arXiv subjects

Daniel Blixt

Publications and source records attributed to Daniel Blixt.

16 recordsLinked to original sources

arXiv2026

Gauge-invariant cosmological perturbations in Type 3 New General Relativity and background-hierarchy bounds

In this paper, we investigate background-hierarchy bounds in Type~3 of New General Relativity (NGR). These bounds arise when the contribution associated with the evolution of the background spacetime exceeds that of the kinetic term in the perturbed Lagrangian. Type~3 of NGR has two free parameters and is described in a pure-tetrad formulation while preserving diffeomorphism invariance and spatial rotations. We first review Type~3 and identify preferable gauge choices for metric-affine gauge theories of gravity with Weitzenb\"ock connection, including NGR, from the viewpoint of symmetry in both Dirac--Bergmann analysis and linear perturbation theory. We then revisit the perturbative analysis of Type~3 and show that the propagating modes are correctly identified even when the perturbed Lagrangian is not written solely in terms of gauge-invariant variables. Finally, we derive the background-hierarchy bounds for the scalar, transverse-vector, and tensor modes around a flat FLRW background, and identify the region of parameter space in which the linear perturbation theory of Type~3 remains viable for cosmological applications.

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arXiv2026

Canonical Vielbeins for General Relativity: D + 1 Decomposition and Constraint Analysis

We provide a self-contained derivation of the Hamiltonian formulation of General Relativity in vielbein variables in $d=D+1$ dimensions. Starting from the Einstein--Hilbert action in a standard metric $D+1$ decomposition, we derive Lorentz- and $\mathrm{SO}(D)$-covariant phase-space actions, identify the primary Lorentz constraints, and obtain the Hamiltonian and momentum constraints. We compute the resulting first-class constraint algebra, relate the vielbein and metric phase-space formulations, and discuss the rotation/boost decomposition. In particular, we construct the boost generator in the $\mathrm{SO}(D)$-covariant formulation, thereby recovering full local Lorentz symmetry.

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arXiv2024

The Hamilton equations in $f(T)$ teleparallel gravity and in New General Relativity

We derive the Hamiltonian function for extended teleparallel theories of gravity in their covariant formulation. In particular, we present the Hamiltonian for $f(T)$ gravity and New General Relativity. From this, we obtain the related Hamilton equations, which are presented both in covariant formulation and Weitzenb\"ock gauge. In this framework, teleparallel equivalent to General Relativity, its $f(T)$ extension and New General Relativity can be compared. We find that $f(T)$ and New General Relativity consistently reduce to the Teleparallel Equivalent to General Relativity, while significant differences appear comparing the Hamilton equations of $f(T)$ with $f(R)$ gravity.

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arXiv2024

Degrees of Freedom of New General Relativity I: Type 2, Type 3, Type 5, and Type 8

We investigate the degrees of freedom of new general relativity. This theory is a three-parameter theory and is classified into nine irreducible types according to the rotation symmetry of $SO(3)$ on each leaf of ADM-foliation. In this work, we focus on unveiling the degrees of freedom of the physically interesting types of NGR: Type 2, Type 3, Type 5, and Type 8, which contain the gravitational propagating degrees of freedom. First, we revisit the theory based on the gauge approach to gravity and reformulate the Lagrangian of the theory. Second, we review the irreducible decomposition of the theory while focusing on the Hamiltonian and the primary constraints in each type. Third, we perform the Dirac-Bergmann analysis to unveil the degrees of freedom of the theory in the case of Type 2, Type 3, Type 5, and Type 8. We find a novel new behavior of constraints in Type 8, which is classified as second-class but not to determine any Lagrange multipliers and to provide the gauge invariance of the theory under the satisfaction of a specific condition of the multipliers. The degrees of freedom of Type 2, Type 3, and Type 5 are unveiled as six, five, and seven, respectively. The degrees of freedom of Type 8 is either four under a specific condition to the Lagrange multipliers or six in the generic case. Finally, we conclude this work with five future perspectives.

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arXiv2024

Foliation-generating observers under Lorentz transformations

In this work, we revise the concept of foliation and related aspects that are crucial when formulating the Hamiltonian evolution for various theories beyond General Relativity. In particular, we show the relation between the kinematic characteristics of timelike congruences (observers) and the existence of foliations orthogonal to them. We then explore how local Lorentz transformations acting on observers affect the existence of transversal foliations, provide examples, and discuss the implications of these results for the $3+1$ formulation of tetrad modified theories of gravity.

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arXiv2024

Revisiting Stability in New General Relativity

We study the degrees of freedom in New General Relativity -- flat and metric compatible family of theories -- around the Minkowski background in a gauge invariant manner. First, we confirm the decoupling case, in which the theory reduces to linearized gravity plus a massless KR field. We then show that, unless they vanish, the vector modes of this theory will be unstable. In addition, we find two new branches of the theories, which are instability-free and propagate linearly two tensor modes and in one of the cases also a massless scalar field. This shows that while the generic theory is ill-behaved, there are three possible realizations of instability-free cases, in contradiction to the previous literature, which states that there is only one healthy theory in addition to general relativity.

