arXiv subjects

Christian Pfeifer

Publications and source records attributed to Christian Pfeifer.

At least 55 records · Page 3Linked to original sources

arXiv2022

Deformed relativistic kinematics on curved spacetime -- a geometric approach

Deformed relativistic kinematics have been considered as a way to capture residual effects of quantum gravity. It has been shown that they can be understood geometrically in terms of a curved momentum space on a flat spacetime. In this article we present a systematic analysis under which conditions and how deformed relativistic kinematics, encoded in a momentum space metric on flat spacetime, can be lifted to curved spacetimes in terms of a self-consistent cotangent bundle geometry, which leads to purely geometric, geodesic motion of freely falling point particles. We comment how this construction is connected to, and offers a new perspective on, non-commutative spacetimes. From geometric consistency conditions we find that momentum space metrics can be consistently lifted to curved spacetimes if they either lead to a dispersion relation which is homogeneous in the momenta, or, if they satisfy a specific symmetry constraint. The latter is relevant for the momentum space metrics encoding the most studied deformed relativistic kinematics. For these, the constraint can only be satisfied in a momentum space basis in which the momentum space metric is invariant under linear local Lorentz transformations. We discuss how this result can be interpreted and the consequences of relaxing some conditions and principles of the construction from which we started.

gr-qc↗

arXiv2022

Black Holes in $f(T,B)$ Gravity: Exact and Perturbed Solutions

Spherically symmetric solutions of theories of gravity built one fundamental class of solutions to describe compact objects like black holes and stars. Moreover, they serve as starting point for the search of more realistic axially symmetric solutions which are capable to describe rotating compact objects. Theories of gravity that do not possess spherically symmetric solutions which meet all observational constraints are easily falsified. In this article, we discuss classes of exact and perturbative spherically symmetric solutions in $f(T,B)$-gravity. The perturbative solutions add to the ones which have already been found in the literature, while the exact solutions are presented here for the first time. Moreover, we present general methods and strategies, like generalized Bianchi identities, to find spherically solutions in modified teleparallel theories of gravity.

gr-qc↗

arXiv2022

A quick guide to spacetime symmetry and symmetric solutions in teleparallel gravity

The notion of spacetime symmetry is essential to describe gravitating physical systems like planets, stars, black holes, or the universe as a whole, since they possess, at least to good approximation, spherical, axial, or spatially homogeneous and isotropic symmetry, respectively. This article gives a quick overview over the known facts on spacetime symmetries in teleparallel gravity. The most general spherical, axial, or spatially homogeneous and isotropic tetrads in Weitzenbck gauge are presented and a brief discussion about symmetric solutions of the anti-symmetric field equations in $f(T,B,ϕ,X)$-gravity is given.

gr-qc↗

arXiv2021

Hamiltonian Analysis In New General Relativity

It is known that one can formulate an action in teleparallel gravity which is equivalent to general relativity, up to a boundary term. In this geometry we have vanishing curvature, and non-vanishing torsion. The action is constructed by three different contractions of torsion with specific coefficients. By allowing these coefficients to be arbitrary we get the theory which is called `new general relativity'. In this note, the Lagrangian for new general relativity is written down in ADM-variables. In order to write down the Hamiltonian we need to invert the velocities to canonical variables. However, the inversion depends on the specific combination of constraints satisfied by the theory (which depends on the coefficients in the Lagrangian). It is found that one can combine these constraints in 9 different ways to obtain non-trivial theories, each with a different inversion formula.

gr-qc↗

arXiv2021

Identifying Berwald Finsler Geometries

Berwald geometries are Finsler geometries close to (pseudo)-Riemannian geometries. We establish a simple first order partial differential equation as necessary and sufficient condition, which a given Finsler Lagrangian has to satisfy to be of Berwald type. Applied to $(α,β)$-Finsler spaces, respectively $(A,B)$-Finsler spacetimes, this reduces to a necessary and sufficient condition for the Levi-Civita covariant derivative of the defining $1$-form. We illustrate our results with novel examples of $(α,β)$-Berwald geometries which represent Finslerian versions of Kundt (constant scalar invariant) spacetimes. The results generalize earlier findings by Tavakol and van den Bergh, as well as the Berwald conditions for Randers and m-Kropina resp. very special/general relativity geometries.

