Betti Hartmann - Academia.edu (original) (raw)
Papers by Betti Hartmann
We construct supersymmetric Q-balls and boson stars in (d + 1) dimensions. These non-topological ... more We construct supersymmetric Q-balls and boson stars in (d + 1) dimensions. These non-topological solitons are solutions of a scalar field model with global U (1) symmetry and a scalar field potential that appears in gauge-mediated supersymmetry (SUSY) breaking in the minimal supersymmetric extension of the Standard Model (MSSM). We are interested in both the asymptotically flat as well as in the asymptotically Anti-de Sitter (AdS) solutions. In particular, we show that for our choice of the potential gravitating, asymptotically flat boson stars exist in (2 + 1) dimensions. We observe that the behaviour of the mass and charge of the asymptotically flat solutions at the approach of the maximal frequency depends strongly on the number of spatial dimensions. For the asymptotically AdS solutions, the model on the conformal boundary can be interpreted as describing d-dimensional condensates of scalar glueballs.
We construct boson stars in (4+1)-dimensional Gauss-Bonnet gravity. We study the properties of th... more We construct boson stars in (4+1)-dimensional Gauss-Bonnet gravity. We study the properties of the solutions in dependence on the coupling constants and investigate these in detail. While the "thick wall" limit is independent of the value of the Gauss-Bonnet coupling, we find that the spiraling behaviour characteristic for boson stars in standard Einstein gravity disappears for large enough values of the Gauss-Bonnet coupling. Our results show that in this case the scalar field can not have arbitrarily high values at the center of the boson star and that it is hence impossible to reach the "thin wall" limit. Moreover, for large enough Gauss-Bonnet coupling we find a unique relation between the mass and the radius (qualitatively similar to those of neutron stars) which is not present in the Einstein gravity limit.
We construct rotating boson stars in (4+1)-dimensional asymptotically Anti-de Sitter space-time (... more We construct rotating boson stars in (4+1)-dimensional asymptotically Anti-de Sitter space-time (aAdS) with two equal angular momenta that are composed out of a massive and self-interacting scalar field. These solutions possess a single Killing vector field. Next to the fundamental solutions radially excited rotating boson stars exist. We find that the behaviour of the solutions for small angular momenta is very well described by the corresponding oscillons. We also discuss the classical stability and find that self-interacting rotating boson stars in aAdS are classically unstable for a large range of the gravitational coupling and the Antide Sitter radius, respectively, can -however -be classically stable for sufficiently large angular momenta. Furthermore, very compact boson stars suffer from a superradiant instability. Our results indicate that this superradiant instability appears only for classically unstable solutions.
Nuclear Physics B - Proceedings Supplements, 2014
The stability of black holes and solitons in d-dimensional Anti-de Sitter (AdS d ) space-time aga... more The stability of black holes and solitons in d-dimensional Anti-de Sitter (AdS d ) space-time against scalar field condensation is discussed. The resulting solutions are "hairy" black holes and solitons, respectively. In particular, we will discuss static black hole solutions with hyperbolic, flat and spherical horizon topology and emphasize that two different type of instabilities exist depending on whether the scalar field is charged or uncharged, respectively. We will also discuss the influence of Gauss-Bonnet curvature terms. The results have applications within the AdS/CFT correspondence and describe e.g. holographic insulator/conductor/superconductor phase transitions.
ABSTRACT We study the geodesic equation in the space-time of an Abelian-Higgs string and discuss ... more ABSTRACT 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. Comment: 20 pages including 14 figures; v2: references added, discussion on null geodesics extended, numerical results added
Classical and Quantum Gravity, 2015
In this paper we analyze Abelian-Higgs strings in Rastall gravity. We construct string solutions ... more In this paper we analyze Abelian-Higgs strings in Rastall gravity. We construct string solutions that asymptote to a flat space-time with a deficit angle by solving the set of coupled non-linear ordinary differential equations numerically. Decreasing the Rastall parameter from its Einstein gravity value we find that the deficit angle of the space-time increases and becomes equal to 2π at some critical value of this parameter that depends on the remaining couplings in the model. For smaller values the resulting solutions are supermassive string solutions possessing a singularity at a finite distance from the string core. Assuming the Higgs boson mass to be on the order of the gauge boson mass we find that also in Rastall gravity this happens only when the symmetry breaking scale is on the order of the Planck mass. We also observe that for specific values of the parameters in the model the energy per unit length becomes proportional to the winding number, i.e. the degree of the map S 1 → S 1 . Unlike in the BPS limit in Einstein gravity, this is, however, not connect to an underlying mathematical structure, but rather constitutes a would-be-BPS bound.
