gen.Rel.Grav

The cylindrically-symmetric static vacuum equations of Conformal Gravity are solved for the case of additional boost symmetry along the axis. We present the complete family of solutions which describe the exterior gravitational field of line sources in Conformal Gravity. We also analyze the null geodesics in these spaces., Comment: Revised version. To be published in Gen.Rel.Grav

Cylindrically-symmetric solutions in Conformal Gravity are investigated and several new solutions are presented and discussed. Among them, a family of vacuum solutions, generalizations of the Melvin solution and cosmic strings of the Abelian Higgs model. The Melvin-like solutions have finite energy per unit length, while the string-like solutions do not., Comment: 22 pages, revised version, accepted for publication in Phys. Rev. D

We study static spherically-symmetric solutions of non-Abelian gauge theory coupled to Conformal Gravity. We find solutions for the self-gravitating pure Yang-Mills case as well as monopole-like solutions of the Higgs system. The former are localized enough to have finite mass and approach asymptotically the vacuum geometry of Conformal Gravity, while the latter do not decay fast enough to have analogous properties., Comment: 12 pages, revised version, accepted for publication in Phys. Rev. D

We study spherically-symmetric structures in Conformal Gravity and in a scalar-tensor extension and gain some more insight about these gravitational theories. In both cases we analyze solutions in two systems: perfect fluid solutions and boson stars of a self-interacting complex scalar field. In the purely tensorial (original) theory we find in a certain domain of parameter space finite mass solutions with a linear gravitational potential but without a Newtonian contribution. The scalar-tensor theory exhibits a very rich structure of solutions whose main properties are discussed. Among them, solutions with a finite radial extension, open solutions with a linear potential and logarithmic modifications and also a (scalar-tensor) gravitational soliton. This may also be viewed as a static self-gravitating boson star in purely tensorial Conformal Gravity., Comment: 24 pages, revised version, accepted for publication in Phys. Rev. D

Cylindrically-symmetric solutions in Conformal Gravity are investigated and several new solutions are presented and discussed. Among them, a family of vacuum solutions, generalizations of the Melvin solution and cosmic strings of the Abelian Higgs model. The Melvin-like solutions have finite energy per unit length, while the string-like solutions do not., Comment: 22 pages, revised version, accepted for publication in Phys. Rev. D

We study static spherically-symmetric solutions of non-Abelian gauge theory coupled to Conformal Gravity. We find solutions for the self-gravitating pure Yang-Mills case as well as monopole-like solutions of the Higgs system. The former are localized enough to have finite mass and approach asymptotically the vacuum geometry of Conformal Gravity, while the latter do not decay fast enough to have analogous properties., Comment: 12 pages, revised version, accepted for publication in Phys. Rev. D

We study spherically-symmetric structures in Conformal Gravity and in a scalar-tensor extension and gain some more insight about these gravitational theories. In both cases we analyze solutions in two systems: perfect fluid solutions and boson stars of a self-interacting complex scalar field. In the purely tensorial (original) theory we find in a certain domain of parameter space finite mass solutions with a linear gravitational potential but without a Newtonian contribution. The scalar-tensor theory exhibits a very rich structure of solutions whose main properties are discussed. Among them, solutions with a finite radial extension, open solutions with a linear potential and logarithmic modifications and also a (scalar-tensor) gravitational soliton. This may also be viewed as a static self-gravitating boson star in purely tensorial Conformal Gravity., Comment: 24 pages, revised version, accepted for publication in Phys. Rev. D

We find new non-Abelian flux tube solutions in a model of $N_f$ scalar fields in the fundamental representation of SU(N)xU(1) with $N \leq N_f$ (the ``extended non-Abelian Higgs model''), and study their main properties. Among the solutions there are spinning strings as well as superconducting ones. The solutions exist only in a non trivial domain of the parameter space defined by the ratio between the SU(N) and U(1) coupling constants, the scalar self-interaction coupling constants, the magnetic fluxes (Abelian as well as non-Abelian) and the ``twist parameter'' which is a non-trivial relative phase of the Higgs fields., Comment: Revised version. To be published in Phys. Rev. D

