arXiv subjects

Christian Pfeifer

Publications and source records attributed to Christian Pfeifer.

At least 19 recordsLinked to original sources

arXiv2026

Reduction of the Finsler gravity vacuum equation and dynamics for the cosmological Landsberg spacetimes

When solving the Einstein vacuum equations, a very helpful feature is that they reduce simply to the vanishing of the Ricci tensor. In Finsler gravity, a promising extension of general relativity that can describe the gravitational field of kinetic gases from a phase space perspective in terms of Finsler geometry, such a reduction is not as straightforward. In this article, we identify precise conditions under which the scalar Finsler gravity vacuum equation (in either its purely metric or its Palatini formulation) reduces to the vanishing of the Finslerian Ricci curvature. Through analytic arguments, we find that this happens if there exists some power $F^n$ of the Finsler function $F$ that is sufficiently regular and whose associated Finsler metric is non-degenerate on the light cones. Moreover, the Landsberg term in the scalar equation must vanish. This result significantly generalizes the findings of [Villasenor2024], where a reduction theorem was established under the quite strong assumption that $F^2$ is regular, which is not satisfied by many examples currently under consideration. We demonstrate the impact of our findings by applying them to solve the Finsler gravity equations for homogeneous and isotropic Finsler spacetime functions of Landsberg type.

gr-qc↗

arXiv2026

Spherically symmetric, asymptotically flat Berwald vacuum solutions in Finsler gravity

So-called Berwald-Finsler spacetimes are Finsler spacetimes that are closest to pseudo-Riemannian geometry, as their canonical nonlinear connection defines an affine connection on spacetime. In spherical symmetry, these geometries can be used to describe the gravitational field outside of compact objects. We solve the Finsler gravity vacuum equation for $SO(3)$-symmetric Berwald spacetimes that are asyptotically flat, but not Ricci flat. We find that among all spherically symmetric Berwald spacetimes, only one class is compatible with asymptotic flatness and a well defined causal structure. For this class, we completely solve the Finsler gravity vacuum equation and find three families of non-Ricci flat solutions -- which represent the first non-trivial, exact spherically symmetric vacuum solutions. They are so-called $(\alpha,\beta)$-Finsler spacetimes that are constructed from a pseudo-Riemannnian metric and a 1-form. In particular, we show, by providing a concrete example, that in Finsler geometry there exist $SO(3)$-symmetric, asymptotically flat vacuum solutions that are not Ricci flat; these solutions are promising candidates to model the gravitational field around compact objects, beyond their Riemannian description.

gr-qc↗

arXiv2026

On the Finsler variational nature of autoparallels in metric-affine geometry

In metric-affine geometry, autoparallels are generically non-variational, i.e., they are not the extremals of any action integral. The existence of a parametrization-invariant action principle for autoparallels is a long-standing open problem, which is equivalent to the so-called Finsler metrizability of the connection -- that is, to the fact that these autoparallels can be interpreted as Finsler geodesics. In this article, we address this problem for the class of torsion-free affine connections with vectorial nonmetricity, which includes, as notable subcases, Weyl and Schr\"odinger connections. For this class, we determine the necessary and sufficient conditions for the existence of a Finsler Lagrangian that metrizes the connection (and depends only algebraically on the metric and on the nonmetricity defining vector field). In the cases where such a Finsler Lagrangian exists, we construct it explicitly. In particular, we show that a broad class of such connections is in fact Finsler metrizable, i.e., the autoparallels of these connections are Finsler geodesics.

math-ph↗

arXiv2025

Unified field theory from Hamilton cotangent bundle geometry - The Einstein-Maxwell system

The unification of all physical fields into one mathematical object and the derivation of all physical field equations from that object in one framework is a long-lasting endeavor in fundamental physics. We suggest a new approach to achieve this goal by encoding physical fields into the geometry of the 1-particle phase space on spacetime (the cotangent bundle) through Hamilton geometry. The fundamental field, which contains information about all physical fields in spacetime and defines the phase space geometry, is a scalar field in phase space that is interpreted as a point-particle Hamiltonian. We construct an action principle for scalar fields in phase space and derive the corresponding scalar field equation. By choosing a specific scalar field, namely the Hamiltonian describing a charged particle in curved spacetime with an electromagnetic field, we show that this phase-space scalar field equation is equivalent to the coupled Einstein-Maxwell equations in spacetime, thus providing a geometric unification of gravity and electromagnetism. We further discuss how this approach differs from previous unification attempts and its potential for describing further physical fields and their dynamics in a unified manner in terms of phase-space geometry.

