arXiv subjects
Publications and source records attributed to Christian G. Boehmer.
Inflation driven by a single dark spinor field is discussed. We define the notion of a dark spinor field and derive the cosmological field equations for such a matter source. The conditions for inflation are determined and an exactly solvable model is presented. We find the power spectrum of the quantum fluctuation of this field and compare the results with scalar field inflation.
We consider the behavior of the tangential velocity of test particles moving in stable circular orbits in f(R) modified theories of gravity. A large number of observations at the galactic scale have shown that the rotational velocities of massive test particles (hydrogen clouds) tend towards constant values at large distances from the galactic center. We analyze the vacuum gravitational field equations in f(R) models in the constant velocity region, and the general form of the metric tensor is derived in a closed form. The resulting modification of the Einstein-Hilbert Lagrangian is of the form R^{1+n}, with the parameter n expressed in terms of the tangential velocity. Therefore we find that to explain the motion of test particles around galaxies requires only very mild deviations from classical general relativity, and that modified gravity can explain the galactic dynamics without the need of introducing dark matter.
We generalize the virial theorem in f(R) modified gravity using the collisionless Boltzmann equation. We find supplementary geometric terms in the modified Einstein equation providing an effective contribution to the gravitational energy. The total virial mass is proportional to the effective mass associated with the new geometrical term, which may account for the well-known virial theorem mass discrepancy in clusters of galaxies. The model predicts that the geometric mass and its effects extend beyond the virial radius of the clusters. We also consider the behavior of the galaxy cluster velocity dispersion in f(R) models. Thus, the f(R) virial theorem can be an efficient tool in observationally testing the viability of this class of generalized gravity models.
Exact solutions of traversable wormholes were recently found under the assumption of spherical symmetry and the existence of a non-static conformal symmetry. In this paper, we verify that in the case of the conformally symmetric spacetimes with a non-static vector field generating the symmetry, the conformal factor $ψ$ can be physically interpreted in terms of a measurable quantity, namely, the tangential velocity of a massive test particle moving in a stable circular orbit in the spacetime. Physical properties of the rotational velocity of test particles and of the redshift of radiation emitted by ultra-relativistic particles rotating around these hypothetical general relativistic objects are further discussed. Finally, specific characteristics and properties of gravitational bremsstrahlung emitted by charged particles in geodesic motion in conformally symmetric wormhole geometries are also explored.
The classical tests of general relativity (perihelion precession, deflection of light, and the radar echo delay) are considered for the Dadhich, Maartens, Papadopoulos and Rezania (DMPR) solution of the spherically symmetric static vacuum field equations in brane world models. For this solution the metric in the vacuum exterior to a brane world star is similar to the Reissner-Nordstrom form of classical general relativity, with the role of the charge played by the tidal effects arising from projections of the fifth dimension. The existing observational solar system data on the perihelion shift of Mercury, on the light bending around the Sun (obtained using long-baseline radio interferometry), and ranging to Mars using the Viking lander, constrain the numerical values of the bulk tidal parameter and of the brane tension.
We examine static perfect fluid spheres in the presence of a cosmological constant. New exact matter solutions are discussed which require the Nariai metric in the vacuum region. We generalize the Einstein static universe such that neither its energy density nor its pressure is constant throughout the spacetime. Using analytical techniques we derive conditions depending on the equation of state to locate the vanishing pressure surface. This surface can in general be located in regions with decreasing area group orbits. We use numerical methods to integrate the field equations for realistic equations of state and find consistent results.
Dark energy and dark matter are the dominant sources in the evolution of the late universe. They are currently only indirectly detected via their gravitational effects, and there could be a coupling between them without violating observational constraints. We investigate the background dynamics when dark energy is modelled as exponential quintessence, and is coupled to dark matter via simple models of energy exchange. We introduce a new form of dark sector coupling, which leads to a more complicated dynamical phase space and has a better physical motivation than previous mathematically similar couplings.
We examine the Schwarzschild interior of a black hole, incorporating quantum gravitational modifications due to loop quantum gravity. We consider an improved loop quantization using techniques that have proven successful in loop quantum cosmology. The central Schwarzschild singularity is resolved and the implications for the fate of an in-falling test particle in the interior region is discussed. The singularity is replaced by a Nariai type Universe. We discuss the resulting conformal diagram, providing a clear geometrical interpretation of the quantum effects.
We suggest a novel extension to the Kaluza-Klein scheme that allows us to obtain consistently all SU(n) Einstein-Yang-Mills theories. This construction is based on allowing the five-dimensional spacetime to carry some non-vanishing torsion; however, the four-dimensional spacetime remains intrinsically torsion-free.