Physics Letters B, 2012
We consider compact boson stars that arise for a V-shaped scalar field potential. They represent ... more We consider compact boson stars that arise for a V-shaped scalar field potential. They represent a one parameter family of solutions of the scaled Einstein-signum-Gordon equations. We analyze the physical properties of these solutions and determine their domain of existence. Along their physically relevant branch emerging from the compact Q-ball solution, their mass increases with increasing radius. Empoying arguments from catastrophe theory we argue that this branch is stable, until the maximal value of the mass is reached. There the mass and size are on the order of magnitude of the Schwarzschild limit, and thus the spiralling respectively oscillating behaviour, well-known for compact stars, sets in.
Physical Review D, 2010
We study rotating boson stars in five spacetime dimensions. The boson fields consist of a complex... more We study rotating boson stars in five spacetime dimensions. The boson fields consist of a complex doublet scalar field. Considering boson stars rotating in two orthogonal planes with both angular momenta of equal magnitude, a special ansatz for the boson field and the metric allows for solutions with nontrivial dependence on the radial coordinate only. The charge of the scalar field equals the sum of the angular momenta. The rotating boson stars are globally regular and asymptotically flat. For our choice of a sixtic potential the rotating boson star solutions possess a flat spacetime limit. We study the solutions in flat and curved spacetime.
Physical Review D, 2012
We study the stability of (4 + 1)-dimensional charged Gauss-Bonnet black holes and solitons. We o... more We study the stability of (4 + 1)-dimensional charged Gauss-Bonnet black holes and solitons. We observe an instability related to the condensation of a scalar field and construct explicit "hairy" black hole and soliton solutions of the full system of coupled field equations. We investigate the cases of a massless scalar field as well as that of a tachyonic scalar field. The solitons with scalar hair exist for a particular range of the charge and the gauge coupling. This range is such that for intermediate values of the gauge coupling a "forbidden band" of charges for the hairy solitons exists. We also discuss the behaviour of the black holes with scalar hair when changing the horizon radius and/or the gauge coupling and find that various scenarios at the approach of a limiting solution appear. One observation is that hairy Gauss-Bonnet black holes never tend to a regular soliton solution in the limit of vanishing horizon radius. We also prove that extremal Gauss-Bonnet black holes can not carry massless or tachyonic scalar hair and show that our solutions tend to their planar counterparts for large charges.
Physical Review D, 2010
We study holographic superconductors in 3+1 dimensions away from the probe limit, i.e. taking bac... more We study holographic superconductors in 3+1 dimensions away from the probe limit, i.e. taking backreaction of the space-time into account. We consider the case of pure Einstein -and Gauss-Bonnet gravity, respectively. Similar to the probe limit we observe that the critical temperature at which condensation sets in decreases with increasing Gauss-Bonnet coupling. The decrease is however stronger when taking back-reaction of the space-time into account. We observe that the critical temperature becomes very small, but stays positive for all values of the Gauss-Bonnet coupling no matter how strong the back-reaction of the space-time is.
