arXiv subjects

Christian Pfeifer

Publications and source records attributed to Christian Pfeifer.

At least 73 records · Page 4Linked to original sources

arXiv2020

Relativistic kinetic gases as direct sources of gravity

We propose a new model for the description of a gravitating multi particle system, viewed as a kinetic gas. The properties of the, colliding or non-colliding, particles are encoded into a so called one-particle distribution function, which is a density on the space of allowed particle positions and velocities, i.e. on the tangent bundle of the spacetime manifold. We argue that an appropriate theory of gravity, describing the gravitational field generated by a kinetic gas, must also be modeled on the tangent bundle. The most natural mathematical framework for this task is Finsler spacetime geometry. Following this line of argumentation, we construct a coupling between the kinetic gas and a recently proposed Finsler geometric extension of general relativity. Additionally, we explicitly show how the coordinate invariance of the action of the kinetic gas leads to a novel formulation of conservation of the energy-momentum distribution of the gas on the tangent bundle.

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arXiv2019

Finsler spacetime geometry in Physics

Finsler geometry naturally appears in the description of various physical systems. In this review I divide the emergence of Finsler geometry in physics into three categories: as dual description of dispersion relations, as most general geometric clock and as geometry being compatible with the relevant Ehlers-Pirani-Schild axioms. As Finsler geometry is a straightforward generalisation of Riemannian geometry there are many attempts to use it as generalized geometry of spacetime in physics. However, this generalisation is subtle due to the existence of non-trivial null directions. I review how a pseudo-Finsler spacetime geometry can be defined such that it provides a precise notion of causal curves, observers and their measurements as well as a gravitational field equation determining the Finslerian spacetime geometry dynamically. The construction of such Finsler spacetimes lays they foundation for comparing their predictions with observations, in astrophysics as well as in laboratory experiments.

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arXiv2019

Photon sphere and perihelion shift in weak $f(T)$ gravity

Among modified theories of gravity, the teleparallel $f(T)$ gravity is an intensively discussed modelin the literature. The best way to investigate its viabilityis to derive observable predictions which yield evidence or constraints for the model, when compared with actual observations. In this paper we derive the photon sphere and the perihelion shift for weak $f(T)$ perturbations of general relativity. We consistently calculate first order teleparallel perturbations of Schwarzschild and Minkowski spacetime geometry, with which we improve and extend existing results in the literature.

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arXiv2019

Finsler gravity action from variational completion

In the attempts to apply Finsler geometry to construct an extension of general relativity, the question about a suitable generalization of the Einstein equations is still under debate. Since Finsler geometry is based on a scalar function on the tangent bundle, the field equation which determines this function should also be a scalar equation. In the literature two such equations have been suggested: the one by Rutz and the one by one of the authors. Here we employ the method of canonical variational completion to show that Rutz equation can not be obtained from a variation of an action and that its variational completion yields the latter field equations. Moreover, to improve the mathematical rigor in the derivation of the Finsler gravity field equation, we formulate the Finsler gravity action on the positive projective tangent bundle. This has the advantage of allowing us to apply the classical variational principle, by choosing the domains of integration to be compact and independent of the dynamical variable. In particular in the pseudo-Riemannian case, the vacuum field equation becomes equivalent to the vanishing of the Ricci tensor.

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arXiv2019

Modified teleparallel theories of gravity in symmetric spacetimes

Teleparallel gravity theories employ a tetrad and a Lorentz spin connection as independent variables in their covariant formulation. In order to solve their field equations, it is helpful to search for solutions which exhibit certain amounts of symmetry, such as spherical or cosmological symmetry. In this article we present how to apply the notion of spacetime symmetries known from Cartan geometry to teleparallel geometries. We explicitly derive the most general tetrads and spin connections which are compatible with axial, spherical, cosmological and maximal symmetry. For homogeneous and isotropic spacetime symmetry we find that the tetrads and spin connection found by the symmetry constraints are universal solutions to the anti-symmetric part of the field equations of any teleparallel theory of gravity. In other words, for cosmological symmetry we find what has become known as "good tetrads" in the context of $f(T)$ gravity.

