arXiv subjects

Claus Lämmerzahl

Publications and source records attributed to Claus Lämmerzahl.

At least 19 recordsLinked to original sources

arXiv2026

Quantum Imaging as alternative readout in atom interferometry: The case of Gravity

We propose a quantum imaging-inspired setup for measuring gravitational fields using an atom that emits a photon at one of two possible locations. The atom acquires a gravitationally induced quantum phase that it shares with the photon. By restoring the path identity of the atom after its interaction with the gravitational field, the gravitationally induced phase can be measured using photon interferometry without the need for additional measurements on the atom. Through repeated measurements with varying interferometric setups, the gravitational potential and inertial acceleration can be deduced.

gr-qc↗

arXiv2026

General Relativistic Chronometry with Clocks on Ground and in Space

One of the main tasks of geodesy is to determine the gravity field of the Earth from measurements performed on ground and in space. High-precision clock comparison has the potential to provide a new observable for the global determination of the Earth's gravitational potential through the gravitational redshift. Towards such a global chronometric geodesy, we derive a general relativistic framework beyond the post-Newtonian level for the relativistic redshift and the timing between observers in stationary spacetimes. These observers are equipped with standard clocks and may move along arbitrary worldlines. The redshift is factorized into geometric, transversal-Doppler, and longitudinal-Doppler contributions, providing a transparent separation of gravitational and kinematic effects. We then show how redshift measurements involving clocks on ground and/or in space can, in principle, be used to determine the mass multipole moments of the underlying spacetime. In the weak field limit, our results recover the corresponding Newtonian and post-Newtonian expressions. The framework is illustrated for different exact vacuum spacetimes and provides a theoretical basis for using clock comparisons as an additional observable for gravity-field recovery and future relativistic geodesy missions.

gr-qc↗

arXiv2026

Nonlinear electrodynamics in Kerr-Newman-NUT-$Λ$ spacetime: exact solutions, horizons, and energy conditions

We construct two exact nonlinear-electrodynamic generalizations of the Kerr-Newman-NUT-$Λ$ spacetime. Imposing alignment between the principal directions of the electromagnetic field and the metric tetrad reduces the Maxwell-Faraday sector to a pair of potentials constrained by a single integrability condition, the key equation. Within the polynomial aligned ansatz considered here, the key equation selects two admissible families, corresponding to electromagnetic potentials that are cubic and quartic polynomials. For each family the Einstein equations reduce to a single radial ordinary differential equation that gives a deformation of the Kerr-like radial metric function which is exactly solved. We derive the corresponding metrics, electromagnetic fields, stress tensors, horizon structure, and we analyze the associated energy conditions. The nonlinear sector breaks conformal invariance and, in the cubic family, can mimic an effective cosmological contribution. The explicit Lagrangians as functions of the electromagnetic invariants are obtained in selected static subsectors. The curvature invariants show that the nonlinear contribution does not remove the Kerr-like curvature singularity, while the solutions present the NUT axial conical singularity.

gr-qc↗

arXiv2026

General orbital perturbation theory in Schwarzschild space-time

We derive general relativistic Gaussian equations for osculating elements for orbits under the influence of a perturbing force without any restrictions in an underlying Schwarzschild space-time. Such a formulation provides a way to describe the evolution of orbital parameters in strong gravity relativistic settings. As examples of external forces we considered Kerr and $q$-metric space-times generated forces, for which we solve equations for osculating elements in linear approximation. For the Kerr space-time in the post-Newtonian limit, our result reproduces the well-known Lense--Thirring precession of the longitude of the ascending node.

gr-qc↗

arXiv2025

Frequency shifts due to relativistic effects and retardation in continuous variable quantum key distribution

Space-based quantum communication naturally involves satellites and ground stations exchanging optical signals at high altitudes and large relative velocities. Starting from general relativistic considerations, we systematically separate the frequency shift into longitudinal Doppler contributions, relativistic corrections, and corrections from the propagation delay (retardation). We find the relativistic corrections to the Keplerian satellite orbits to be negligible on the considered timescale, compared to the gravitational and special relativistic time dilation contributions to the frequency shift. Somewhat surprisingly, we find the contribution from the retardation effect to be on the same order of magnitude as the relativistic contributions. To analyze the significance of these effects, we investigate secret key rates for a continuous variable quantum key distribution protocol for various configurations of satellite orbits and ground stations. We find that the corrections from relativistic effects and retardation significantly impact the communication performance and should be taken into account.

quant-ph↗

arXiv2025

Equilibrium models of Weyssenhoff spin fluid accretion tori around Kerr black holes

