arXiv subjects

Claus Laemmerzahl

Publications and source records attributed to Claus Laemmerzahl.

At least 19 recordsLinked to original sources

arXiv2024

Potentials for general-relativistic geodesy

Geodesy in a Newtonian framework is based on the Newtonian gravitational potential. The general-relativistic gravitational field, however, is not fully determined by a single potential. The vacuum field around a stationary source can be decomposed into two scalar potentials and a tensorial spatial metric, which together serve as the basis for general-relativistic geodesy. One of the scalar potentials is a generalization of the Newtonian potential while the second one describes the influence of the rotation of the source on the gravitational field for which no non-relativistic counterpart exists. In this paper the operational realizations of these two potentials, and also of the spatial metric, are discussed. For some analytically given spacetimes the two potentials are exemplified and their relevance for practical geodesy on Earth is outlined.

gr-qc↗

arXiv2023

Stationary equilibrium torus supported by Weyssenhoff ideal spin fluid in Schwarzschild spacetime -- I: Case of constant specific angular momentum distribution

We consider a non-self-gravitating geometrically thick torus described by Weyssenhoff ideal spin fluid in a black hole spacetime. The Weyssenhof spin fluid shares the same symmetries of the background geometry, i,e. stationarity and axisymmetry and further describes circular orbital motion in the black hole spacetime. We further assume that assume the alignment of the spin is perpendicular to the equatorial plane. Under this setup, we determine the integrability conditions of the general relativistic momentum conservation equation of Weyssenhoff ideal spin fluid using the Frenkel spin supplementary condition. In the light of the integrability conditions, we then present stationary equilibrium solutions of the spin fluid torus with constant specific angular momentum distributions around the Schwarzschild black hole by numerically solving the general relativistic momentum conservation equation. Our study reveals that both the iso-pressure and iso-density surfaces of torus get significantly modified in comparison to the ideal fluid torus without a spin fluid, owing to the spin tensor and its coupling to the curvature of the Schwarzschild black hole. In fact, the size of the torus is also found to be enhanced (diminished) depending on positive (negative) magnitude of spin parameter $s_0$. We finally estimate the magnitude of $s_0$ by assuming the torus to be composed of spin-1/2 particles.

gr-qc↗

arXiv2022

Role of indistinguishability and entanglement in Hong-Ou-Mandel interference and finite bandwidth effects of frequency entangled photons

We investigate the relation between indistinguishability and quantum entanglement in Hong- Ou-Mandel-interference experiments theoretically and relate these quantum mechanical principles to the theorem of entanglement monogamy. Employing Glaubers theory of quantum coherence we compute the detection statistics in HOM-interference of frequency entangled photons, and find a new additional term in the coincidence detection probability, which is related to the spectral indistinguishability of the considered photons that arises from finite bandwidth effects, and therefore is relevant in the limit of low frequency separations or large single-photon bandwidths. Compared to previous work in that context we treat all photonic degrees of freedom (DOF) on equal footing.

quant-ph↗

arXiv2022

Observer dependence of photon bunching: The influence of the relativistic redshift on Hong-Ou-Mandel interference

We study the influence of the relativistic redshift on Hong-Ou-Mandel (HOM) interference, and present a genuine quantum test of general relativity. We use Glauber's theory of quantum coherence to predict the coincidence probability of realistic broadband photons in HOM-experiments in a non-relativistic setting. We extend the quantum field theoretical framework previously developed to describe the deformation of the spectral profile of single photons in curved spacetimes to a multi-photon framework, which is exact for inertial observers in a flat spacetime and an approximation when observers are located in a curved spacetime. We find that, in case of frequency entangled photons, a mutual redshift between the sender and the receiver can change the coincidence statistics from photon bunching to photon anti-bunching, and vice versa. This implies that the (anti-) symmetry of the photonic spectral wave function is an observer dependent notion, and that this can be probed via HOM-experiments in a relativistic setting.

