arXiv subjects
Publications and source records attributed to Franz E. Schunck.
We investigate the possible gravitational redshift values for boson stars with a self-interaction, studying a wide range of possible masses. We find a limiting value of z_lim \simeq 0.687 for stable boson star configurations. We can exclude the direct observation of boson stars. X-ray spectroscopy is perhaps the most interesting possibility.
We investigate the stability of general-relativistic boson stars by classifying singularities of differential mappings and compare it with the results of perturbation theory. Depending on the particle number, the star has the following regimes of behavior: stable, metastable, pulsation, and collapse.
We reconsider the nonlinear second order Abel equation of Stewart and Lyth, which follows from a nonlinear second order slow-roll approximation. We find a new eigenvalue spectrum in the blue regime. Some of the discrete values of the spectral index n_s have consistent fits to the cumulative COBE data as well as to recent ground-base CMB experiments.
We use the informations known so far about elementary particles in order to construct a simple model. We find a reason for the gyromagnetic factor of 2 for leptons and a vivid imagination for the weak interaction. By this, we understand, why the elementary particles with lowest mass are stable and all other unstable.
We present a model which determines the correct value of the magnetic dipole moment of the electron. By this, we find a physical meaning for the electron spin.
There is accumulating evidence that (fundamental) scalar fields may exist in Nature. The gravitational collapse of such a boson cloud would lead to a boson star (BS) as a new type of a compact object. Similarly as for white dwarfs and neutron stars, there exists a limiting mass, below which a BS is stable against complete gravitational collapse to a black hole. According to the form of the self-interaction of the basic constituents and the spacetime symmetry, we can distinguish mini-, axidilaton, soliton, charged, oscillating and rotating BSs. Their compactness prevents a Newtonian approximation, however, modifications of general relativity, as in the case of Jordan-Brans-Dicke theory as a low energy limit of strings, would provide them with gravitational memory. In general, a BS is a compact, completely regular configuration with structured layers due to the anisotropy of scalar matter, an exponentially decreasing 'halo', a critical mass inversely proportional to constituent mass, an effective radius, and a large particle number. Due to the Heisenberg principle, there exists a completely stable branch, and as a coherent state, it allows for rotating solutions with quantised angular momentum. In this review, we concentrate on the fascinating possibilities of detecting the various subtypes of (excited) BSs: Possible signals include gravitational redshift and (micro-)lensing, emission of gravitational waves, or, in the case of a giant BS, its dark matter contribution to the rotation curves of galactic halos.
A possible equivalence of scalar dark matter, the inflaton, and modified gravity is analyzed. After a conformal mapping, the dependence of the effective Lagrangian on the curvature is not only singular but also bifurcates into several almost Einsteinian spaces, distinguished only by a different effective gravitational strength and cosmological constant. A swallow tail catastrophe in the bifurcation set indicates the possibility for the coexistence of different Einsteinian domains in our Universe. This `triple unification' may shed new light on the nature and large scale distribution not only of dark matter but also on `dark energy', regarded as an effective cosmological constant, and inflation.
Galactic dark matter is modelled by a scalar field in order to effectively modify Kepler's law without changing standard Newtonian gravity. In particular, a solvable toy model with a self-interaction U(Phi) borrowed from non-topological solitons produces already qualitatively correct rotation curves and scaling relations. Although relativistic effects in the halo are very small, we indicate corrections arising from the general relativistic formulation. Thereby, we can also probe the weak gravitational lensing of our soliton type halo. For cold scalar fields, it corresponds to a gravitationally confined Boson-Einstein condensate, but of galactic dimensions.
Oscillatons are solutions of the coupled Einstein-Klein-Gordon (EKG) equations that are globally regular and asymptotically flat. By means of a Legendre transformation we are able to visualize the behaviour of the corresponding objects in non-linear gravity where the scalar field has been absorbed by means of the conformal mapping.
By using the rather stringent nonlinear second order slow-roll approximation, we reconsider the nonlinear second order Abel equation of Stewart and Lyth. We determine a new blue eigenvalue spectrum. Some of the discrete values of the spectral index $n_s$ have consistent fits to the cumulative COBE data as well as to recent ground-base CMB experiments.