The construction of equilibrium models of accretion disks around compact objects has become a highly relevant topic in the recent times, thanks to the current understanding that indicates a direct relationship between these objects with the electromagnetic emission of supermassive compact objects residing at center of the galaxies M87 and Milky Way, both observed by the Event Horizon Telescope Collaboration. As the physical properties of the compact sources are estimated using the results of computer simulations of the system comprising of the disk plus the compact object, adding new physical ingredients to the initial data of the simulation is pertinent to enhance our knowledge about these objects. In this work, we thus present equilibrium solutions of geometrically thick, non-self-gravitating, constant orbital specific angular momentum, neutral Weyssenhoff spin fluid accretion tori in the Kerr spacetime, building upon a previous work that was restricted to the Schwarzschild geometry. Our models are obtained under the assumptions of stationarity and axisymmetry in the fluid quantities, circularity of the flow and a polytropic equation of state. We study how the deviations from an ideal no-spin fluid depend on both the magnitude of the macroscopic spin of the fluid and on the spin parameter of the Kerr black hole, carefully encompassing both the co-rotating and the counter-rotating cases. Our results demonstrate that the characterstic radii, the thickness and the radial extent of such a torus can change importantly in the presence of the macroscopic spin of the ideal fluid. We also find some limitations of our approach that constraint the amount of spin the fluid can have in the rotating Kerr background. Finally, we present a parameter space exploration that gives us additional constraints on the possible values of the fluid spin denoted by the parameter $s_0$.

gr-qc↗

arXiv2025

The scalar angular Teukolsky equation and its solution for the Taub-NUT spacetime

The Taub-NUT spacetime offers many curious insights into the solutions of Einstein's electrovacuum equation. In the Bonnor interpretation, this spacetime possesses so-called Misner strings, which induce phenomena strikingly analogous to Dirac strings in the context of magnetic monopoles. The study of scattering in the latter case leads to a quantization of the product of electric charge and magnetic moment, sometimes called the Dirac condition. To enable a thorough discussion of scattering on the Taub-NUT spacetime, linear perturbations are considered in the Newman-Penrose formalism and separated into angular and radial equations. The angular Teukolsky equation is discussed in detail, and eigenvalues are derived to subsequently solve the differential equation in terms of solutions to the confluent Heun equation. In the Bonnor interpretation of the Taub-NUT spacetime, there is no analog property to the Dirac condition. The choice of spacetime parameters remains unconstrained. However, for a particular parameter choice, one can rederive the well-known \enquote{Misner} condition, in which a product of frequency and NUT charge is of integer value, as well as another product additionally including the Manko-Ruiz parameter. The results of this work will allow us to solve analytically for wave-optical scattering in order to, e.g., examine the wave-optical image of Taub-NUT black holes.

gr-qc↗

arXiv2025

General Relativity and Geodesy

Mass redistribution on Earth due to dynamic processes such as ice melting and sea level rise leads to a changing gravitational field, observable by geodetic techniques. Monitoring this change over time allows us to learn more about our planet and its dynamic evolution. In this paper, we highlight the impact of General Relativity (GR) on geodesy: it provides corrections essential for the interpretation of high-precision measurements and enables a completely novel measurement approach using chronometry, i.e., clock-based observations. Focusing on the latter, we review the construction of the relativistic gravity potential and the corresponding geoid definition as an isochronometric surface to elucidate the comparison to the conventional Newtonian geoid. Furthermore, we comment on additional potentials due to the non-Newtonian degrees of freedom of the relativistic gravitational field, and assess the feasibility of clock-based measurements for Gravity Field Recovery (GFR) from space. Although clock observations in space demonstrate technical promise for GFR, achieving the necessary precision for practical applications remains challenging.

gr-qc↗

arXiv2024

Pulse shape optimization against Doppler shifts and delays in optical quantum communication

High relative velocities and large distances in space-based quantum communication with satellites in lower earth orbits can lead to significant Doppler shifts and delays of the signal impairing the achievable performance if uncorrected. We analyze the influence of systematic and stochastic Doppler shift and delay in the specific case of a continuous variable quantum key distribution (CV-QKD) protocol and identify the generalized correlation function, the ambiguity function, as a decisive measure of performance loss. Investigating the generalized correlations as well as private capacity bounds for specific choices of spectral amplitude shape (Gaussian, single- and double-sided Lorentzian), we find that this choice has a significant impact on the robustness of the quantum communication protocol to spectral and temporal synchronization errors. We conclude that optimizing the pulse shape can be a building block in the resilient design of quantum network infrastructure.