gr-qc↗

arXiv2025

Universality of free fall in Planck-scale deformed Newtonian gravity

The universality of free fall is one of the most cherished principles in classical gravity. Its fate in the quantum world is one of the key questions in fundamental physics. We investigate the universality of free fall in the context of Planck scale modifications of Newtonian gravity. Starting from a doubly-special-relativity setting we take the Newtonian limit to obtain deformed Galilean relativity. We study the interaction between two test particles, subject to deformed Galilean relativity, and a classical, undeformed gravitational source, the Earth. Such an interaction is investigated here for the first time. Considering the two test particles falling freely in the source's gravitational field, we examine whether the universality of free fall is affected by deformed relativistic symmetries. We show that, in general, the universality of free fall is violated. Remarkably, we find that there exist distinguished models for which the universality of free fall is realized and which predict a specific modification of the Newtonian potential.

gr-qc↗

arXiv2025

Light deflection in axially symmetric stationary spacetimes filled with a moving medium

The deflection of light rays near gravitating objects can be influenced not only by gravity itself but also by the surrounding medium. Analytical studies of such effects are possible within the geometrical optics approximation, where the medium introduces additional light bending due to refraction. These studies typically assume a cold non-magnetized plasma, for which light propagation is independent of the medium's velocity. In this paper, we extend the analysis to the general case of dispersive refractive media in motion and study its influence on light deflection. We consider an axially symmetric stationary spacetime filled with a moving medium, motivated by the interplay between rotational effects originating from the spacetime and those induced by the medium's motion. We begin by analyzing light deflection in the equatorial plane of a rotating object in the presence of a radially moving and rotating medium. Assuming a specific form of the refractive index enables a fully analytic treatment. In the particular cases of either pure radial or pure rotational motion, we obtain explicit expressions for the deflection angle. Next, we analyze the case of a slowly moving medium and identify two particularly interesting results. First, we show that, to the first order in the medium's velocity, the radial motion does not affect the light deflection. Second, assuming slow rotation of the gravitating object, we demonstrate that the black hole rotation and the medium motion can produce equivalent observational signatures. We find the quantitative condition under which these effects compensate each other. This relation becomes particularly clear for a Kerr black hole, discussed as an example.

gr-qc↗

arXiv2025

Coupling Electromagnetism to Torsion: Black Holes and Spin-Charge Interactions

The coupling between matter fields and gravity, encoded in the geometry of spacetime, can be realized in various ways. Most commonly, a minimal coupling principle is employed, meaning that all matter fields, except spinors, couple only to the spacetime metric, while spinors additionally couple to the spacetime connection. Non-minimal couplings between matter fields and spacetime curvature can arise, for example, from quantum field theory on curved spacetime through renormalization corrections, in gauge theories of gravity, and in effective field theories. In this article, we consider a non-minimal coupling $F^{\mu\nu}\tilde{R}_{\mu\nu}$ between the field strength tensor of the electromagnetic field $F_{\mu\nu}$ and the antisymmetric part of the Ricci tensor $\tilde{R}_{[\mu\nu]}$ in Riemann--Cartan geometry, which is based on a general metric-compatible connection with torsion. We find an exact four-dimensional vacuum solution that generalizes the Reissner--Nordstr{\"o}m black hole from Einstein--Maxwell and reveals new interactions between the intrinsic torsion-spin charge and the electric charge. Qualitatively, this solution exhibits two distinct features: the effective charge is not constrained to be positive, and the sign of the electric charge influences its gravitational effects. We also derive slowly rotating solutions in three dimensions, representing a generalized slowly rotating BTZ black hole solution with couplings among the magnetic and electric charges, the angular momentum, and the intrinsic torsion-spin charge.

gr-qc↗

arXiv2025

The path towards measuring the gravitational field of proton bunches at accelerators

The Newtonian law describing the gravitational interaction of non-relativistic (slowly moving) gravitating matter, has been tested in many laboratory experiments with very high precision. In contrast, the post Minkowskian predictions for the gravitational field of ultra-relativistic matter, dominated by momentum instead of rest mass, have not been tested directly yet. The intense ultra-relativistic proton beam in the LHC storage ring offers the potential to test general relativity and alternative gravitational theories in this parameter regime for the first time in controlled lab-scale experiments. If successful, this would open the road to a novel use case of the LHC, where non-trivial gravitational physics could be studied likely in a parasitic mode, without the necessity of dedicated filling patterns. While the technical challenges are formidable, they should also lead to the development of ultra-high-sensitive acceleration sensors with abundant applications in other parts of science and technology. The present document summarizes the status of the theoretical studies in this direction, points out the challenges, and possible ways of addressing them. It was submitted as a contribution to the European Strategy for Particle Physics (ESPP) 2026 Update.

hep-ex↗

arXiv2025

From kinetic gases to an exponentially expanding universe - The Finsler-Friedmann equation

