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Bjoern S. Schmekel

Publications and source records attributed to Bjoern S. Schmekel.

15 recordsLinked to original sources
arXiv2023

Constraints on the Lepton Charge, Spin and Mass from Quasi-Local Energy

The masses of the elementary particles as well as their charges and spins belong to the fundamental physical constants. Presently, no fundamental theory describing them is available, so their values remain mysterious. In this work we offer an approach based on the Brown-York quasi-local energy which includes the self-energy of an object. In order to compute this energy we model the spacetime of the renormalized electron (and other leptons) by the Kerr-Newman metric. Placing conditions on the associated energies at different radii we arrive at various constraints on the mass, charge and spin which are derived from the Planck scale. The large gap between the TeV-scale and the Planck energy is due to the highly non-trivial behavior of the used quasi-local potential.

physics.gen-ph↗
arXiv2023

Extracting Dynamical Degrees of Freedom From the Quasi-Local Energy Term in the Gravitational Action

It is shown that under proper conditions in an appropriate coordinate system with a suitable time slicing the Hamiltonian and the Einstein-Hilbert action including all necessary boundary terms can be written on shell in terms of the Brown-York quasi-local energy in the absence of matter. If matter is present the non-vanishing bulk term only consists of stress-energy. It is argued that the dynamical content of general relativity is stored in the quasi-local energy term. The results underscore the interpretation of the Brown-York quasi-local energy as the field energy of the gravitational field plus stress-energy. As an application we derive uncertainty relations of the time-energy kind which may be useful in the understanding of gravity induced quantum state reduction and the more conventional kind for conjugate variables. The latter is computed for a modified Vaidya metric which may be used in the investigation of black hole radiance. The boundary terms expressed as quasi-local energy cancel second derivatives in the action leaving only a square of a first derivative term in the chosen gauge which is desirable for a quantization of the action.

gr-qc↗
arXiv2021

Application of the Argument Principle to Functions Expressed as Mellin Transforms

We describe a numerical algorithm for evaluating the numbers of roots minus the number of poles contained in a region based on the argument principle with the function of interest being written as a Mellin transformation of a usually simpler function. Because the function to be transformed may be simpler than its Mellin transform whose roots are to be sought we express the final integrals in terms of the former accepting higher dimensional integrals. Nonlinear terms are expressed as convolutions approximating reciprocal values by exponential sums. As an example the final expression is applied to the Riemann Zeta function. The procedure is very inefficient numerically. However, depending on the function to be investigated it may be possible to find analytical estimates of the resulting integrals.

math.GM↗
arXiv2020

Note on the Conservation of Quasi-Local Energy in an Expanding Universe

Whether energy is conserved in a universe which keeps expanding is an intriguing question. It is tempting to argue that the total energy within the universe would have to increase as the universe expands. Upon more detailed inspection the question is a lot harder to settle since defining what is meant by energy or even what is meant by energy being conserved is a difficult problem in general relativity. Using the definition of quasi-local energy provided by Brown and York we try to answer the question in which sense the total energy in an expanding (or collapsing) universe is conserved.

gr-qc↗
arXiv2019

Quasi-Local Energy of a Charged Rotating Object Described by the Kerr-Newman Metric

The Brown-York quasi-local energy of a charged rotating black hole described by the Kerr-Newman metric and enclosed by a fixed-radius surface is computed. No further assumptions on the angular momentum or the radial coordinate in Boyer-Lindquist coordinates were made. The result can be expressed in terms of incomplete elliptic integrals and is used to analyze the self-energy of an electron which is assumed to be described by the Kerr-Newman metric. For this purpose the small sphere limit is investigated thoroughly comparing the analysis with known results. Evaluating the energy using the mass, angular momentum and charge of an electron a value in the order of the Planck energy is obtained in the small sphere limit as long as the Kerr-Newman metric acting as exterior solution can be used as a description of spacetime.

gr-qc↗
arXiv2018

Quasi-Local Energy of a Rotating Object Described by Kerr Spacetime

The Brown-York quasi-local energy of a rotating black hole described by the Kerr metric and enclosed by a fixed-radius surface is calculated by direct computation. No special assumptions on the angular momentum or the radial coordinate in Boyer-Lindquist coordinates were placed. The arbitrary reference term has been set to zero. The result may be relevant for applications in astrophysics, for modeling elementary particles or for extensions of the framework of quasi-local quantities. An analytic expression in terms of incomplete elliptic integrals is given.

gr-qc↗
arXiv2010

Do Computer Simulations Allow a Better Understanding of Basic Electrical Circuits than Real Lab Experiments?