Exact solutions of traversable wormholes are found under the assumption of spherical symmetry and the existence of a {\it non-static} conformal symmetry, which presents a more systematic approach in searching for exact wormhole solutions. In this work, a wide variety of solutions are deduced by considering choices for the form function, a specific linear equation of state relating the energy density and the pressure anisotropy, and various phantom wormhole geometries are explored. A large class of solutions impose that the spatial distribution of the exotic matter is restricted to the throat neighborhood, with a cut-off of the stress-energy tensor at a finite junction interface, although asymptotically flat exact solutions are also found. Using the ``volume integral quantifier,'' it is found that the conformally symmetric phantom wormhole geometries may, in principle, be constructed by infinitesimally small amounts of averaged null energy condition violating matter. Considering the tidal acceleration traversability conditions for the phantom wormhole geometry, specific wormhole dimensions and the traversal velocity are also deduced.
The cosmological constant sets certain scales important in cosmology. We show that Lambda in conjunction with other parameters like the Schwarzschild radius leads to scales relevant not only for cosmological but also for astrophysical applications. Of special interest is the extension of orbits and velocity of test particles traveling over Mpc distances. We will show that there exists a lower and an upper cut-off on the possible velocities of test particles. For a test body moving in a central gravitational field Lambda enforces a maximal value of the angular momentum if we insist on bound orbits of the test body which move at a distance larger than the Schwarzschild radius.
Astrophysical bounds on the cosmological constant are examined for spherically symmetric bodies. Similar limits emerge from hydrostatical and gravitational equilibrium and the validity of the Newtonian limit. It is argued that the bound coming from the analysis of exact solutions is not a feature of the relativistic theory since it also emerges from the Newtonian theory. The methods in use seem to be disjoint from the basic principles, however they have the same implication regarding the upper bounds. Therefore we will compare different inequalities and comment on the possible relationship between them.
We analyze the stability of the Einstein static universe by considering homogeneous scalar perturbations in the context of f(R) modified theories of gravity. By considering specific forms of f(R), the stability regions of the solutions are parameterized by a linear equation of state parameter w=p/rho. Contrary to classical general relativity, it is found that in f(R) gravity a stable Einstein cosmos with a positive cosmological constant does indeed exist. Thus, we are lead to conclude that, in principle, modifications in f(R) gravity stabilize solutions which are unstable in general relativity.
The equation of motion for test particles in $f(R)$ modified theories of gravity is derived. By considering an explicit coupling between an arbitrary function of the scalar curvature, $R$, and the Lagrangian density of matter, it is shown that an extra force arises. This extra force is orthogonal to the four-velocity and the corresponding acceleration law is obtained in the weak field limit. Connections with MOND and with the Pioneer anomaly are further discussed.
The Florides solution, proposed as an alternative to the interior Schwarzschild solution, represents a static and spherically symmetric geometry with vanishing radial stresses. It is regular at the center, and is matched to an exterior Schwarzschild solution. The specific case of a constant energy density has been interpreted as the field inside an Einstein cluster. In this work, we are interested in analyzing the geometry throughout the permitted range of the radial coordinate without matching it to the Schwarzschild exterior spacetime at some constant radius hypersurface. We find an interesting picture, namely, the solution represents a three-sphere, whose equatorial two-sphere is singular, in the sense that the curvature invariants and the tangential pressure diverge. As far as we know, such singularities have not been discussed before. In the presence of a large negative cosmological constant (anti-de Sitter) the singularity is removed.
The present paper analyses the Einstein-Cartan theory of gravitation with Elko spinors as sources of curvature and torsion. After minimally coupling the Elko spinors to torsion, the spin angular momentum tensor is derived and its structure is discussed. It shows a much richer structure than the Dirac analogue and hence it is demonstrated that spin one half particles do not necessarily yield only an axial vector torsion component. Moreover, it is argued that the presence of Elko spinors partially solves the problem of minimally coupling Maxwell fields to Einstein-Cartan theory.
This diploma thesis analyses static, spherically symmetric perfect fluid solutions to Einstein's field equations with cosmological constant. Constant density solutions are derived for different values of the cosmological constant. Eleven types of solutions are found, with an overview given at page 41. Furthermore the existence of a global solution is proved for a cosmological constant smaller than 4 Pi the boundary density, which is given by the equation of state.
Einstein's field equations with cosmological constant are analysed for a static, spherically symmetric perfect fluid having constant density. Five new global solutions are described. One of these solutions has the Nariai solution joined on as an exterior field. Another solution describes a decreasing pressure model with exterior Schwarzschild-de Sitter spacetime having decreasing group orbits at the boundary. Two further types generalise the Einstein static universe. The other new solution is unphysical, it is an increasing pressure model with a geometric singularity.