arXiv subjects
Publications and source records attributed to Günter Scharf.
We study inhomogeneous perturbations away from the strongly homogeneous background cosmology previously studied. The problem is greatly simplified by using the mapping on the inner Schwarzschild solution. The resulting linear perturbation equations can be solved by power series. The solution leads to a finite energy density, but the pressure must be zero.
We assume a one-to-one correspondence between comoving coordinates and the cosmic rest frame in a spherically symmetric inhomogeneous universe. This strongly restricts the solutions of Einstein's equations: (i) The pressure must be zero. (ii) The metric does not depend on the radial coordinate, the FLRW cosmology is excluded (strong homogeneity). (iii) The unique solution corresponds to the Datt-Ruban solution. Beside the Hubble constant it contains one free constant of integration which can be chosen in order to represent the measured Hubble diagram without using a cosmological constant.
We study Einstein's equations with an isotropic but inhomogeneous metric in the cosmic rest frame. The equations are solved perturbatively in the late Universe. The leading plus next-to-leading order results agree with observations without using a cosmological constant or dark matter.
We show that the Schwarzschild solution can be embedded in a class of nonstandard solutions of the vacuum Einstein's equations with arbitrary rotation curves. These nonstandard solutions have to be taken as physical if dark matter as needed in the standard theory cannot be found. As a consequence general relativity is considered as a classical field theory in Minkowski space and not as a geometric theory in the sense of Einstein.
Considering radial geodesics in the Robertson-Walker metric leads us to abandon the co-moving coordinates. Instead we work in the cosmic rest frame. Since then the matter is in motion, the solution of Einstein's equations is more complicated. We calculate the first correction to standard cosmology which has an off-diagonal term b dt dr in the metric. It describes the late universe. We then solve Maxwell's equations in the new metric and discuss redshift and luminosities. We obtain the correct age of the universe T=14 Gyr= 1/H, without assuming a cosmological constant.
We revisit the Kerr metric in Boyer-Lindquist coordinates and construct the corresponding class of nonstandard solutions of Einstein's equations. These solutions can be used to describe the outer part of spiral galaxies without assuming dark matter.
We study Einstein's equations with matter in hydrostatic equilibrium in the nonstandard gauge which was recently investigated in the vacuum case. We obtain spherically symmetric solutions for any given rotation curve. These solutions can be used to describe the bulge of a galaxy without assuming dark matter.
We show that Einstein's equations in a non-standard gauge have vacuum solutions with an asymptotically flat rotation curve as it is observed in the dark halos of galaxies. Introducing a material disk into this model we find a matter density in accordance with the Tully-Fisher relation.
We continue to study the spherically symmetric vacuum solutions of the tensor-four-scalars theory which is a modification of general relativity. Our aim is to construct vacuum solutions with asymptotically constant circular velocity curves which can be used to represent the dark halo outside the baryonic matter. These solutions are obtained by means of a new non-standard gauge in the field equations. The metric is expressed in terms of the rotation curve $V(r)$ in closed form.
We continue the study of the tensor-four-scalars theory which is a modification of general relativity. We include normal matter by applying the displace, cut, and reflect method to our previous vacuum solutions with dark halo. The resulting disklike solution has physical and unphysical features: the matter density for large radius is proportional to the forth power of the circular velocity in agreement with the Tully-Fisher relation; but the radial pressure is negative.
Based on the derivation of the macroscopic Maxwell's equations by spatial averaging of the microscopic equations, we discuss the electrophysiology of living organs. Other methods of averaging (or homogenization) like the bidomain model are not compatible with Maxwell's theory. We also point out that modeling the active cells by source currents is not a suitable description of the situation from first principles. Instead, it turns out that the main source of the measured electrical potentials is the polarization charge density which exists at the membranes of the active cells and adds up to a macroscopic polarization. The latter is the source term in the Laplace equation, the solution of which gives the measured far-field potential. As a consequence it is the polarization or dipole density which is best suited for localization of cardiac arrhythmia.
We consider the supersymmetric vector multiplet in a purely quantum framework. We obtain some discrepancies with respect to the literature in the expression of the super-propagator and we prove that the model is consistent only for positive mass. The gauge structure is constructed purely deductive and leads to the necessity of introducing scalar ghost superfields, in analogy to the usual gauge theories. The construction of a consistent supersymmetric gauge theory based on the vector model depends crucially one the definition of gauge invariance. We find some significant difficulties to impose a supersymmetric gauge invariance condition for the usual expressions from the literature.
A recent construction of the electroweak theory, based on perturbative quantum gauge invariance alone, is extended to the case of more generations of fermions with arbitrary mixing. The conditions implied by second order gauge invariance lead to an isolated solution for the fermionic couplings in agreement with the standard model. Third order gauge invariance determines the Higgs potential. The resulting massive gauge theory is manifestly gauge invariant, after construction.
The concept of perturbative gauge invariance formulated exclusively by means of asymptotic fields is used to construct massive gauge theories. We consider the interactions of $r$ massive and $s$ massless gauge fields together with $(r+s)$ fermionic ghost and anti-ghost fields. First order gauge invariance requires the introduction of unphysical scalars (Goldstone bosons) and fixes their trilinear couplings. At second order additional physical scalars (Higgs fields) are necessary, their coupling is further restricted at third order. In case of one physical scalar all couplings are determined by gauge invariance, including the Higgs potential. For three massive and one massless gauge field the $SU(2)\times U(1)$ electroweak theory comes out as the unique solution.