math.DG↗

arXiv2021

Review of the Hamiltonian analysis in teleparallel gravity

We review different approaches to the Hamiltonian analysis of teleparallel theories of gravity. In particular the Hamiltonian analysis for $f(\mathbb{T})$ theories led to disputed results in the literature. The aim of this review is to relate the different notations and assumptions in the different approaches in a comprehensive way, so that they can be compared more easily. To do this we present the primary constraints of the $f({\mathbb{T}_{\textrm{NGR}}})$ gravity class of theories for the first time. The particular cases studied in the literature, $f(\mathbb{T})$ gravity and new general relativity, are contained in this parent theory. We compare their Hamiltonian analyses done by different authors in the literature among each other by relating them to our analysis of $f({\mathbb{T}_{\textrm{NGR}}})$ in detail.

gr-qc↗

arXiv2021

Reaching the Planck scale with muon lifetime measurements

Planck scale modified dispersion relations are one way how to capture the influence of quantum gravity on the propagation of fundamental point particles effectively. We derive the time dilation between an observer's or particle's proper time, given by a Finslerian length measure induced from a modified dispersion relation, and a reference laboratory time. To do so, the Finsler length measure for general first order perturbations of the general relativistic dispersion relation is constructed explicitly. From this we then derive the time dilation formula for the $κ$-Poincaré dispersion relation in several momentum space bases, as well as for modified dispersion relations considered in the context of string theory and loop quantum gravity. Most interestingly we find that the momentum Lorentz factor in the present and future colliders can, in principle, become large enough to constrain the Finsler realization of the $κ$-Poincaré dispersion relation in the bicrossproduct basis as well as a string theory inspired modified dispersion relation, at Planck scale sensitivity with the help of the muon's lifetime.

hep-ph↗

arXiv2021

Static spherically symmetric black holes in weak f(T)-gravity

With the advent of gravitational wave astronomy and first pictures of the "shadow" of the central black hole of our milky way, theoretical analyses of black holes (and compact objects mimicking them sufficiently closely) have become more important than ever. The near future promises more and more detailed information about the observable black holes and black hole candidates. This information could lead to important advances on constraints on or evidence for modifications of general relativity. More precisely, we are studying the influence of weak teleparallel perturbations on general relativistic vacuum spacetime geometries in spherical symmetry. We find the most general family of spherically symmetric, static vacuum solutions of the theory, which are candidates for describing teleparallel black holes which emerge as perturbations to the Schwarzschild black hole. We compare our findings to results on black hole or static, spherically symmetric solutions in teleparallel gravity discussed in the literature, by comparing the predictions for classical observables such as the photon sphere, the perihelion shift, the light deflection, and the Shapiro delay. On the basis of these observables, we demonstrate that among the solutions we found, there exist spacetime geometries that lead to much weaker bounds on teleparallel gravity than those found earlier. Finally, we move on to a discussion of how the teleparallel perturbations influence the Hawking evaporation in these spacetimes.

gr-qc↗

arXiv2021

Teleparallel axions and cosmology

We consider the most general teleparallel theory of gravity whose action is a linear combination of the five scalar invariants which are quadratic in the torsion tensor. Since two of these invariants possess odd parity, they naturally allow for a coupling to pseudo-scalar fields, thus yielding a Lagrangian which is even under parity transformations. In analogy to similar fields in gauge theories, we call these pseudo-scalar fields \emph{teleparallel axions}. For the most general coupling of a single axion field, we derive the cosmological field equations. We find that for a family of cosmologically symmetric teleparallel geometries, which possess non-vanishing axial torsion, the axion coupling contributes to the cosmological dynamics in the early universe. Most remarkably, this contribution is also present when the axion is coupled to the teleparallel equivalent of general relativity, hence allowing for a canonical coupling of a pseudo-scalar to general relativity. For this case we schematically present the influence of the axion coupling on the fixed points in the cosmological dynamics understood as dynamical system. Finally, we display possible generalizations and similar extensions in other geometric frameworks to model gravity.