gr-qc↗

arXiv2019

On the Applicability of the Geodesic Deviation Equation in General Relativity

Within the theory of General Relativity, we study the solution and range of applicability of the standard geodesic deviation equation in highly symmetric spacetimes. In the Schwarzschild spacetime, the solution is used to model satellite orbit constellations and their deviations around a spherically symmetric Earth model. We investigate the spatial shape and orbital elements of perturbations of circular reference curves. In particular, we reconsider the deviation equation in Newtonian gravity and then determine relativistic effects within the theory of General Relativity by comparison. The deviation of nearby satellite orbits, as constructed from exact solutions of the underlying geodesic equation, is compared to the solution of the geodesic deviation equation to assess the accuracy of the latter. Furthermore, we comment on the so-called Shirokov effect in the Schwarzschild spacetime and limitations of the first order deviation approach.

gr-qc↗

arXiv2017

Redshift and frequency comparison in Schwarzschild spacetime

We derive exact expressions for the relativistic redshift between an Earth-bound observer, that is meant to model a standard clock on the Earth's surface, and various (geodesic) observers in the Schwarzschild spacetime. We assume that the observers exchange radial light signals to compare the frequencies of standard clocks, which they transport along their respective worldlines. We calculate the redshift between an Earth-bound clock and static observers, observers in radial free fall, on circular geodesics, and on arbitrary bound quasi-elliptical orbits. For the latter case, we consider as examples an almost circular orbit, the Schwarzschild analog of Galileo satellites 5 orbits with a moderate eccentricity, and a highly elliptical orbit as special examples. Furthermore, we also use orbits close to a Schwarzschild black hole to highlight the influence of the relativistic perigee precession on the redshift signal. Calculating a post-Newtonian expansion of our results, the total redshift is decomposed into its special relativistic Doppler parts and the gravitational part due to the theory of General Relativity. To investigate the impact of higher order relativistic multipole moments on the gravitational redshift, we consider static observers in a general Weyl spacetime. We give a general expression for the mutual redshift of their standard clocks and consider in particular the effect of the relativistic quadrupole as a modification of the Schwarzschild result.

gr-qc↗

arXiv2017

Pseudo-Newtonian equations for evolution of particles and fluids in stationary space-times

Pseudo-Newtonian potentials are a tool often used in theoretical astrophysics to capture some key features of a black-hole space-time in a Newtonian framework. As a result, one can use Newtonian numerical codes, and Newtonian formalism in general, in an effective description of important astrophysical processes such as accretion onto black holes. In this paper we develop a general pseudo-Newtonian formalism which pertains to the motion of particles, light, and fluids in stationary space-times. In return, we are able to assess the applicability of the pseudo-Newtonian scheme. The simplest and most elegant formulas are obtained in space-times without gravitomagnetic effects, such as the Schwarzschild rather than the Kerr space-time; the quantitative errors are smallest for motion with low binding energy. Included is a ready-to-use set of fluid equations in Schwarzschild space-time in Cartesian and radial coordinates.

gr-qc↗

arXiv2017

The Milky Way's Supermassive Black Hole: How good a case is it? A Challenge for Astrophysics & Philosophy of Science

The compact and, with 4.3+-0.3 million solar masses, very massive object located at the center of the Milky Way is currently the very best candidate for a supermassive black hole (SMBH) in our immediate vicinity. The strongest evidence for this is provided by measurements of stellar orbits, variable X-ray emission, and strongly variable polarized near-infrared emission from the location of the radio source Sagittarius~A* (SgrA*) in the middle of the central stellar cluster. If SgrA* is indeed a SMBH it will, in projection onto the sky, have the largest event horizon and will certainly be the first and most important target of the Event Horizon Telescope (EHT) Very Long Baseline Interferometry (VLBI) observations currently being prepared. These observations in combination with the infrared interferometry experiment GRAVITY at the Very Large Telescope Interferometer (VLTI) and other experiments across the electromagnetic spectrum might yield proof for the presence of a black hole at the center of the Milky Way. It is, however, unclear when the ever mounting evidence for SgrA* being associated with a SMBH will suffice as a convincing proof. Additional compelling evidence may come from future gravitational wave observatories. This manuscript reviews the observational facts, theoretical grounds and conceptual aspects for the case of SgrA* being a black hole. We treat theory and observations in the framework of the philosophical discussions about "(Anti)Realism and Underdetermination", as this line of arguments allows us to describe the situation in observational astrophysics with respect to supermassive black holes. Questions concerning the existence of supermassive black holes and in particular SgrA* are discussed using causation as an indispensable element. We show that the results of our investigation are convincingly mapped out by this combination of concepts.

