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F. R. Klinkhamer

Publications and source records attributed to F. R. Klinkhamer.

At least 73 records · Page 4Linked to original sources
arXiv2014

Comparison of spacetime defects which are homeomorphic but not diffeomorphic

Certain remnants of a quantum spacetime foam can be modeled by a distribution of defects embedded in a flat classical spacetime. The presence of such spacetime defects affects the propagation of elementary particles. In this article, we show explicitly that both topology and differential structure of the defects are important for the particle motion. Specifically, we consider three types of spacetime defects which are described by the same topological manifold $\mathbb{R}\times\big(\mathbb{R}P^3-\{\text{point}\}\big)$ but which are not diffeomorphic to each other. We investigate the propagation of a massless scalar field over the three different manifolds and find different solutions of the \mbox{Klein--Gordon} equation.

hep-th↗
arXiv2014

Skyrmion spacetime defect

A finite-energy static classical solution is obtained for standard Einstein gravity coupled to an $SO(3)\times SO(3)$ chiral model of scalars [a Skyrme model]. This nonsingular localized solution has nontrivial topology for both the spacetime manifold and the $SO(3)$ matter fields. The solution corresponds to a single spacetime defect embedded in flat Minkowski spacetime.

gr-qc↗
arXiv2014

A new type of nonsingular black-hole solution in general relativity

Certain exact solutions of the Einstein field equations over nonsimply-connected manifolds are reviewed. These solutions are spherically symmetric and have no curvature singularity. They provide a regularization of the standard Schwarzschild solution with a curvature singularity at the center. Spherically symmetric collapse of matter in $\mathbb{R}^4$ may result in these nonsingular black-hole solutions, if quantum-gravity effects allow for topology change near the center or if nontrivial topology is already present as a remnant from a quantum spacetime foam.

gr-qc↗
arXiv2014

A nonsingular spacetime defect

A nonsingular localized static classical solution is constructed for standard Einstein gravity coupled to an $SO(3)\times SO(3)$ chiral model of scalars (Skyrme model). This solution corresponds to a spacetime defect and its construction proceeds in three steps. First, an \textit{Ansatz} is presented for a solution with nonsimply connected topology of the spacetime manifold. Second, an exact vacuum solution of the reduced field equations is obtained. Third, matter fields are included and a particular exact solution of the reduced field equations is found. The latter solution has a diverging total energy, but its existence at least demonstrates that a nonsingular defect-type solution having nonsimply connected topology is possible with nontrivial matter fields.

gr-qc↗
arXiv2014

Black-hole solution without curvature singularity and closed timelike curves

With a prescribed Coulomb-type energy-momentum tensor, an exact solution of the Einstein field equations over a nonsimply-connected manifold is presented. This spherically symmetric solution has neither curvature singularities nor closed timelike curves. It can be considered to be a regularization of the singular Reissner-Nordstrom solution over a simply-connected manifold.

gr-qc↗
arXiv2013

Black-hole solution without curvature singularity

An exact solution of the vacuum Einstein field equations over a nonsimply-connected manifold is presented. This solution is spherically symmetric and has no curvature singularity. It can be considered to be a regularization of the Schwarzschild solution over a simply-connected manifold, which has a curvature singularity at the center. Spherically symmetric collapse of matter in R^4 may result in this nonsingular black-hole solution, if quantum-gravity effects allow for topology change near the center.

gr-qc↗
arXiv2013

Standard Model Higgs field and energy scale of gravity

The effective potential of the Higgs scalar field in the Standard Model may have a second degenerate minimum at an ultrahigh vacuum expectation value. This second minimum then determines, by radiative corrections, the values of the top-quark and Higgs-boson masses at the standard minimum corresponding to the electroweak energy scale. An argument is presented that this ultrahigh vacuum expectation value is proportional to the energy scale of gravity, E_{Planck} \equiv \sqrt{\hbar c^5/G_N}, considered to be characteristic of a spacetime foam. In the context of a simple model, the existence of kink-type wormhole solutions places a lower bound on the ultrahigh vacuum expectation value and this lower bound is of the order of E_{Planck}.

hep-ph↗
arXiv2013

Neutrino mass and the Standard Model

It is pointed out (not for the first time) that the minimal Standard Model, without additional gauge-singlet right-handed neutrinos or isotriplet Higgs fields, allows for nonvanishing neutrino masses and mixing. The required interaction term is nonrenormalizable and violates the global B-L symmetry. The ultimate explanation of this interaction term may or may not rely on grand unification.