gr-qc↗

arXiv2021

General Teleparallel Modifications of Schwarzschild Geometry

Teleparallel theories of gravity are described in terms of the tetrad of a metric and a flat connection with torsion. In this paper, we study spherical symmetry in a modified teleparallel theory of gravity which is based on an arbitrary function of the five possible scalars constructed from the irreducible parts of torsion. This theory is a generalisation of the so-called New General Relativity theory. We find that only two scalars are different to zero in spherical symmetry and we solve the corresponding field equations analytically for conformal Teleparallel gravity, and then perturbatively around Schwarzschild geometry for the general perturbative theory around GR. Finally, we compute phenomenological effects from the perturbed solutions such as the photon sphere, perihelion shift, Shapiro delay, and the light deflection. We find their correspondent correction to the standard GR contribution and their dependence on the three model parameters.

gr-qc↗

arXiv2021

Exploring Axial Symmetry in Modified Teleparallel Gravity

Axially symmetric spacetimes play an important role in the relativistic description of rotating astrophysical objects like black holes, stars, etc. In gravitational theories that venture beyond the usual Riemannian geometry by allowing independent connection components, the notion of symmetry concerns, not just the metric, but also the connection. As discovered recently, in teleparallel geometries, axial symmetry can be realised in two branches, while only one of these has a continuous spherically symmetric limit. In the current paper, we consider a very generic $f(T,B,ϕ,X)$ family of teleparallel gravities, whose action depends on the torsion scalar $T$ and the boundary term $B$, as well as a scalar field $ϕ$ with its kinetic term $X$. As the field equations can be decomposed into symmetric and antisymmetric (spin connection) parts, we thoroughly analyse the antisymmetric equations and look for solutions of axial spacetimes which could be used as ansätze to tackle the symmetric part of the field equations. In particular, we find solutions corresponding to a generalisation of the Taub-NUT metric, and the slowly rotating Kerr spacetime. Since this work also concerns a wider issue of how to determine the spin connection in teleparallel gravity, we also show that the method of "turning off gravity" proposed in the literature, does not always produce a solution to the antisymmetric equations.

gr-qc↗

arXiv2021

Canonical variational completion and 4D Gauss-Bonnet gravity

Recently, a proposal to obtain a finite contribution of second derivative order to the gravitational field equations in $D = 4$ dimensions from a renormalized Gauss-Bonnet term in the action has received a wave of attention. It triggered a discussion whether the employed renormalization procedure yields a well-defined theory. One of the main criticisms is based on the fact that the resulting field equations cannot be obtained as the Euler-Lagrange equations from a diffeomorphism invariant action. In this work, we use techniques from the inverse calculus of variations to point out that the renormalized truncated Gauss-Bonnet equations cannot be obtained from any action at all (either diffeomorphism invariant or not), in any dimension. Then, we employ canonical variational completion, based on the notion of Vainberg-Tonti Lagrangian - which consists in adding a canonically defined correction term to a given system of equations, so as to make them derivable from an action. To apply this technique to the suggested $4$D renormalized Gauss-Bonnet equations, we extend the variational completion algorithm to some classes of PDE systems for which the usual integral providing the Vainberg-Tonti Lagrangian diverges. We discover that in $D>4$ the suggested field equations can be variationally completed, choosing either the metric or its inverse as field variables; both approaches yield consistently the same Lagrangian, whose variation leads to fourth order field equations. In $D=4$, the Lagrangian of the variationally completed theory diverges in both cases.

gr-qc↗

arXiv2020

Inequalities from Lorentz-Finsler norms

We show that Lorentz-Finsler geometry offers a powerful tool in obtaining inequalities. With this aim, we first point out that a series of famous inequalities such as: the (weighted) arithmetic-geometric mean inequality, Aczél's, Popoviciu's and Bellman's inequalities, are all particular cases of a reverse Cauchy-Schwarz, respectively, of a reverse triangle inequality holding in Lorentz-Finsler geometry. Then, we use the same method to prove some completely new inequalities, including two refinements of Aczél's inequality.