quant-ph↗

arXiv2024

Gaussian orbital perturbation theory in Schwarzschild space-time in terms of elliptic functions

General relativistic Gauss equations for osculating elements for bound orbits under the influence of a perturbing force in an underlying Schwarzschild space-time have been derived in terms of Weierstrass elliptic functions. Thereby, the perturbation forces are restricted to act within the orbital plane only. These equations are analytically solved in linear approximation for several different perturbations such as cosmological constant perturbation, quantum correction to the Schwarzschild metric, and hybrid Schwarzschild/post-Newtonian $2.5$ order self-force for binary systems in an effective one-body framework.

gr-qc↗

arXiv2024

Entanglement dynamics of photon pairs and quantum memories in the gravitational field of the earth

We investigate the effect of entanglement dynamics due to gravity -- the basis of a mechanism of universal decoherence -- for photonic states and quantum memories in Mach-Zehnder and Hong-Ou-Mandel interferometry setups in the gravitational field of the earth. We show that chances are good to witness the effect with near-future technology in Hong-Ou-Mandel interferometry. This would represent an experimental test of theoretical modeling combining a multi-particle effect predicted by the quantum theory of light and an effect predicted by general relativity. Our article represents the first analysis of relativistic gravitational effects on space-based quantum memories which are expected to be an important ingredient for global quantum communication networks.

quant-ph↗

arXiv2024

Exact wave-optical imaging of a Kerr-de Sitter black hole using Heun's equation

Spacetime perturbations due to scalar, vector, and tensor fields on a fixed background geometry can be described in the framework of Teukolsky's equation. In this work, wave scattering is treated analytically, using the Green's function method and solutions to the separated radial and angular differential equations in combination with a partial wave technique for a scalar and monochromatic perturbation. The results are applied to analytically describe wave-optical imaging via Kirchhoff-Fresnel diffraction, leading to, e.g., the formation of observable black hole shadows. A comparison to the ray-optical description is given, providing new insights into wave-optical effects and properties. On a Kerr-de Sitter spacetime, the cosmological constant changes the singularity structure of the Teukolsky equation and allows for an analytical, exact solution via a transformation into the Heun's differential equation, which is the most general, second-order differential equation with four regular singularities. The scattering of waves originating from a point source involves a solution in terms of the so-called Heun's function $Hf$. It is used to find angular solutions, which form a complete set of orthonormal functions similar to the spherical harmonics. Our approach allows to solve the scattering problem while taking into account the complex interplay of Heun's functions around local singularities.

gr-qc↗

arXiv2023

Gravitomagnetic Clock Effect: Using GALILEO to explore General Relativity

All experiments to date are in remarkable agreement with the predictions of Einstein's theory of gravity, General Relativity. Besides the classical tests, involving light deflection, orbit precession, signal delay, and the gravitational redshift, modern technology has pushed the limits even further. Gravitational waves have been observed multiple times as have been black holes, arguably amongst the most fascinating objects populating our universe. Moreover, geodetic satellite missions have enabled the verification of yet another prediction: gravitomagnetism. This phenomenon arises due to the rotation of a central body, e.g., the Earth, which is dragging spacetime along. One resulting effect on satellite orbits is the observed Lense-Thirring effect. Another predicted, yet unverified, effect is the so-called gravitomagnetic clock effect, which was first described by Cohen and Mashhoon as the proper time difference of two counter-revolving clocks in an orbit around a rotating mass. A theoretical framework is introduced that describes a gravitomagnetic clock effect based on a stationary spacetime model. An incremental definition of a suitable observable follows, which can be accessed via orbit data obtained from the European satellite navigation system Galileo, and an implementation of the framework for use with real satellite and clock data is presented. The technical requirements on a satellite mission are studied to measure the gravitomagnetic clock effect at the state-of-the-art in satellite laser ranging and modelling of gravitational and non-gravitational perturbations. Based on the analysis within this work, a measurement of the gravitomagnetic clock effect is highly demanding, but might just be within reach in the very near future based on current and upcoming technology.

gr-qc↗

arXiv2022

Equivalence of Active and Passive Gravitational Mass Tested with Lunar Laser Ranging

LLR measures the distance between observatories on Earth and retro-reflectors on Moon since 1969. In this paper, we study the possible violation of the equality of passive and active gravitational mass ($m_{a}/m_{p}$), for Aluminium (Al) and Iron (Fe), using LLR data. Our new limit of $3.9\cdot10^{-14}$ is about 100 times better than that of Bartlett and Van Buren [1986] reflecting the benefit of the many years of LLR data.