Several Authors have demonstrated that substituting computer simulations for real experiments conducted in a lab may help to improve students' understanding of the material. In the present work we try to understand the reasons for this intriguing finding and investigate possible prerequisites necessary to achieve this outcome. The study was conducted in an introductory college-level physics class in Germany. All simulations were performed using PSPICE.

physics.ed-ph↗
arXiv2009

Collisionless Beam-Radiation Processes in the Laboratory and Astrophysics

Plasma instabilities can be encountered in many branches of physics. This work focuses on relativistic plasmas with applications in theoretical astrophysics and particle accelerator physics. Even though these fields seem to be unrelated the underlying plasma physics processes are often very similar. Two plasma instabilities - the beam-beam instability and the coherent synchrotron radiation instability - are analyzed. The former severely limits the achievable luminosity in storage rings and is related to the two-stream instability which has been proposed as a candidate for the radiation mechanism of radio pulsars. The main emphasis is on coherent synchrotron radiation which can lead to prohibitive energy losses in bunch compressors. Coherent synchrotron radiation also makes up the intense emission of radio waves by pulsars. Simple models based on the linearized Vlasov equation and relativistic magnetohydrodynamics which allow to compute detailed spectra of the emitted radiation are developed.

astro-ph.HE↗
arXiv2006

Coherent Synchrotron Radiation for Laminar Flows

We investigate the effect of shear in the flow of charged particle equilibria that are unstable to the Coherent Synchrotron Radiation (CSR) instability. Shear may act to quench this instability because it acts to limit the size of the region with a fixed phase relation between emitters. The results are important for the understanding of astrophysical sources of coherent radiation where shear in the flow is likely.

astro-ph↗
arXiv2006

Self-Renormalization of the Classical Quasilocal Energy

Pointlike objects cause many of the divergences that afflict physical theories. For instance, the gravitational binding energy of a point particle in Newtonian mechanics is infinite. In general relativity, the analog of a point particle is a black hole and the notion of binding energy must be replaced by quasilocal energy. The quasilocal energy (QLE) derived by York, and elaborated by Brown and York, is finite outside the horizon but it was not considered how to evaluate it inside the horizon. We present a prescription for finding the QLE inside a horizon, and show that it is finite at the singularity for a variety of types of black hole. The energy is typically concentrated just inside the horizon, not at the central singularity.

gr-qc↗
arXiv2005

Path Integral Over Black Hole Fluctuations

Evaluating a functional integral exactly over a subset of metrics that represent the quantum fluctuations of the horizon of a black hole, we obtain a Schroedinger equation in null coordinate time for the key component of the metric. The equation yields a current that preserves probability if we use the most natural choice of functional measure. This establishes the existence of blurred horizons and a thermal atmosphere. It has been argued previously that the existence of a thermal atmosphere is a direct concomitant of the thermal radiation of black holes when the temperature of the hole is greater than that of its larger environment, which we take as zero.

hep-th↗
arXiv2005

Simulation of Coherent Synchrotron Radiation Emission from Rotating Relativistic Electron Layers

The electromagnetic radiation of a rotating relativistic electron layers is studied numerically using particle-in-cell simulation. The results of the simulation confirm all relevant scaling properties predicted by theoretical models. These models may turn out to be important for the understanding of the coherent synchrotron radiation (CSR) instability that may occur in systems as diverse as particle accelerators radio pulsars.

astro-ph↗
arXiv2005

Bunching instability of rotating relativistic electron layers and coherent synchrotron radiation

We study the stability of a collisionless, relativistic, finite-strength, cylindrical layer of charged particles in free space by solving the linearized Vlasov-Maxwell equations and compute the power of the emitted electromagnetic waves. The layer is rotating in an external magnetic field parallel to the layer. This system is of interest to understanding the high brightness temperature of pulsars which cannot be explained by an incoherent radiation mechanism. Coherent synchrotron radiation has also been observed recently in bunch compressors used in particle accelerators. We consider equilibrium layers with a `thermal' energy spread and therefore a non-zero radial thickness. The particles interact with their retarded electromagnetic self-fields. The effect of the betatron oscillations is retained. A short azimuthal wavelength instability is found which causes a modulation of the charge and current densities. The growth rate is found to be an increasing function of the azimuthal wavenumber, a decreasing function of the Lorentz factor, and proportional to the square root of the total number of electrons. We argue that the growth of the unstable perturbation saturates when the trapping frequency of electrons in the wave becomes comparable to the growth rate. Owing to this saturation we can predict the radiation spectrum for a given set of parameters. Our predicted brightness temperatures are proportional to the square of the number of particles and scale by the inverse five-third power of the azimuthal wavenumber which is in rough accord with the observed spectra of radio pulsars.

astro-ph↗
arXiv2002

Equilibrium Distribution and Tune Shift of Beams in a Linear Collider

The evolution of two colliding beams in a linear accelerator can be described by two coupled Vlasov equations. In PEP-NOTE-325 by S. Kheifets and A. W. Chao the case without external focusing was considered. In this paper we derive the equilibrium distribution and the tune shift in the presence of external focusing. Motion is considered only in the vertical direction and the beams are presumed to be one-dimensional.

physics.acc-ph↗