A new kind of Q-balls is found: Q-balls in a non-linear sigma model. Their main properties are presented together with those of their self-gravitating generalization, sigma model Q-stars. A simple special limit of solutions which are bound by gravity alone (``sigma stars'') is also discussed briefly. The analysis is based on calculating the mass, global U(1) charge and binding energy for families of solutions parameterized by the central value of the scalar field. Two kinds (differing by the potential term) of the new sigma model Q-balls and Q-stars are analyzed. They are found to share some characteristics while differing in other respects like their properties for weak central scalar fields which depend strongly on the form of the potential term. They are also compared with their ``ordinary'' counterparts and although similar in some respects, significant differences are found like the existence of an upper bound on the central scalar field. The sigma model Q-stars also contain non-solitonic solutions whose relation with sigma star solutions is discussed., Comment: Erroneous fig 5 corrected

The properties of several types of Q-stars are studied and compared with their flat space analogues, i.e. Q-balls. The analysis is based on calculating the mass, global U(1) charge and binding energy for families of solutions parametrized by the central value of the scalar field. The two most frequently used Q-star models (differing by their potential term) are studied. Although there are general similarities between both Q-star types, there are important differences as well as new features with respect to the non-gravitating systems. We find non-solitonic solutions which do not have a flat space limit, in the weak (scalar) field region as well as in the opposite region of strong central scalar field for which there does not exist Q-ball solutions at all., Comment: To appear in the proceedings of 11th Marcel Grossmann Meeting, Berlin, July 2006

A new kind of Q-balls is found: Q-balls in a non-linear sigma model. Their main properties are presented together with those of their self-gravitating generalization, sigma model Q-stars. A simple special limit of solutions which are bound by gravity alone (``sigma stars'') is also discussed briefly. The analysis is based on calculating the mass, global U(1) charge and binding energy for families of solutions parameterized by the central value of the scalar field. Two kinds (differing by the potential term) of the new sigma model Q-balls and Q-stars are analyzed. They are found to share some characteristics while differing in other respects like their properties for weak central scalar fields which depend strongly on the form of the potential term. They are also compared with their ``ordinary'' counterparts and although similar in some respects, significant differences are found like the existence of an upper bound on the central scalar field. The sigma model Q-stars also contain non-solitonic solutions whose relation with sigma star solutions is discussed., Comment: Erroneous fig 5 corrected

The properties of several types of Q-stars are studied and compared with their flat space analogues, i.e. Q-balls. The analysis is based on calculating the mass, global U(1) charge and binding energy for families of solutions parametrized by the central value of the scalar field. The two most frequently used Q-star models (differing by their potential term) are studied. Although there are general similarities between both Q-star types, there are important differences as well as new features with respect to the non-gravitating systems. We find non-solitonic solutions which do not have a flat space limit, in the weak (scalar) field region as well as in the opposite region of strong central scalar field for which there does not exist Q-ball solutions at all., Comment: To appear in the proceedings of 11th Marcel Grossmann Meeting, Berlin, July 2006

A field-theoretical model for non-singular global cosmic strings is presented. The model is a non-linear sigma model with a potential term for a self-gravitating complex scalar field. Non-singular stationary solutions with angular momentum and possibly linear momentum are obtained by assuming an oscillatory dependence of the scalar field on t, phi and z. This dependence has an effect similar to gauging the global U(1) symmetry of the model, which is actually a Kaluza-Klein reduction from four to three spacetime dimensions. The method of analysis can be regarded as an extension of the gravito-electromagnetism formalism beyond the weak field limit. Some D=3 self-dual solutions are also discussed., Comment: 20 pages Latex, 12 PS figures included. Minor corrections. Version to appear in Phys.Rev.D

We argue that the starting point of Kaluza's idea of unifying electrodynamics and gravity was the analogy between gravitation and electromagnetism which was pointed out by Einstein and Thirring. It seems that Kaluza's attention was turned to this point by the three papers on the Lense-Thirring effect and the analogy between gravitation and electromagnetism which were published a short time before Kaluza's paper was submitted. We provide here an English translation of the third of these papers.