Physical Review D, 2009
ABSTRACT We study angularly excited as well as interacting non-topological solitons, so-called Q-... more ABSTRACT We study angularly excited as well as interacting non-topological solitons, so-called Q-balls and their gravitating counterparts, so-called boson stars in 3+1 dimensions. Q-balls and boson stars carry a non-vanishing Noether charge and arise as solutions of complex scalar field models in a flat space-time background and coupled minimally to gravity, respectively. We present examples of interacting Q-balls that arise due to angular excitations, which are closely related to the spherical harmonics. We also construct explicit examples of rotating boson stars that interact with non-rotating boson stars. We observe that rotating boson stars tend to absorb the non-rotating ones for increasing, but reasonably small gravitational coupling. This is a new phenomenon as compared to the flat space-time limit and is related to the negative contribution of the rotation term to the energy density of the solutions. In addition, our results indicate that a system of a rotating and non-rotating boson star can become unstable if the direct interaction term in the potential is large enough. This instability is related to the appearance of ergoregions. Comment: 20 pages including 9 figures; for higher quality figures please contact the authors; v2: minor changes, final version to appear in Phys. Rev. D
Journal of High Energy Physics, 2005
ABSTRACT
We study spherically symmetric soliton solutions in a model with a conformally coupled scalar fie... more We study spherically symmetric soliton solutions in a model with a conformally coupled scalar field as well as in full conformal gravity. We observe that a new type of limiting behaviour appears for particular choices of the self-coupling of the scalar field, i.e. the solitons interpolate smoothly between the Antide Sitter vacuum and an uncharged configuration. Furthermore, within conformal gravity the qualitative approach of a limiting solution does not change when varying the charge of the scalar field -contrary to the Einstein-Hilbert case. However, it changes with the scalar self-coupling.
We study Abelian strings in a fixed de Sitter background. We find that the gauge and Higgs fields... more We study Abelian strings in a fixed de Sitter background. We find that the gauge and Higgs fields extend smoothly across the cosmological horizon and that the string solutions have oscillating scalar fields outside the cosmological horizon for all currently accepted values of the cosmological constant. If the gauge to Higgs boson mass ratio is small enough, the gauge field function has a power-like behaviour, while it is oscillating outside the cosmological horizon if Higgs and gauge boson mass are comparable. Moreover, we observe that Abelian strings exist only up to a maximal value of the cosmological constant and that two branches of solutions exist that meet at this maximal value. We also construct radially excited solutions that only exist for non-vanishing values of the cosmological constant and are thus a novel feature as compared to flat space-time. Considering the effect of the de Sitter string on the space-time, we observe that the deficit angle increases with increasing cosmological constant.
Physical Review D, 2009
We investigate the properties of interacting Q-balls and boson stars that sit on top of each othe... more We investigate the properties of interacting Q-balls and boson stars that sit on top of each other in great detail. The model that describes these solutions is essentially a (gravitating)
Journal of High Energy Physics, 2013
We study field theoretical models for cosmic strings with flat directions in curved space-time. M... more We study field theoretical models for cosmic strings with flat directions in curved space-time. More precisely, we consider minimal models with semilocal, axionic and tachyonic strings, respectively. In flat space-time, isolated static and straight cosmic strings solutions of these models have a flat direction, i.e., a uniparametric family of configurations with the same energy exists which is associated with a zero mode. We prove that this zero mode survives coupling to gravity, and study the role of the flat direction when coupling the string to gravity. Even though the total energy of the solution is the same, and thus the global properties of the family of solutions remains unchanged, the energy density, and therefore the gravitational properties, are different. The local structure of the solutions depends strongly on the value of the parameter describing the flat direction; for example, for a supermassive string, the value of the free parameter can determine the size of the space-time.
Physical Review D - Particles, Fields, Gravitation and Cosmology, 2005
We study two classes of static uniform black string solutions in a (4 + 1)-dimensional SU(2) Eins... more We study two classes of static uniform black string solutions in a (4 + 1)-dimensional SU(2) Einstein-Yang-Mills model. These configurations possess a regular event horizon and corresponds in a 4−dimensional picture to axially symmetric black hole solutions in an Einstein-Yang-Mills-Higgs-U(1)-dilaton theory. In this approach, one set of solutions possesses a nonzero magnetic charge, while the other solutions represent black holes located in between a monopole-antimonopole pair. A detailed analysis of the solutions' properties is presented, the domain of existence of the black strings being determined. New four dimensional solutions are found by boosting the five dimensional configurations. We also present an argument for the non-existence of finite mass hyperspherically symmetric black holes in SU(2) Einstein-Yang-Mills theory. * yves.brihaye@umh.ac.be † b.hartmann@iu-bremen.de ‡ radu@thphys.nuim.ie
Physical Review B, 2003
We consider a Fröhlich-type Hamiltonian on a hexagonal lattice. Aiming to describe nanotubes, we ... more We consider a Fröhlich-type Hamiltonian on a hexagonal lattice. Aiming to describe nanotubes, we choose this 2-dimensional lattice to be periodic and to have a large extension in one (x) direction and a small extension in the other (y) direction. We study the existence of solitons in this model using both analytical and numerical methods. We find exact solutions of our equations and discuss some of their properties.