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arXiv2024

Primary constraints in general teleparallel quadratic gravity

The primary constraints for general teleparallel quadratic gravity are presented. They provide a basic classification of teleparallel theories from the perspective of the full nonlinear theory and represent the first step towards a full-fledged Hamiltonian analysis. The results are consistent with the limit of metric and symmetric teleparallel quadratic gravity. In the latter case we also present novel results, since symmetric teleparallel theories have only been partially studied so far. Apart from the general results, we also present the special cases of teleparallel theories classically equivalent to general relativity, which differ by a boundary term from the formulation of Einstein and Hilbert. This affects the constraint algebra as the primary constraints involve a mix of torsion and non-metricity, implying that the symmetries of general relativity are realized in a more intricate way compared to the teleparallel case. In this context, a more detailed understanding will provide insights for energy and entropy in gravity, quantum gravity and numerical relativity of this alternative formulation of general relativity. The primary constraints are presented both in the standard formulation and in irreducible parts of torsion and non-metricity. The special role of axial torsion and its connection to the one-parameter of viable new general relativity is confirmed. Furthermore, we find that one of the irreducible parts of non-metricity affects the primary constraint for shift but not lapse.

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arXiv2023

The Gauss-Bonnet topological scalar in the Geometric Trinity of Gravity

The Gauss-Bonnet topological scalar is presented in metric-teleparallel formalism as well as in the symmetric and general teleparallel formulations. In all of the aforementioned frameworks, the full expressions are provided explicitly in terms of torsion, non-metricity and Levi-Civita covariant derivative. The number of invariant terms of this form is counted and compared with the number which can appear in the corresponding effective field theory. Although the difference in this number is not very large, it is found that the Gauss-Bonnet invariant excludes some of the effective field theory terms. This result sheds new light on how General Relativity symmetries can be maintained at higher order in teleparallel theories: this fact appears to be highly nontrivial in the teleparallel formulation. The importance of the so-called ``pseudo-invariant'' theories like $f(T)$- and $f(T,T_\mathcal{G})$-gravity is further discussed in the context of teleparallel Gauss-Bonnet gravity.

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arXiv2023

Geometry and covariance of symmetric teleparallel theories of gravity

We present the geometric foundations and derivations of equations of motion for symmetric teleparallel theories of gravity in the coincident gauge and covariant frameworks. We discuss the theoretical challenges introduced by the auxiliary fields responsible for the covariantisation procedure. We elucidate a tetradic structure interpretation behind this covariant formulation. Regarding the effect of covariantisation at the level of the equations of motion, we explicitly show that the only physical change, in case of setting an arbitrary energy-momentum tensor to the right hand side, resides in the requirement of the fulfillment of the covariant conservation laws. Also, we have explicitly introduced the fundamental covariantly-conserved teleparallel tetrad for the symmetric teleparallel frameworks.

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arXiv2023

Teleparallel bigravity

We write down the teleparallel equivalent to Hassan-Rosen bigravity, which is written using a torsionful but curvature-free connection. The theories only differ by a boundary term. The equivalence was proven, both by using perturbation theory and Hamiltonian analysis. It is further shown how one can construct novel bigravity theories within the teleparallel framework. Some of those are analyzed through perturbation theory, and it is found that all of the considered novel bigravity theories suffer from pathologies. In particular, it is found that a construction with two copies of new general relativity leads to ghostly degrees of freedom which are not present in the single tetrad teleparallel corresponding theory. We demonstrate how the teleparallel framework allows to easily create theories with derivative interaction. However, it is shown through perturbation theory that the simplest model is not viable. Furthermore, we demonstrate some steps in the Hamiltonian analysis of teleparallel bigravity with two copies of new general relativity and some toy models. The results rule out some of the novel teleparallel bigravity theories, but also demonstrate techniques in perturbation theory and Hamiltonian analysis which could be further used for more profound theories in the future.

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arXiv2022

Hamilton's equations in the covariant teleparallel equivalent of general relativity

We present Hamilton's equations for the teleparallel equivalent of general relativity (TEGR), which is a reformulation of general relativity based on a curvatureless, metric compatible, and torsionful connection. For this, we consider the Hamiltonian for TEGR obtained through the vector, antisymmetric, symmetric and trace-free, and trace irreducible decomposition of the phase space variables. We present the Hamiltonian for TEGR in the covariant formalism for the first time in the literature, by considering a spin connection depending on Lorentz matrices. We introduce the mathematical formalism necessary to compute Hamilton's equations in both Weitzenbock gauge and covariant formulation, where for the latter we must introduce new fields: Lorentz matrices and their associated momenta. We also derive explicit relations between the conjugate momenta of the tetrad and the conjugate momenta for the metric that are traditionally defined in GR, which are important to compare both formalisms.

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arXiv2022

Lorentz gauge-invariant variables in torsion-based theories of gravity

General relativity dynamics can be derived from different actions -- which depart from the Einstein-Hilbert action in boundary terms -- and for different choices of the dynamical variables. Among them, the teleparallel equivalent of general relativity is a torsion-based theory for the tetrad field. More general torsion-based theories have been built in the last years, intending to supersede general relativity. There are two current ways to formulate such theories; one includes a spin-connection and the other does not. We discuss the notion of Lorentz gauge invariance in such theories, and give a simple but important proof that both formulations are physically equivalent.

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arXiv2020

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.

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arXiv2019

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.

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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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arXiv2018

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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