A field-theoretical model for non-singular global cosmic strings is presented. The model is a non-linear sigma model with a potential term for a self-gravitating complex scalar field. Non-singular stationary solutions with angular momentum and possibly linear momentum are obtained by assuming an oscillatory dependence of the scalar field on t, phi and z. This dependence has an effect similar to gauging the global U(1) symmetry of the model, which is actually a Kaluza-Klein reduction from four to three spacetime dimensions. The method of analysis can be regarded as an extension of the gravito-electromagnetism formalism beyond the weak field limit. Some D=3 self-dual solutions are also discussed., Comment: 20 pages Latex, 12 PS figures included. Minor corrections. Version to appear in Phys.Rev.D

Cosmic strings are considered in two types of gauged sigma models, which generalize the gravitating Abelian Higgs model. The two models differ by whether the U(1) kinetic term is of the Maxwell or Chern-Simons form. We obtain the self-duality conditions for a general two-dimensional target space defined in terms of field dependent "dielectric functions". In particular, we analyze analytically and numerically the equations for the case of O(3) models (two-sphere as target space), and find cosmic string solutions of several kinds as well as gravitating vortices. We classify the solutions by their flux and topological charge. We note an interesting connection between the Maxwell and Chern-Simons type models, which is responsible for simple relations between the self-dual solutions of both types. There is however a significant difference between the two systems, in that only the Chern-Simons type sigma model gives rise to spinning cosmic vortices., Comment: 18 pages, 8 figures; final version to appear in PRD. Minor changes

Cosmic strings are considered in two types of gauged sigma models, which generalize the gravitating Abelian Higgs model. The two models differ by whether the U(1) kinetic term is of the Maxwell or Chern-Simons form. We obtain the self-duality conditions for a general two-dimensional target space defined in terms of field dependent "dielectric functions". In particular, we analyze analytically and numerically the equations for the case of O(3) models (two-sphere as target space), and find cosmic string solutions of several kinds as well as gravitating vortices. We classify the solutions by their flux and topological charge. We note an interesting connection between the Maxwell and Chern-Simons type models, which is responsible for simple relations between the self-dual solutions of both types. There is however a significant difference between the two systems, in that only the Chern-Simons type sigma model gives rise to spinning cosmic vortices., Comment: 18 pages, 8 figures; final version to appear in PRD. Minor changes

The static string-like solutions of the Abelian Higgs model coupled to dilaton gravity are analyzed and compared to the non-dilatonic case. Except for a special coupling between the Higgs Lagrangian and the dilaton, the solutions are flux tubes that generate a non-asymptotically flat geometry. Any point in parameter space corresponds to two branches of solutions with two different asymptotic behaviors. Unlike the non-dilatonic case, where one branch is always asymptotically conic, in the present case the asymptotic behavior changes continuously along each branch., Comment: 15 pages, 6 figures. To be published in Phys. Rev. D

The static string-like solutions of the Abelian Higgs model coupled to dilaton gravity are analyzed and compared to the non-dilatonic case. Except for a special coupling between the Higgs Lagrangian and the dilaton, the solutions are flux tubes that generate a non-asymptotically flat geometry. Any point in parameter space corresponds to two branches of solutions with two different asymptotic behaviors. Unlike the non-dilatonic case, where one branch is always asymptotically conic, in the present case the asymptotic behavior changes continuously along each branch., Comment: 15 pages, 6 figures. To be published in Phys. Rev. D