We investigate the gravitational field of a kinetic gas beyond its usual derivation from the second moment of the one-particle distribution function (1PDF), that serves as energy-momentum tensor in the Einstein equations. This standard procedure raises the question why the other moments of the 1PDF (which are needed to fully characterize the kinematical properties of the gas) do not contribute to the gravitational field and what could be their relevance in addressing the dark energy problem? Using the canonical coupling of the entire 1PDF to Finsler spacetime geometry via the Finsler gravity equation, we show that these higher moments contribute non-trivially. A Finslerian geometric description of our universe allows us to determine not only the scale factor but also of the causal structure dynamically. We find that already a Finslerian vacuum solution naturally permits an exponential expanding universe, without the need for a cosmological constant or any additional quantities. This solution possesses a causal structure which is a mild deformation of the causal structure of Friedmann-Lema\^itre-Robertson-Walker (FLRW) geometry; close to the rest frame defined by cosmological time (i.e., for slowly moving objects), the causal structures of the two geometries are nearly indistinguishable.

gr-qc↗

arXiv2024

Cosmological Landsberg Finsler spacetimes

We locally classify all possible cosmological homogeneous and isotropic Landsberg-type Finsler structures, in 4-dimensions. Among them, we identify viable non-stationary Finsler spacetimes, i.e. those geometries leading to a physical causal structure and a dynamical universe. Noting that any non-stationary Landsberg metric must be actually non-Berwaldian (i.e., it should be a so-called 'unicorn'), we construct the unique Finsler, non-Berwaldian Landsberg generalization of Friedmann-Lemaitre-Robertson-Walker geometry.

math-ph↗

arXiv2024

Gravitational attraction of ultra-relativistic matter: A new testbed for modified gravity at the Large Hadron Collider

We derive the scalar-tensor modification of the gravitational field of an ultrarelativistic particle beam and its effect on a test particle that is used as sensor. To do so, we solve the linearized scalar-tensor gravity field equations sourced by an energy-momentum tensor of a moving point particle. The geodesic equation and the geodesic deviation equation then predict the acceleration of the test particle as well as the momentum transfer due to a passing source. Comparing the momentum transfer predicted by general relativity and scalar tensor gravity, we find that there exists a relevant parameter regime where this difference increases significantly with the velocity of the source particle. Since ultrarelativistic particles are available at accelerators like the Large Hadron Collider, ultraprecise acceleration sensors in the vicinity of the particle beam could potentially detect deviations from general relativity or constrain modified gravity models.

gr-qc↗

arXiv2024

Experimental Bounds on Deformed Muon Lifetime Dilation

We analyze Planck scale induced modifications of the relativistic time dilation using data from the Muon Storage Ring experiment at CERN. By examining the lifetimes of muons, we establish, for the first time, a constraint on such quantum gravity-inspired deformations using this channel. The magnitude of the effect indicates that the study of cosmic rays is a well suited arena for this scenario. We show, that the spectrum of muons would be significantly affected for particles at the PeV scale. Since this later observation of the effect of time dilation is more indirect compared to a direct lifetime measurement, we encourage to perform a high precision measurement of the muon lifetime as a function of the muon's energy.

gr-qc↗

arXiv2024

Weak equivalence principle and nonrelativistic limit of general dispersion relations

We study the weak equivalence principle in the context of modified dispersion relations, a prevalent approach to quantum gravity phenomenology. We find that generic modified dispersion relations violate the weak equivalence principle. The acceleration in general depends on the mass of the test body, unless the Hamiltonian is either two-homogeneous in the test particles' 4-momenta or the corresponding Lagrangian differs from the homogeneous case by a total derivative only. The key ingredient of this calculation is a $3+1$ decomposition of the parametrization invariant relativistic test particle action derived from the dispersion relation. Additionally, we apply a perturbative expansion in the test particle's spatial velocity and the inverse speed of light. To quantify our result, we provide a general formula for the E\"otv\'os factor of modified dispersion relations. As a specific example, we study the point-particle motion determined from the $\kappa$-Poincar\'e dispersion relation in the bicrossproduct basis. Comparing the ensuing non-vanishing E\"otv\'os factor to recent data from the MICROSCOPE experiment, we obtain a bound of the model parameter $\hat{\Xi} {}^{-1}\geq10^{15}{\rm GeV}/c^2$.

gr-qc↗

arXiv2024

Deflection of light rays in a moving medium around a spherically symmetric gravitating object