math.DG↗

arXiv2020

The kinetic gas universe

A description of many-particle systems, which is more fundamental than the fluid approach, is to consider them as a kinetic gas. In this approach the dynamical variable in which the properties of the system are encoded, is the distribution of the gas particles in position and velocity space, called 1-particle distribution function (1PDF). However, when the gravitational field of a kinetic gas is derived via the Einstein-Vlasov equations, the information about the velocity distribution of the gas particles is averaged out and therefore lost. We propose to derive the gravitational field of a kinetic gas directly from its 1PDF, taking the velocity distribution fully into account. We conjecture that this refined approach could possibly account for the observed dark energy phenomenology.

gr-qc↗

arXiv2020

Propagation of gravitational waves in teleparallel gravity theories

We investigate propagation of gravitational waves in the most general teleparallel gravity model with second order field equations around the Minkowski background. We argue that in this case the most general Lagrangian at the first order of perturbations is given by the linear combination of quadratic invariants and hence coincides with the well-known new general relativity model. We derive the linearized field equations and analyze them using the principal polynomial and the Newman-Penrose formalism. We demonstrate that all gravitational wave modes propagate at the speed of light and there are up to six possible polarizations. We show that two tensorial modes of general relativity are always present and the number of extra polarizations depends on the free parameters of the new general relativity model.

gr-qc↗

arXiv2020

Propagation of gravitational waves in symmetric teleparallel gravity theories

Symmetric teleparallel gravity (STG) offers an interesting third geometric interpretation of gravitation besides its formulation in terms of a spacetime metric and Levi-Civita connection or its teleparallel formulation. It describes gravity through a connection which is not metric compatible, however is torsion and curvature free. We investigate the propagation velocity of the gravitational waves around Minkowski spacetime and their potential polarizations in a general class of STG theories, the so-called "newer general relativity" class. It is defined in terms of the most general Lagrangian that is quadratic in the nonmetricity tensor, does not contain its derivatives and is determined by five free parameters. In our work we employ the principal symbol method and the Newman-Penrose formalism, to find that all waves propagate with the speed of light, i.e., on the Minkowski spacetime light cone, and to classify the theories according to the number of polarizations of the waves depending on the choice of the parameters in the Lagrangian. In particular it turns out that there exist more theories than just the reformulation of general relativity which allow only for two polarization modes. We also present a visualization of the parameter space of the theory to better understand the structure of the model.

gr-qc↗

arXiv2020

Cosmological Finsler Spacetimes

Applying the cosmological principle to Finsler spacetimes, we identify the Lie Algebra of symmetry generators of spatially homogeneous and isotropic Finsler geometries, thus generalising Friedmann-Lemaître-Robertson-Walker geometry. In particular, we find the most general spatially homogeneous and isotropic Berwald spacetimes, which are Finsler spacetimes that can be regarded as closest to pseudo-Riemannian geometry. They are defined by a Finsler Lagrangian built from a zero-homogeneous function on the tangent bundle, which encodes the velocity dependence of the Finsler Lagrangian in a very specific way. The obtained cosmological Berwald geometries are candidates for the description of the geometry of the universe, when they are obtained as solutions from a Finsler gravity equation.

gr-qc↗

arXiv2020

On the non metrizability of Berwald Finsler spacetimes

We investigate whether Szabo's metrizability theorem can be extended to Finsler spaces of indefinite signature. For smooth, positive definite Finsler metrics, this important theorem states that, if the metric is of Berwald type (i.e., its Chern-Rund connection defines an affine connection on the underlying manifold), then it is affinely equivalent to a Riemann space, meaning that its affine connection is the Levi-Civita connection of some Riemannian metric. We show for the first time that this result does not extend to Finsler spacetimes. More precisely, we find a large class of Berwald spacetimes for which the Ricci tensor of the affine connection is not symmetric. The fundamental difference from positive definite Finsler spaces that makes such an asymmetry possible, is the fact that generally, Finsler spacetimes satisfy certain smoothness properties only on a proper conic subset of the slit tangent bundle. Indeed, we prove that when the Finsler Lagrangian is smooth on the entire slit tangent bundle, the Ricci tensor must necessarily be symmetric. For large classes of Finsler spacetimes, however, the Berwald property does not imply that the affine structure is equivalent to the affine structure of a pseudo-Riemannian metric. Instead, the affine structure is that of metric-affine geometry with vanishing torsion.

math.DG↗