Physical Review D, 2013
We study the geodesic motion of test particles in the space-time of non-compact boson stars. Thes... more We study the geodesic motion of test particles in the space-time of non-compact boson stars. These objects are made of a self-interacting scalar field and -depending on the scalar field's mass -can be as dense as neutron stars or even black holes. In contrast to the former these objects do not contain a well-defined surface, while in contrast to the latter the space-time of boson stars is globally regular, can -however -only be given numerically. Hence, the geodesic equation also has to be studied numerically. We discuss the possible orbits for massive and massless test particles and classify them according to the particle's energy and angular momentum. The space-time of a boson star approaches the Schwarzschild space-time asymptotically, however deviates strongly from it close to the center of the star. As a consequence, we find additional bound orbits of massive test particles close to the center of the star that are not present in the Schwarzschild case. Our results can be used to make predictions about extreme-mass-ratio inspirals (EMRIs) and we hence compare our results to recent observational data of the stars orbiting Sagittarius A * -the radiosource at the center of our own galaxy.
Physical Review D, 2008
This investigation follows up the suggestion that the equation of state for superconducting cosmi... more This investigation follows up the suggestion that the equation of state for superconducting cosmic strings provided by Witten's prototype biscalar field model can be well represented by an effective Lagrangian of simple logarithmic form depending on only 3 independent parameters. The numerical work described here confirms the validity of this approximation, and initiates the evaluation of the 3 required parameters, as functions of the masses and other parameters specifying the underlying U(1) × U(1) scalar field model in the limit for which the relevant gauge coupling constants are small.In this limit, subject to calibration of the relevant length and mass scales, the scalar field model is characterised by just 3 dimensionless ratios which (in order to provide conducting strings) must be subject to three inequalities (of which two have obvious analytic expressions). It is found here that when all three of these inequalities are satisfied by a reasonably large margin, there is a simple empirical formula that can be used to provide a fairly accurate prescription for the algebraic dependence on these 3 dimensionless ratios of the 3 parameters required for the logarithmic equation of state.
We construct supersymmetric Q-balls and boson stars in (d + 1) dimensions. These non-topological ... more We construct supersymmetric Q-balls and boson stars in (d + 1) dimensions. These non-topological solitons are solutions of a scalar field model with global U (1) symmetry and a scalar field potential that appears in gauge-mediated supersymmetry (SUSY) breaking in the minimal supersymmetric extension of the Standard Model (MSSM). We are interested in both the asymptotically flat as well as in the asymptotically Anti-de Sitter (AdS) solutions. In particular, we show that for our choice of the potential gravitating, asymptotically flat boson stars exist in (2 + 1) dimensions. We observe that the behaviour of the mass and charge of the asymptotically flat solutions at the approach of the maximal frequency depends strongly on the number of spatial dimensions. For the asymptotically AdS solutions, the model on the conformal boundary can be interpreted as describing d-dimensional condensates of scalar glueballs.
We construct boson stars in (4+1)-dimensional Gauss-Bonnet gravity. We study the properties of th... more We construct boson stars in (4+1)-dimensional Gauss-Bonnet gravity. We study the properties of the solutions in dependence on the coupling constants and investigate these in detail. While the "thick wall" limit is independent of the value of the Gauss-Bonnet coupling, we find that the spiraling behaviour characteristic for boson stars in standard Einstein gravity disappears for large enough values of the Gauss-Bonnet coupling. Our results show that in this case the scalar field can not have arbitrarily high values at the center of the boson star and that it is hence impossible to reach the "thin wall" limit. Moreover, for large enough Gauss-Bonnet coupling we find a unique relation between the mass and the radius (qualitatively similar to those of neutron stars) which is not present in the Einstein gravity limit.