hep-ph↗
arXiv2012

Gravity Without Curved Spacetime: A Simple Calculation

Classical-particle trajectories are calculated for the static Einstein universe without requiring that the 3-space be closed and curved. Freely-moving test particles are found to return to their starting positions because of strong gravitational-field effects. Possible implications for the underlying (quantum) theory of gravity are briefly discussed.

gr-qc↗
arXiv2012

De-Sitter-spacetime instability from a nonstandard vector field

It is found that de-Sitter spacetime, the constant-curvature matter-free solution of the Einstein equations with a positive cosmological constant, becomes classically unstable due to the dynamic effects of a certain type of vector field (fundamentally different from a gauge field). The perturbed de-Sitter universe evolves towards a final exotic singularity. The relevant vector-field configurations violate the strong and dominant energy conditions.

gr-qc↗
arXiv2012

Spontaneously broken Lorentz invariance from the dynamics of a heavy sterile neutrino

A relativistic theory for neutrino superluminality is presented (in principle, the same mechanism applies also to other fermions). The theory involves the standard-model particles and one additional heavy sterile neutrino with an energy-scale close to or above the electroweak one, all particles propagating in the usual 3+1 spacetime dimensions. Lorentz violation results from spontaneous symmetry breaking in the sterile-neutrino sector. The theory tries, as far as possible, to be consistent with the existing experimental data from neutrino physics and to keep the number of assumptions minimal. There are clear experimental predictions which can be tested.

hep-ph↗
arXiv2012

Possible solution to the main cosmological constant problem

A modified-gravity-type model of two hypothetical massless vector fields is presented. These vector fields are gravitationally coupled to standard matter and an effective cosmological constant. Considered in a cosmological context, the vector fields dynamically cancel an arbitrary cosmological constant, and flat Minkowski spacetime appears as the limit of attractor-type solutions of the field equations. Asymptotically, the field equations give rise to a standard Friedmann-Robertson-Walker universe and standard Newtonian gravitational dynamics of small systems.

hep-th↗
arXiv2012

Vector-field model with compensated cosmological constant and radiation-dominated FRW phase

A special model of a massless vector-field is presented, which has an extra modified-gravity-type interaction term in the action. The cosmology of the model is studied with standard noninteracting relativistic matter added. It is found that this cosmology can have an early phase where the vector-field starts to compensate a (Planck-scale) cosmological constant and a late Friedmann-Robertson-Walker (FRW) phase where the relativistic-matter energy density dominates the dynamic vacuum energy density.

gr-qc↗
arXiv2012

Entropic-gravity derivation of MOND

A heuristic entropic-gravity derivation has previously been given of the gravitational two-body force of modified Newtonian dynamics (MOND). Here, it is shown that also another characteristic of MOND can be recovered, namely, the external field effect (implying a violation of the Strong Equivalence Principle). In fact, the derivation gives precisely the modified Poisson equation which Bekenstein and Milgrom proposed as a consistent nonrelativistic theory of MOND.

gr-qc↗
arXiv2012

Reconsidering a higher-spin-field solution to the main cosmological constant problem

Following an earlier suggestion by Dolgov, we present a specific model of two massless vector fields which dynamically cancel a cosmological constant of arbitrary magnitude and sign. Flat Minkowski spacetime appears asymptotically as an attractor of the field equations. Unlike the original model, the new model does not upset the local Newtonian gravitational dynamics.

hep-th↗
arXiv2012

Dynamically broken Lorentz invariance from the Higgs sector?

The original Abelian U(1) Higgs model in flat spacetime is enlarged by the addition of one real scalar with a particular potential. It is then shown that, while maintaining the original masses of the vector boson and Higgs scalar, there exists a time-dependent homogeneous solution of the classical field equations, which corresponds to dynamical breaking of Lorentz invariance (DBLI). The same DBLI mechanism holds for the standard model enlarged by the addition of a real isosinglet scalar with an appropriate potential. The resulting DBLI with an assumed TeV energy scale would manifest itself primarily in the interactions of the two scalar particles. In principle, this DBLI could feed into the neutrino sector and give rise to a superluminal maximum velocity.

hep-ph↗
arXiv2012

Newton's gravitational coupling constant from a quantum of area

A previous calculation of Newton's gravitational coupling constant G is generalized. This generalization makes it possible to have "atoms of two-dimensional space" with an integer dimension d_{atom} of the internal space, where the case d_{atom}=1 is excluded. Given the quantum of area l^2, the final formula for G is inversely proportional to the logarithm of the integer d_{atom}. The generalization used may be interpreted as a modification of the energy equipartition law of the microscopic degrees of freedom responsible for gravity, suggesting some form of long-range interaction between these degrees of freedom themselves.

hep-th↗