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arXiv2019

On the gauge fixing in the Hamiltonian analysis of general teleparallel theories

The covariant formulation of teleparallel gravity theories must include the spin connection, which has 6 degrees of freedom. One can, however, always choose a gauge such that the spin connection is put to zero. In principle this gauge may affect counting of degrees of freedom in the Hamiltonian analysis. We show for general teleparallel theories of gravity, that fixing the gauge such that the spin connection vanishes in fact does not affect the counting of degrees of freedom. This manifests in the fact that the momenta of the Lorentz transformations which generate the spin connection are fully determined by the momenta of the tetrads.

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arXiv2019

Flat connection for rotating vacuum spacetimes in extended teleparallel gravity theories

Teleparallel geometry utilizes Weitzenböck connection which has nontrivial torsion but no curvature and does not directly follow from the metric like Levi-Civita connection. In extended teleparallel theories, for instance in $f(T)$ or scalar-torsion gravity, the connection must obey its antisymmetric field equations. So far only a few analytic solutions were known. In this note we solve the $f(T,ϕ)$ gravity antisymmetric vacuum field equations for a generic rotating tetrad ansatz in Weyl canonical coordinates, and find the corresponding spin connection coefficients. By a coordinate transformation we present the solution also in Boyer-Lindquist coordinates, often used to study rotating solutions in general relativity. The result hints for the existence of another branch of rotating solutions besides the Kerr family in extended teleparallel gravities.

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arXiv2019

Hamiltonian and primary constraints of new general relativity

We derive the kinematic Hamiltonian for the so-called "new general relativity" class of teleparallel gravity theories, which is the most general class of theories whose Lagrangian is quadratic in the torsion tensor and does not contain parity violating terms. Our approach makes use of an explicit expression for the flat, in general, nonvanishing spin connection, which avoids the use of Lagrange multipliers, while keeping the theory invariant under local Lorentz transformations. We clarify the relation between the dynamics of the spin connection degrees of freedom and the tetrads. The terms constituting the Hamiltonian of the theory can be decomposed into irreducible parts under the rotation group. Using this, we demonstrate that there are nine different classes of theories, which are distinguished by the occurrence or non-occurrence of certain primary constraints. We visualize these different classes and show that the decomposition into irreducible parts allows us to write the Hamiltonian in a common form for all nine classes, which reproduces the specific Hamiltonians of more restricted classes in which particular primary constraints appear.

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arXiv2019

Observables from modified dispersion relations on curved spacetimes:circular orbits, redshift and lateshift

The Hamiltonian formulation of modified dispersion relations (MDRs) allows for their implementation on generic curved spacetimes. In turn it is possible to derive phenomenological effects. I will present how to construct the kappa-Poincare dispersion relation on curved spacetimes, its spherically symmetric realizations, among them the kappa deformation of Schwarzschild spacetime, and its implementation on Friedmann-Lemaitre-Robertson-Walker spacetimes with arbitrary scale factor. In addition we will construct the general first order modifications of the general relativistic dispersion relation. Afterwards we will use the perturbative MDRs to calculate specific observables such as the redshift, lateshift and photon circular orbits.

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arXiv2019

Observers' measurements of time and length in premetric electrodynamics

The notion of observers' and their measurements is closely tied to the Lorentzian metric geometry of spacetime, which in turn has its roots in the symmetries of Maxwell's theory of electrodynamics. Modifying either the one, the other, or both ingredients to our modern understanding of physics, requires also a reformulation of the observer model used. In this presentation we will consider a generalized theory of electrodynamics, so called local and linear premetric, or area metric, electrodynamics and its corresponding spacetime structure. On this basis we will describe an observer's measurement of time and spatial length. A general algorithm how to determine observer measurements will be outlined and explicitly applied to a first order premetric perturbation of Maxwell electrodynamics. The later contains for example the photon sector of the minimal standard model extension. Having understood an observer's measurement of time and length we will derive the relativistic observables time dilation and length contraction. In the future a modern relativistic description of the classical tests of special relativity shall be performed, including a consistent observer model.