We discuss boson stars as possible gravitational lenses and study the lensing effect by these objects made of scalar particles. The mass and the size of a boson star may vary from an individual Newtonian object similar to the Sun to the general relativistic size and mass of a galaxy close to its Schwarzschild radius. We assume boson stars to be transparent which allows the light to pass through them though the light is gravitationally deflected. We assume boson stars of the mass $M = 10^{10}M_\odot$ to be on non-cosmological distance from the observer. We discuss the lens equation for these stars as well as the details of magnification. We find that there are typically three images of a star but the deflection angles may vary from arcseconds to even degrees. There is one tangential critical curve (Einstein ring) and one radial critical curve for tangential and radial magnification, respectively. Moreover, the deflection angles for the light passing in the gravitational field of boson stars can be very large (even of the order of degrees) which reflects the fact they are very strong relativistic objects. We also propose a suitable formula for the lens equation for such large deflection angles, and with the reservation that large deflection angle images are highly demagnified but in the area of the tangential critical curve, their existence may help in observational detection of suitable lenses possessing characteristic features of boson stars which could also serve as a direct evidence for scalar fields in the universe.
The present surge for the astrophysical relevance of boson stars stems from the speculative possibility that these compact objects could provide a considerable fraction of the non-baryonic part of dark matter within the halo of galaxies. For a very light `universal' axion of effective string models, their total gravitational mass will be in the most likely range of \sim 0.5 M_\odot of MACHOs. According to this framework, gravitational microlensing is indirectly ``weighing" the axion mass, resulting in \sim 10^{-10} eV/c^2. This conclusion is not changing much, if we use a dilaton type self-interaction for the bosons. Moreover, we review their formation, rotation and stability as likely candidates of astrophysical importance.
We study boson star configurations with generic, but not non-topological, self-interaction terms, i.e. we do not restrict ourselves just to consider the standard $λ|ψ|^4$ interaction but more general U(1)-symmetry-preserving profiles. We find that when compared with the usual potential, similar results for masses and number of particles appear. However, changes are of order of few percent of the star masses. We explore the stability properties of the configurations, that we analyze using catastrophe theory. We also study possible observational outputs: gravitational redshifts, rotation curves of accreted particles, and lensing phenomena, and compare with the usual case.
We investigate the gravitational evolution of dark matter halos made up of a massless bosonic field. The coupled Einstein-Klein-Gordon equations are solved numerically, showing that such a boson halo is stable and can be formed under a large class of initial conditions. We also present an analytical proof that such objects are stable in the Newtonian limit. In the context of boson stars made of massive scalar fields, we introduce new solutions with an oscillatory scalar field, similar to boson halos. We find that these solutions are unstable.
We analyze the spherically symmetric Einstein field equation with a massless complex scalar field. We can use the Newtonian solutions to fit the rotation curve data of spiral and dwarf galaxies. From the general relativistic solutions, we can derive high gravitational redshift values.
Boson stars are descendants of the so-called geons of Wheeler, except that they are built from scalar particles instead of electromagnetic fields. If scalar fields exist in nature, such localized configurations kept together by their self-generated gravitational field can form within Einstein's general relativity. In the case of complex scalar fields, an absolutely stable branch of such non-topological solitons with conserved particle number exists. Our present surge stems from the speculative possibility that these compact objects could provide a considerable fraction of the non-baryonic part of dark matter. In any case, they may serve as a convenient "laboratory" for studying numerically rapidly rotating bodies in general relativity and the generation of gravitational waves.
The regular solutions for the Ginzburg-Landau (-Nielsen-Olesen) Abelian gauge model are studied numerically. We consider the static isolated cylindrically symmetric configurations. The well known (Abrikosov) vortices, which present a particular example of such solutions, play an important role in the theory of type II superconductors and in the models of structure formation in the early universe. We find new regular static isolated cylindrically symmetric solutions which we call the type B and the flux tube solutions. In contrast to the pure vortex configurations which have finite energy, the new regular solutions possess a finite Gibbs free energy. The flux tubes appear to be energetically the most preferable configurations in the interval of external magnetic fields between the thermodynamic critical value $H_{c}$ and the upper critical field $H_{c_2}$, while the pure vortex dominate only between the lower critical field $H_{c_1}$ and $H_{c}$. Our conclusion is thus that type B and flux tube solutions are important new elements necessary for the correct understanding of a transition from the vortex state to the completely normal state.
We present new regular static isolated cylindrically symmetric solutions for the Ginzburg-Landau model which have finite Gibbs free energy. These configurations (which we call the {\it flux tube} and {\it type B} solutions) are energetically favorable in the interval of the external magnetic fields between the thermodynamic critical value $H_{c}$ and the upper critical field $H_{c_2}$ which indicates that they are important new elements of the mixed state describing a transition from vortices to the normal state.