In most analytical studies of light ray propagation in curved spacetimes around a gravitating object surrounded by a medium, it is assumed that the medium is a cold nonmagnetized plasma. The distinctive feature of this environment is that the equations of motion of the rays are independent of the plasma velocity, which, however, is not the case in other media. In this paper, we consider the deflection of light rays propagating near a spherically symmetric gravitating object in a moving dispersive medium given by a general refractive index. The deflection is studied when the motion of the medium is defined either as a radially falling onto a gravitating object (e.g., black hole), or rotating in the equatorial plane. For both cases the deflection angles are obtained. These examples demonstrate that fully analytic expressions can be obtained if the Hamiltonian for the rays takes a rather general form as a polynomial in a given momentum component. The general expressions are further applied to three specific choices of refractive indices and these cases are compared. Furthermore, the light rays propagating around a gravitating object surrounded by a generally moving medium are further studied as a small perturbation of the cold plasma model. The deflection angle formula is hence expressed as a sum of zeroth and first order components, where the zeroth order term corresponds to the known cold plasma case and the first order correction can be interpreted as caused by small difference in the refractive index compared to the cold plasma. The results presented in this paper allow to describe the effects caused by the motion of a medium and thus go beyond cold nonmagnetized plasma model.

gr-qc↗

arXiv2023

Spherically symmetric vacuum solutions in 1-Parameter New General Relativity and their phenomenology

In this work, we study spherically symmetric vacuum solutions in 1-parameter New General Relativity (NGR), a specific theory in teleparallel gravity which is constructed from the three possible quadratic scalars obtained from torsion with arbitrary coefficients satisfying the requirements for the absence of ghosts. In this class of modified theories of gravity, the observable effects of gravity result from the torsion rather than the curvature of the spacetime. Unlike in GR, where the fundamental quantity is the metric from which the Levi-Civita connection is derived, in teleparallel theories of gravity the fundamental variable is the tetrad, from which one constructs the metric and the teleparallel connection. We consider the most general tetrad for spherical symmetry and we derive the corresponding field equations. Under adequate assumptions, we find three different branches of vacuum solutions and discuss their associated phenomenology. In particular, we analyze the photon sphere, the classical tests of GR such as the light deflection, the Shapiro delay, and the perihelion shift, and also the Komar mass, while providing a detailed comparison with their Schwarzschild spacetime counterparts. Finally, we analyze how the observational imprints from accretion disks and shadows are affected in comparison with their GR counterparts, and conclude that the free parameters of the model might induce additional attractive or repulsive effects to the propagation of photons, depending on their values.

gr-qc↗

arXiv2023

Thomas--Wigner rotation as a holonomy for spin-$1/2$ particles

The Thomas--Wigner rotation (TWR) results from the fact that a combination of boosts leads to a non-trivial rotation of a physical system. Its origin lies in the structure of the Lorentz group. In this article we discuss the idea that the TWR can be understood in the geometric manner, being caused by the non-trivially curved relativistic momentum space, i.e. the mass shell, seen as a Riemannian manifold. We show explicitly how the TWR for a massive spin-$1/2$ particle can be calculated as a holonomy of the mass shell. To reach this conclusion we recall how to construct the spin bundle over the mass shell manifold.

quant-ph↗

arXiv2023

Modified particle lifetimes as a signature of deformed relativity

We demonstrate a compatibility between the relativity principle and the clock postulate in deformed special relativity, by identifying the relevant deformed Lorentz transformations in position space between arbitrary frames. This result leads to a first-principles correction to the dilated lifetime of fundamental particles. It turns out that these modified time dilations offer a way to scrutinize Lorentz invariance (or deviations thereof) to high precision.

gr-qc↗

arXiv2023

Distinctive Features of Hairy Black Holes in Teleparallel Gauss-Bonnet Gravity

We examine the teleparallel formulation of non-minimally coupled scalar Einstein-Gauss-Bonnet gravity. In the teleparallel formulation, gravity is described by torsion instead of curvature, causing the usual Gauss-Bonnet invariant expressed through curvature to decay into two separate invariants built from torsion. Consequently, the teleparallel formulation permits broader possibilities for non-minimal couplings between spacetime geometry and the scalar field. In our teleparallel theory, there are two different branches of equations in spherical symmetry depending on how one solves the antisymmetric part of the field equations, leading to a real and a complex tetrad. We first show that the real tetrad seems to be incompatible with the regularity of the equations at the event horizon, which is a symptom that scalarized black hole solutions beyond the Riemannian Einstein-Gauss-Bonnet theory might not exist. Therefore, we concentrate our study on the complex tetrad. This leads to the emergence of scalarized black hole solutions, where the torsion acts as the scalar field source. Extending our previous work, we study monomial non-minimal couplings of degrees one and two, which are intensively studied in conventional, curvature-based, scalar Einstein-Gauss-Bonnet gravity. We discover that the inclusion of torsion can potentially alter the stability of the resulting scalarized black holes. Specifically, our findings indicate that for a quadratic coupling, which is entirely unstable in the pure curvature formulation, the solutions induced by torsion may exhibit stability within certain regions of the parameter space. In a limiting case, we were also able to find black holes with a strong scalar field close to the horizon but with a vanishing scalar charge.

gr-qc↗