We construct rotating boson stars in (4+1)-dimensional asymptotically Anti-de Sitter space-time (... more We construct rotating boson stars in (4+1)-dimensional asymptotically Anti-de Sitter space-time (aAdS) with two equal angular momenta that are composed out of a massive and self-interacting scalar field. These solutions possess a single Killing vector field. Next to the fundamental solutions radially excited rotating boson stars exist. We find that the behaviour of the solutions for small angular momenta is very well described by the corresponding oscillons. We also discuss the classical stability and find that self-interacting rotating boson stars in aAdS are classically unstable for a large range of the gravitational coupling and the Antide Sitter radius, respectively, can -however -be classically stable for sufficiently large angular momenta. Furthermore, very compact boson stars suffer from a superradiant instability. Our results indicate that this superradiant instability appears only for classically unstable solutions.
Nuclear Physics B - Proceedings Supplements, 2014
The stability of black holes and solitons in d-dimensional Anti-de Sitter (AdS d ) space-time aga... more The stability of black holes and solitons in d-dimensional Anti-de Sitter (AdS d ) space-time against scalar field condensation is discussed. The resulting solutions are "hairy" black holes and solitons, respectively. In particular, we will discuss static black hole solutions with hyperbolic, flat and spherical horizon topology and emphasize that two different type of instabilities exist depending on whether the scalar field is charged or uncharged, respectively. We will also discuss the influence of Gauss-Bonnet curvature terms. The results have applications within the AdS/CFT correspondence and describe e.g. holographic insulator/conductor/superconductor phase transitions.
ABSTRACT We study the geodesic equation in the space-time of an Abelian-Higgs string and discuss ... more ABSTRACT 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. Comment: 20 pages including 14 figures; v2: references added, discussion on null geodesics extended, numerical results added
Classical and Quantum Gravity, 2015
In this paper we analyze Abelian-Higgs strings in Rastall gravity. We construct string solutions ... more In this paper we analyze Abelian-Higgs strings in Rastall gravity. We construct string solutions that asymptote to a flat space-time with a deficit angle by solving the set of coupled non-linear ordinary differential equations numerically. Decreasing the Rastall parameter from its Einstein gravity value we find that the deficit angle of the space-time increases and becomes equal to 2π at some critical value of this parameter that depends on the remaining couplings in the model. For smaller values the resulting solutions are supermassive string solutions possessing a singularity at a finite distance from the string core. Assuming the Higgs boson mass to be on the order of the gauge boson mass we find that also in Rastall gravity this happens only when the symmetry breaking scale is on the order of the Planck mass. We also observe that for specific values of the parameters in the model the energy per unit length becomes proportional to the winding number, i.e. the degree of the map S 1 → S 1 . Unlike in the BPS limit in Einstein gravity, this is, however, not connect to an underlying mathematical structure, but rather constitutes a would-be-BPS bound.
Physics Letters B, 2012
We consider compact boson stars that arise for a V-shaped scalar field potential. They represent ... more We consider compact boson stars that arise for a V-shaped scalar field potential. They represent a one parameter family of solutions of the scaled Einstein-signum-Gordon equations. We analyze the physical properties of these solutions and determine their domain of existence. Along their physically relevant branch emerging from the compact Q-ball solution, their mass increases with increasing radius. Empoying arguments from catastrophe theory we argue that this branch is stable, until the maximal value of the mass is reached. There the mass and size are on the order of magnitude of the Schwarzschild limit, and thus the spiralling respectively oscillating behaviour, well-known for compact stars, sets in.
Physical Review D, 2010
We study rotating boson stars in five spacetime dimensions. The boson fields consist of a complex... more We study rotating boson stars in five spacetime dimensions. The boson fields consist of a complex doublet scalar field. Considering boson stars rotating in two orthogonal planes with both angular momenta of equal magnitude, a special ansatz for the boson field and the metric allows for solutions with nontrivial dependence on the radial coordinate only. The charge of the scalar field equals the sum of the angular momenta. The rotating boson stars are globally regular and asymptotically flat. For our choice of a sixtic potential the rotating boson star solutions possess a flat spacetime limit. We study the solutions in flat and curved spacetime.