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arXiv2018

A local quantum Mach principle and the metricity of spacetime

We revisit the old question of what distinguishes the formulation of spacetime geometry in terms of a Lorentzian metric physically from more general geometric structures. Our approach to this question is operational and leads us to also revisit the notion of local inertial frames, arising in operational formulations of the equivalence and Mach's principle, both of which can be interpreted in generalized geometries. We extend the notion of inertial laboratory frames by taking serious that all matter inside the lab is fundamentally quantum and considering how it may couple to the quantum gravitational degrees of freedom generating the ambient effective spacetime structure. This revolves around the question of which structures an agent inside the inertial laboratory has available to operationally define the orientation of their reference frame, an aspect on which both the equivalence and Mach's principle are silent. We then contemplate the situation of a completely inertial laboratory, which, in terms of the quantum matter experiments inside it, is not only isolated from any matter outside it, but also from a direct coupling to effective quantum gravitational degrees of freedom. We formulate this as a local Mach principle (LMP): a local inertial laboratory has to be self-sufficient, so that an agent can only resort to relations among the quantum matter systems inside it to self-generate any reference structures relative to which to orient their frame. The transformations between different frame orientations thereby originate in the local quantum matter structures. Combining this with dispersion relations leads to various non-trivial compatibility conditions on the spacetime structures encoded by them. This permits us to formulate additional operational assumptions under which the LMP singles out Lorentzian metric spacetimes within generalized geometries defined by dispersion relations.

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arXiv2018

Berwald spacetimes and very special relativity

In this work we study Berwald spacetimes and their vacuum dynamics, where the latter are based on a Finsler generalization of the Einstein's equations derived from an action on the unit tangent bundle. In particular, we consider a specific class of spacetimes which are non-flat generalizations of the very special relativity (VSR) line element, to which we refer as very general relativity (VGR). We derive necessary and sufficient conditions for the VGR line element to be of Berwald type. We present two novel examples with the corresponding vacuum field equations: a Finslerian generalization of vanishing scalar invariant (VSI) spacetimes in Einstein's gravity as well as the most general homogeneous and isotropic VGR spacetime.

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arXiv2018

Wormholes in conformal gravity

We present a new class of solutions for static spherically symmetric wormhole spacetimes in conformal gravity and outline a detailed method for their construction. As an explicit example, we construct a class of traversable and non-traversable wormholes that are locally conformal to Schwarzschild-(anti) de Sitter spacetimes. These wormhole spacetimes are exact vacuum solutions in, but not being limited to, Weyl gravity and conformal scalar-tensor theories. Importantly, the method implies that every conformal theory of gravity with static spherically symmetric solutions will trivially contain wormholes without the need for exotic matter. Applying those results on gravitational theories that possess conformal symmetry in the ultraviolet regime, the central singularities of black holes can be replaced with wormhole throats. We speculate on possible phenomenological consequences. We also discuss the inclusion of matter fields and give explicit examples of charged wormholes in Weyl gravity and conformal scalar-tensor gravity.

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arXiv2018

Teleparallel theories of gravity as analogue of non-linear electrodynamics

The teleparallel formulation of gravity theories reveals close structural analogies to electrodynamics, which are more hidden in their usual formulation in terms of the curvature of spacetime. We show how every locally Lorentz invariant teleparallel theory of gravity with second order field equations can be understood as built from a gravitational field strength and excitation tensor which are related to each other by a constitutive relation, analogous to the axiomatic construction of theories of electrodynamics. We demonstrate how the previously studied models of $f(\mathbb{T})$ and $f(T_\text{ax},T_\text{ten},T_\text{vec})$ gravity as well as teleparallel dark energy can be formulated in this language. The advantage of this approach to gravity is that the field equations for different models all take the same compact form and general results can be obtained. An important new such result we find is a constraint which relates the field equations of the tetrad and the spin connection.