astro-ph.HE↗

arXiv2015

On geodesic deviation in Schwarzschild spacetime

For metrology, geodesy and gravimetry in space, satellite based instruments and measurement techniques are used and the orbits of the satellites as well as possible deviations between nearby ones are of central interest. The measurement of this deviation itself gives insight into the underlying structure of the spacetime geometry, which is curved and therefore described by the theory of general relativity (GR). In the context of GR, the deviation of nearby geodesics can be described by the Jacobi equation that is a result of linearizing the geodesic equation around a known reference geodesic with respect to the deviation vector and the relative velocity. We review the derivation of this Jacobi equation and restrict ourselves to the simple case of the spacetime outside a spherically symmetric mass distribution and circular reference geodesics to find solutions by projecting the Jacobi equation on a parallel propagated tetrad as done by Fuchs. Using his results, we construct solutions of the Jacobi equation for different physical initial scenarios inspired by satellite gravimetry missions and give a set of parameter together with their precise impact on satellite orbit deviation. We further consider the Newtonian analog and construct the full solution, that exhibits a similar structure, within this theory.

gr-qc↗

arXiv2012

Astrodynamical Space Test of Relativity using Optical Devices I (ASTROD I) - Mission Overview

ASTROD I is the first planned space mission in a series of ASTROD missions for testing relativity in space using optical devices. The main aims are: (i) to test General Relativity with an improvement of three orders of magnitude compared to current results, (ii) to measure solar and solar system parameters with improved accuracy, (iii) to test the constancy of the gravitational constant and in general to get a deeper understanding of gravity. The first ideas for the ASTROD missions go back to the last century when new technologies in the area of laser physics and time measurement began to appear on the horizon. ASTROD is a mission concept that is supported by a broad international community covering the areas of space technology, fundamental physics, high performance laser and clock technology and drag free control. While ASTROD I is a single-spacecraft concept that performes measurements with pulsed laser ranging between the spacecraft and earthbound laser ranging stations, ASTROD-GW is planned to be a three spacecraft mission with inter-spacecraft laser ranging. ASTROD-GW would be able to detect gravitational waves at frequencies below the eLISA/NGO bandwidth. As a third step Super-ASTROD with larger orbits could even probe primordial gravitational waves. This article gives an overview on the basic principles especially for ASTROD I.

gr-qc↗

arXiv2012

Observable effects in a class of spherically symmetric static Finsler spacetimes

After some introductory discussion of the definition of Finsler spacetimes and their symmetries, we consider a class of spherically symmetric and static Finsler spacetimes which are small perturbations of the Schwarzschild spacetime. The deviations from the Schwarzschild spacetime are encoded in three perturbation functions $ϕ_0(r)$, $ϕ_1(r)$ and $ϕ_2(r)$ which have the following interpretations: $ϕ_0$ perturbs the time function, $ϕ_1$ perturbs the radial length measurement and $ϕ_2$ introduces a spatial anisotropy which is a genuine Finsler feature. We work out the equations of motion for freely falling particles and for light rays, i.e. the timelike and lightlike geodesics, in this class of spacetimes, and we discuss the bounds placed on the perturbation functions by observations in the Solar system.

gr-qc↗

arXiv2011

Particle motion in Horava-Lifshitz black hole space-times

We study the particle motion in the space-time of a Kehagias-Sfetsos (KS) black hole. This is a static spherically symmetric solution of a Horava-Lifshitz gravity model that reduces to General Relativity in the IR limit and deviates slightly from detailed balance. Taking the viewpoint that the model is essentially a (3+1)-dimensional modification of General Relativity we use the geodesic equation to determine the motion of massive and massless particles. We solve the geodesic equation exactly by using numerical techniques. We find that neither massless nor massive particles with non-vanishing angular momentum can reach the singularity at r=0. Next to bound and escape orbits that are also present in the Schwarzschild space-time we find that new types of orbits exist: manyworld bound orbits as well as two-world escape orbits. We also discuss observables such as the perihelion shift and the light deflection.

gr-qc↗

arXiv2010

Test particle motion in the space-time of a Kerr black hole pierced by a cosmic string