Physical Review D, 2012
We study the stability of (4 + 1)-dimensional charged Gauss-Bonnet black holes and solitons. We o... more We study the stability of (4 + 1)-dimensional charged Gauss-Bonnet black holes and solitons. We observe an instability related to the condensation of a scalar field and construct explicit "hairy" black hole and soliton solutions of the full system of coupled field equations. We investigate the cases of a massless scalar field as well as that of a tachyonic scalar field. The solitons with scalar hair exist for a particular range of the charge and the gauge coupling. This range is such that for intermediate values of the gauge coupling a "forbidden band" of charges for the hairy solitons exists. We also discuss the behaviour of the black holes with scalar hair when changing the horizon radius and/or the gauge coupling and find that various scenarios at the approach of a limiting solution appear. One observation is that hairy Gauss-Bonnet black holes never tend to a regular soliton solution in the limit of vanishing horizon radius. We also prove that extremal Gauss-Bonnet black holes can not carry massless or tachyonic scalar hair and show that our solutions tend to their planar counterparts for large charges.
Physical Review D, 2010
We study holographic superconductors in 3+1 dimensions away from the probe limit, i.e. taking bac... more We study holographic superconductors in 3+1 dimensions away from the probe limit, i.e. taking backreaction of the space-time into account. We consider the case of pure Einstein -and Gauss-Bonnet gravity, respectively. Similar to the probe limit we observe that the critical temperature at which condensation sets in decreases with increasing Gauss-Bonnet coupling. The decrease is however stronger when taking back-reaction of the space-time into account. We observe that the critical temperature becomes very small, but stays positive for all values of the Gauss-Bonnet coupling no matter how strong the back-reaction of the space-time is.
Physical Review D, 2009
ABSTRACT We study angularly excited as well as interacting non-topological solitons, so-called Q-... more ABSTRACT We study angularly excited as well as interacting non-topological solitons, so-called Q-balls and their gravitating counterparts, so-called boson stars in 3+1 dimensions. Q-balls and boson stars carry a non-vanishing Noether charge and arise as solutions of complex scalar field models in a flat space-time background and coupled minimally to gravity, respectively. We present examples of interacting Q-balls that arise due to angular excitations, which are closely related to the spherical harmonics. We also construct explicit examples of rotating boson stars that interact with non-rotating boson stars. We observe that rotating boson stars tend to absorb the non-rotating ones for increasing, but reasonably small gravitational coupling. This is a new phenomenon as compared to the flat space-time limit and is related to the negative contribution of the rotation term to the energy density of the solutions. In addition, our results indicate that a system of a rotating and non-rotating boson star can become unstable if the direct interaction term in the potential is large enough. This instability is related to the appearance of ergoregions. Comment: 20 pages including 9 figures; for higher quality figures please contact the authors; v2: minor changes, final version to appear in Phys. Rev. D
Journal of High Energy Physics, 2005
ABSTRACT
We study spherically symmetric soliton solutions in a model with a conformally coupled scalar fie... more We study spherically symmetric soliton solutions in a model with a conformally coupled scalar field as well as in full conformal gravity. We observe that a new type of limiting behaviour appears for particular choices of the self-coupling of the scalar field, i.e. the solitons interpolate smoothly between the Antide Sitter vacuum and an uncharged configuration. Furthermore, within conformal gravity the qualitative approach of a limiting solution does not change when varying the charge of the scalar field -contrary to the Einstein-Hilbert case. However, it changes with the scalar self-coupling.
We study Abelian strings in a fixed de Sitter background. We find that the gauge and Higgs fields... more We study Abelian strings in a fixed de Sitter background. We find that the gauge and Higgs fields extend smoothly across the cosmological horizon and that the string solutions have oscillating scalar fields outside the cosmological horizon for all currently accepted values of the cosmological constant. If the gauge to Higgs boson mass ratio is small enough, the gauge field function has a power-like behaviour, while it is oscillating outside the cosmological horizon if Higgs and gauge boson mass are comparable. Moreover, we observe that Abelian strings exist only up to a maximal value of the cosmological constant and that two branches of solutions exist that meet at this maximal value. We also construct radially excited solutions that only exist for non-vanishing values of the cosmological constant and are thus a novel feature as compared to flat space-time. Considering the effect of the de Sitter string on the space-time, we observe that the deficit angle increases with increasing cosmological constant.