gr-qc↗

arXiv2022

Result of the MICROSCOPE Weak Equivalence Principle test

The space mission MICROSCOPE dedicated to the test of the Equivalence Principle (EP) operated from April 25, 2016 until the deactivation of the satellite on October 16, 2018. In this analysis we compare the free-fall accelerations ($a_{\rm A}$ and $a_{\rm B}$) of two test masses in terms of the Eötvös parameter $η({\rm{A, B}}) = 2 \frac{a_{\rm A}- a_{\rm B}}{a_{\rm A}+ a_{\rm B}}$. No EP violation has been detected for two test masses, made from platinum and titanium alloys, in a sequence of 19 segments lasting from 13 to 198 hours down to the limit of the statistical error which is smaller than $10^{-14}$ for $ η({\rm{Ti, Pt}})$. Accumulating data from all segments leads to $η({\rm{Ti, Pt}}) =[-1.5\pm{}2.3{\rm (stat)}\pm{}1.5{\rm (syst)}] \times{}10^{-15}$ showing no EP violation at the level of $2.7\times{}10^{-15}$ if we combine stochastic and systematic errors quadratically. This represents an improvement of almost two orders of magnitude with respect to the previous best such test performed by the Eöt-Wash group. The reliability of this limit has been verified by comparing the free falls of two test masses of the same composition (platinum) leading to a null Eötvös parameter with a statistical uncertainty of $1.1\times{}10^{-15}$.

gr-qc↗

arXiv2022

MICROSCOPE mission: final results of the test of the Equivalence Principle

The MICROSCOPE mission was designed to test the Weak Equivalence Principle (WEP), stating the equality between the inertial and the gravitational masses, with a precision of $10^{-15}$ in terms of the Eötvös ratio $η$. Its experimental test consisted of comparing the accelerations undergone by two collocated test masses of different compositions as they orbited the Earth, by measuring the electrostatic forces required to keep them in equilibrium. This was done with ultra-sensitive differential electrostatic accelerometers onboard a drag-free satellite. The mission lasted two and a half years, cumulating five-months-worth of science free-fall data, two thirds with a pair of test masses of different compositions -- Titanium and Platinum alloys -- and the last third with a reference pair of test masses of the same composition -- Platinum. We summarize the data analysis, with an emphasis on the characterization of the systematic uncertainties due to thermal instabilities and on the correction of short-lived events which could mimic a WEP violation signal. We found no violation of the WEP, with the Eötvös parameter of the Titanium and Platinum pair constrained to $η({\rm Ti, Pt})~=~ [-1.5 \pm 2.3~{\rm (stat)} \pm 1.5~{\rm (syst)}]~\times 10^{-15}$ at $1σ$ in statistical errors.

gr-qc↗

arXiv2021

Ultracold atom interferometry in space

Bose-Einstein condensates (BECs) in free fall constitute a promising source for space-borne matter-wave interferometry. Indeed, BECs enjoy a slowly expanding wave function, display a large spatial coherence and can be engineered and probed by optical techniques. On a sounding rocket, we explore matter-wave fringes of multiple spinor components of a BEC released in free fall employing light-pulses to drive Bragg processes and induce phase imprinting. The prevailing microgravity played a crucial role in the observation of these interferences which not only reveal the spatial coherence of the condensates but also allow us to measure differential forces. Our work establishes matter-wave interferometry in space with future applications in fundamental physics, navigation and Earth observation.

physics.atom-ph↗

arXiv2020

MICROSCOPE instrument description and validation

Dedicated accelerometers have been developed for the MICROSCOPE mission taking into account the specific range of acceleration to be measured on board the satellite. Considering one micro-g and even less as the full range of the instrument, leads to a customized concept and a high performance electronics for the sensing and servo-actuations of the accelerometer test-masses. In addition to a very accurate geometrical sensor core, a high performance electronics architecture provides the measurement of the weak electrostatic forces and torques applied to the test-masses. A set of capacitive sensors delivers the position and the attitude of the test-mass with respect to a very steady gold coated cage made in silica. The voltages applied on the electrodes surrounding each test-mass are finely controlled to generate the adequate electrical field and so the electrostatic pressures on the test-mass. This field maintains the test-mass motionless with respect to the instrument structure. Digital control laws are implemented in order to enable instrument operation flexibility and a weak position sensor noise. These electronics provide both the scientific data for MICROSCOPE's test of General Relativity and the data for the satellite drag-free and attitude control system (DFACS).

physics.ins-det↗