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arXiv2018

Observers' measurements in premetric electrodynamics I: Time and radar length

The description of an observer's measurement in general relativity and the standard model of particle physics is closely related to the spacetime metric. In order to understand and interpret measurements, which test the metric structure of the spacetime, like the classical Michelson-Morley, Ives-Stilwell, Kennedy-Thorndike experiments or frequency comparison experiments in general, it is necessary to describe them in theories, which go beyond the Lorentzian metric structure. However, this requires a description of an observer's measurement without relying on a metric. We provide such a description of an observer's measurement of the fundamental quantities time and length derived from a premetric perturbation of Maxwell's electrodynamics and a discussion on how these measurements influence classical relativistic observables like time dilation and length contraction. Most importantly, we find that the modification of electrodynamics influences the measurements at two instances: the propagation of light is altered as well as the observer's proper time normalization. When interpreting the results of a specific experiment, both effects cannot be disentangled, in general, and have to be taken into account.

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arXiv2018

Redshift and lateshift from homogeneous and isotropic modified dispersion relations

Observables which would indicate a modified vacuum dispersion relations, possibly caused by quantum gravity effects, are a four momentum dependence of the cosmological redshift and the existence of a so called lateshift effect for massless or very light particles. Existence or non-existence of the later is currently analyzed on the basis of the available observational data from gamma ray bursts and compared to predictions of specific modified dispersion relation models. We consider the most general perturbation of the general relativistic dispersion relation of freely falling particles on homogeneous and isotropic spacetimes and derive the red- and lateshift to first order in the perturbation. Our result generalizes the existing formulae in the literature and we find that there exist modified dispersion relations causing both, one or none of the two effects to first order.

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arXiv2018

Scalar-torsion theories of gravity II: $L(T, X, Y, ϕ)$ theory

We consider Lorentz invariant scalar-tensor teleparallel gravity theories with a Lagrangian built from the torsion scalar, a scalar field, its kinetic term and a derivative coupling between the torsion and the scalar field. The field equations of the theory are derived and the relation between the spin connection and the antisymmetric part of the tetrad field equations is found explicitly, which is an important consistency result for Lorentz invariant teleparallel theories of gravity. Afterwards we study the behaviour of this class of theories under conformal transformations and find that such transformations map different theories in this class onto each other.

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arXiv2018

Hamilton Geometry - Phase Space Geometry from Modified Dispersion Relations

Quantum gravity phenomenology suggests an effective modification of the general relativistic dispersion relation of freely falling point particles caused by an underlying theory of quantum gravity. Here we analyse the consequences of modifications of the general relativistic dispersion on the geometry of spacetime in the language of Hamilton geometry. The dispersion relation is interpreted as the Hamiltonian which determines the motion of point particles. It is a function on the cotangent bundle of spacetime, i.e. on phase space, and determines the geometry of phase space completely, in a similar way as the metric determines the geometry of spacetime in general relativity. After a review of the general Hamilton geometry of phase space we discuss two examples. The phase space geometry of the metric Hamiltonian $H_g(x,p)=g^{ab}(x)p_ap_b$ and the phase space geometry of the first order q-de Sitter dispersion relation of the form $H_{qDS}(x,p)=g^{ab}(x)p_ap_b + \ell G^{abc}(x)p_ap_bp_c$ which is suggested from quantum gravity phenomenology. We will see that for the metric Hamiltonian $H_g$ the geometry of phase space is equivalent to the standard metric spacetime geometry from general relativity. For the q-de Sitter Hamiltonian $H_{qDS}$ the Hamilton equations of motion for point particles do not become autoparallels but contain a force term, the momentum space part of phase space is curved and the curvature of spacetime becomes momentum dependent.

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