Physical Review D, 2009
We investigate the properties of interacting Q-balls and boson stars that sit on top of each othe... more We investigate the properties of interacting Q-balls and boson stars that sit on top of each other in great detail. The model that describes these solutions is essentially a (gravitating)
Journal of High Energy Physics, 2013
We study field theoretical models for cosmic strings with flat directions in curved space-time. M... more We study field theoretical models for cosmic strings with flat directions in curved space-time. More precisely, we consider minimal models with semilocal, axionic and tachyonic strings, respectively. In flat space-time, isolated static and straight cosmic strings solutions of these models have a flat direction, i.e., a uniparametric family of configurations with the same energy exists which is associated with a zero mode. We prove that this zero mode survives coupling to gravity, and study the role of the flat direction when coupling the string to gravity. Even though the total energy of the solution is the same, and thus the global properties of the family of solutions remains unchanged, the energy density, and therefore the gravitational properties, are different. The local structure of the solutions depends strongly on the value of the parameter describing the flat direction; for example, for a supermassive string, the value of the free parameter can determine the size of the space-time.
Physical Review D - Particles, Fields, Gravitation and Cosmology, 2005
We study two classes of static uniform black string solutions in a (4 + 1)-dimensional SU(2) Eins... more We study two classes of static uniform black string solutions in a (4 + 1)-dimensional SU(2) Einstein-Yang-Mills model. These configurations possess a regular event horizon and corresponds in a 4−dimensional picture to axially symmetric black hole solutions in an Einstein-Yang-Mills-Higgs-U(1)-dilaton theory. In this approach, one set of solutions possesses a nonzero magnetic charge, while the other solutions represent black holes located in between a monopole-antimonopole pair. A detailed analysis of the solutions' properties is presented, the domain of existence of the black strings being determined. New four dimensional solutions are found by boosting the five dimensional configurations. We also present an argument for the non-existence of finite mass hyperspherically symmetric black holes in SU(2) Einstein-Yang-Mills theory. * yves.brihaye@umh.ac.be † b.hartmann@iu-bremen.de ‡ radu@thphys.nuim.ie
Physical Review B, 2003
We consider a Fröhlich-type Hamiltonian on a hexagonal lattice. Aiming to describe nanotubes, we ... more We consider a Fröhlich-type Hamiltonian on a hexagonal lattice. Aiming to describe nanotubes, we choose this 2-dimensional lattice to be periodic and to have a large extension in one (x) direction and a small extension in the other (y) direction. We study the existence of solitons in this model using both analytical and numerical methods. We find exact solutions of our equations and discuss some of their properties.
Physical Review D, 2013
We study the geodesic motion of test particles in the space-time of non-compact boson stars. Thes... more We study the geodesic motion of test particles in the space-time of non-compact boson stars. These objects are made of a self-interacting scalar field and -depending on the scalar field's mass -can be as dense as neutron stars or even black holes. In contrast to the former these objects do not contain a well-defined surface, while in contrast to the latter the space-time of boson stars is globally regular, can -however -only be given numerically. Hence, the geodesic equation also has to be studied numerically. We discuss the possible orbits for massive and massless test particles and classify them according to the particle's energy and angular momentum. The space-time of a boson star approaches the Schwarzschild space-time asymptotically, however deviates strongly from it close to the center of the star. As a consequence, we find additional bound orbits of massive test particles close to the center of the star that are not present in the Schwarzschild case. Our results can be used to make predictions about extreme-mass-ratio inspirals (EMRIs) and we hence compare our results to recent observational data of the stars orbiting Sagittarius A * -the radiosource at the center of our own galaxy.
Physical Review D, 2008
This investigation follows up the suggestion that the equation of state for superconducting cosmi... more This investigation follows up the suggestion that the equation of state for superconducting cosmic strings provided by Witten's prototype biscalar field model can be well represented by an effective Lagrangian of simple logarithmic form depending on only 3 independent parameters. The numerical work described here confirms the validity of this approximation, and initiates the evaluation of the 3 required parameters, as functions of the masses and other parameters specifying the underlying U(1) × U(1) scalar field model in the limit for which the relevant gauge coupling constants are small.In this limit, subject to calibration of the relevant length and mass scales, the scalar field model is characterised by just 3 dimensionless ratios which (in order to provide conducting strings) must be subject to three inequalities (of which two have obvious analytic expressions). It is found here that when all three of these inequalities are satisfied by a reasonably large margin, there is a simple empirical formula that can be used to provide a fairly accurate prescription for the algebraic dependence on these 3 dimensionless ratios of the 3 parameters required for the logarithmic equation of state.