We study the geodesic equation in the space-time of a Kerr black hole pierced by an infinitely thin cosmic string and give the complete set of analytical solutions of this equation for massive and massless particles in terms of Mino time that allows to decouple the r- and theta-component of the geodesic equation. The solutions of the geodesic equation can be classified according to the particle's energy and angular momentum, the mass and angular momentum per mass of the black hole. We give examples of orbits showing the influence of the cosmic string. We also discuss the perihelion shift and the Lense-Thirring effect for bound orbits and show that the presence of a cosmic string enhances both effects. Comparing our results with experimental data from the LAGEOS satellites we find an upper bound on the energy per unit length of a string piercing the earth which is approximately 10^{16} kg/m. Our work has also applications to the recently suggested explanation of the alignment of the polarization vector of quasars using remnants of cosmic string decay in the form of primordial magnetic field loops.

gr-qc↗

arXiv2010

Analytic treatment of complete and incomplete geodesics in Taub-NUT space-times

We present the complete set of analytical solutions of the geodesic equation in Taub-NUT space-times in terms of the Weierstrass elliptic function. We systematically study the underlying polynomials and characterize the motion of test particles by its zeros. Since the presence of the "Misner string" in the Taub-NUT metric has led to different interpretations, we consider these in terms of the geodesics of the space-time. In particular, we address the geodesic incompleteness at the horizons discussed by Misner and Taub, and the analytic extension of Miller, Kruskal and Godfrey, and compare with the Reissner-Nordström space-time.

gr-qc↗

arXiv2010

Probing the quantum-gravity realm with slow atoms

For the study of Planck-scale modifications of the energy-momentum dispersion relation, which had been previously focused on the implications for ultrarelativistic (ultrafast) particles, we consider the possible role of experiments involving nonrelativistic particles, and particularly atoms. We extend a recent result establishing that measurements of "atom-recoil frequency" can provide insight that is valuable for some theoretical models. And from a broader perspective we analyze the complementarity of the nonrelativistic and the ultrarelativistic regimes in this research area.

gr-qc↗

arXiv2010

The complete set of solutions of the geodesic equations in the space-time of a Schwarzschild black hole pierced by a cosmic string

We study the geodesic equations in the space-time of a Schwarzschild black hole pierced by an infinitely thin cosmic string and give the complete set of analytical solutions of these equations for massive and massless particles, respectively. The solutions of the geodesic equations can be classified according to the particle's energy and angular momentum, the ratio between the component of the angular momentum aligned with the axis of the string and the total angular momentum, the deficit angle of the space-time and as well the horizon radius (or mass) of the black hole. For bound orbits of massive test particles we calculate the perihelion shift, we discuss light deflection and comment on the Newtonian limit.

gr-qc↗

arXiv2009

Constraining the energy-momentum dispersion relation with Planck-scale sensitivity using cold atoms

We use the results of ultra-precise cold-atom-recoil experiments to constrain the form of the energy-momentum dispersion relation, a structure that is expected to be modified in several quantum-gravity approaches. Our strategy of analysis applies to the nonrelativistic (small speeds) limit of the dispersion relation, and is therefore complementary to an analogous ongoing effort of investigation of the dispersion relation in the ultrarelativistic regime using observations in astrophysics. For the leading correction in the nonrelativistic limit the exceptional sensitivity of cold-atom-recoil experiments remarkably allows us to set a limit within a single order of magnitude of the desired Planck-scale level, thereby providing the first example of Planck-scale sensitivity in the study of the dispersion relation in controlled laboratory experiments. For the next-to-leading term we obtain a limit which is a few orders of magnitude away from the Planck scale, but still amounts to the best limit on a class of Lorentz-symmetry test theories that has been extensively used to investigate the hypothesis of "deformation" (rather than breakdown) of spacetime symmetries.

gr-qc↗

arXiv2009

Charged Boson Stars and Black Holes

We consider boson stars and black holes in scalar electrodynamics with a V-shaped scalar potential. The boson stars come in two types, having either ball-like or shell-like charge density. We analyze the properties of these solutions and determine their domains of existence. When mass and charge become equal, the space-times develop a throat. The shell-like solutions need not be globally regular, but may possess a horizon. The space-times then consist of a Schwarzschild-type black hole in the interior, surrounded by a shell of charged matter, and thus a Reissner-Nordstroem-type space-time in the exterior. These solutions violate black hole uniqueness. The mass of the black hole solutions is related to the mass of the regular shell-like solutions by a mass formula of the type first obtained within the isolated horizon framework.

gr-qc↗