The static string-like solutions of the Abelian Higgs model coupled to dilaton gravity are analyzed and compared to the non-dilatonic case. Except for a special coupling between the Higgs Lagrangian and the dilaton, the solutions are flux tubes that generate a non-asymptotically flat geometry. Any point in parameter space corresponds to two branches of solutions with two different asymptotic behaviors. Unlike the non-dilatonic case, where one branch is always asymptotically conic, in the present case the asymptotic behavior changes continuously along each branch., Comment: 15 pages, 6 figures. To be published in Phys. Rev. D

The static cylindrically symmetric solutions of the gravitating Abelian Higgs model form a two parameter family. In this paper we give a complete classification of the string-like solutions of this system. We show that the parameter plane is composed of two different regions with the following characteristics: One region contains the standard asymptotically conic cosmic string solutions together with a second kind of solutions with Melvin-like asymptotic behavior. The other region contains two types of solutions with bounded radial extension. The border between the two regions is the curve of maximal angular deficit of $2\pi$., Comment: 12 pages, 4 figures

The static cylindrically symmetric solutions of the gravitating Abelian Higgs model form a two parameter family. In this paper we give a complete classification of the string-like solutions of this system. We show that the parameter plane is composed of two different regions with the following characteristics: One region contains the standard asymptotically conic cosmic string solutions together with a second kind of solutions with Melvin-like asymptotic behavior. The other region contains two types of solutions with bounded radial extension. The border between the two regions is the curve of maximal angular deficit of $2\pi$., Comment: 12 pages, 4 figures

Cosmic string solutions of the abelian Higgs model with conformal coupling to gravity are shown to exist. The main characteristics of the solutions are presented and the differences with respect to the minimally coupled case are studied. An important difference is the absence of Bogomolnyi cosmic string solutions for conformal coupling. Several new features of the abelian Higgs cosmic strings of both types are discussed. The most interesting is perhaps a relation between the angular deficit and the central magnetic field which is bounded by a critical value., Comment: 22 pages, 10 figures; to appear in Phys. Rev. D

Cosmic string solutions of the abelian Higgs model with conformal coupling to gravity are shown to exist. The main characteristics of the solutions are presented and the differences with respect to the minimally coupled case are studied. An important difference is the absence of Bogomolnyi cosmic string solutions for conformal coupling. Several new features of the abelian Higgs cosmic strings of both types are discussed. The most interesting is perhaps a relation between the angular deficit and the central magnetic field which is bounded by a critical value., Comment: 22 pages, 10 figures; to appear in Phys. Rev. D

The explicit relationship is determined between the interior properties of a static cylindrical matter distribution and the metric of the exterior space-time according to Einstein gravity for space-time dimensionality larger or equal to four. This is achieved through use of a coordinate system isotropic in the transverse coordinates. As a corollary, similar results are obtained for a spherical matter distribution in Brans-Dicke gravity for dimensions larger than or equal to three. The approach used here leads to consistency conditions for those parameters characterizing the exterior metric. It is shown that these conditions are equivalent to the requirement of hydrostatic equilibrium of the matter distribution (generalized Oppenheimer-Volkoff equations). These conditions lead to a consistent Newtonian limit where pressures and the gravitational constant go to zero at the same rate., Comment: 10 pages, RevTex, no figures

The explicit relationship is determined between the interior properties of a static cylindrical matter distribution and the metric of the exterior space-time according to Einstein gravity for space-time dimensionality larger or equal to four. This is achieved through use of a coordinate system isotropic in the transverse coordinates. As a corollary, similar results are obtained for a spherical matter distribution in Brans-Dicke gravity for dimensions larger than or equal to three. The approach used here leads to consistency conditions for those parameters characterizing the exterior metric. It is shown that these conditions are equivalent to the requirement of hydrostatic equilibrium of the matter distribution (generalized Oppenheimer-Volkoff equations). These conditions lead to a consistent Newtonian limit where pressures and the gravitational constant go to zero at the same rate., Comment: 10 pages, RevTex, no figures