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In this work, we study cosmological spacetime configurations in f(Q) gravity with nonvanishing symmetric teleparallel connections. It is known that the spatially flat, homogeneous and isotropic connections can be classified into three sets. Focusing on two of those, we explore the stability of cosmological background evolution near the general relativity regime across radiation, matter, dark energy, and geometric dark energy dominated eras. Our results show that for the standard connection set 1 the general relativity regime can be realized in two ways and both exhibit stable behavior throughout all evolutionary epochs. Conversely, for the alternative connection set 2 the trivial general relativity limit is stable, while the nontrivial option exhibits stability during the radiation era and marginal stability during the matter era, but for the dark energy and geometric dark energy eras our results are inconclusive. Furthermore, we discuss the general conditions on the function f(Q) that physically viable models should obey, and point out that for a generic f(Q) the alternative connection sets 2 and 3 are prone to trigger a sudden singularity. This can happen even near the otherwise good looking general relativity regime, as we demonstrate by an explicit numerical example. Hence the alternative configurations could be problematic already on the background level., Comment: 25 pages, 2 figures

General relativity (GR) admits two alternative formulations with the same dynamics attributing the gravitational phenomena to torsion or nonmetricity of the manifold's connection. They lead, respectively, to the teleparallel equivalent of general relativity (TEGR) and the symmetric teleparallel equivalent of general relativity (STEGR). In this work, we focus on STEGR and present its differences with the conventional, curvature-based GR. We exhibit the 3+1 decomposition of the STEGR Lagrangian in the coincident gauge and present the Hamiltonian, and the Hamiltonian and momenta constraints. For a particular case of spherical symmetry, we explicitly show the differences in the Hamiltonian between GR and STEGR, one of the few genuinely different features of both formulations of gravity, and the repercussions it might encompass to numerical relativity., Comment: 12 pages, no figures; v2: crucial mistake corrected, updated discussion, comments welcome

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., Comment: minor amendments; 19 pages

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., Comment: 22 Pages, No figures

We study various forms of diagonal tetrads that accommodate Black Hole solutions in $f(T)$ gravity with certain symmetries. As is well-known, vacuum spherically symmetric diagonal tetrads lead to rather boring cases of constant torsion scalars. We extend this statement to other possible horizon topologies, namely, spherical, hyperbolic and planar horizons. All such cases are forced to have constant torsion scalars to satisfy the anti-symmetric part of the field equations. We give a full classification of possible vacuum static solutions of this sort. Furthermore, we discuss addition of time-dependence in all the above cases. We also show that if all the components of a diagonal tetrad depend only on one coordinate, then the anti-symmetric part of the field equations is automatically satisfied. This result applies to the flat horizon case with Cartesian coordinates. For solutions with a planar symmetry (or a flat horizon), one can naturally use Cartesian coordinates on the horizon. In this case, we show that the presence of matter is required for existence of non-trivial solutions. This is a novel and very interesting feature of these constructions. We present two new exact solutions, the first is a magnetic Black Hole which is the magnetic dual of a known electrically charged Black Hole in literature. The second is a dyonic Black Hole with electric and magnetic charges. We present some features of these Black holes, namely, extremality conditions, mass, behavior of torsion and curvature scalars near the singularity., Comment: pdfLaTeX, 21 pages, one figure. Submitted to EPJC

Possible models of modified gravity are being extensively studied now, with most phenomenological motivations coming from puzzles and tensions in cosmology due to a natural desire to better fit the known and newly coming data. At the same time, available experimental evidence is limited for testing gravity as a force beyond the regimes in which the theory of general relativity has proven to be successful. This situation leads researchers to look for ``the simplest modification'' to general relativity in a certain class of models, which is enough to solve one or more problems. As a result, we are lost amid a variety of theories with no deeper guiding principle. We give a general review of existing approaches and discuss the current state of the art., Comment: 13 pages, 1 figure. v2: matches the published version

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., Comment: 7 pages, matches the published version

In this article we explore local Lorentz transformations in theories of gravity based on the teleparallel formalism. For the teleparallel equivalent of general relativity (TEGR), the spin connection plays no role in the equations of motion, and therefore it is possible to simply put it equal to zero with no change in physical quantities, and then the theory is formulated purely in terms of the tetrad field which can be freely chosen in any way. In nonlinear modifications of TEGR, this is a more intricate issue, and vanishing spin connection is then the Weitzenb\"{o}ck gauge choice which imposes restrictions on the choice of tetrad. This has led to considering the so-called covariant formulation of $f(T)$ gravity. We examine the primary constraints arising when passing to the Hamiltonian framework, and compute their algebra. We show that the problems of local Lorentz symmetry breaking still appear in this formulation, even if in a different disguise., Comment: 19 pages, no figures, comments welcome

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., Comment: Matches published version in JCAP. 29 pages, 1 figure

We study properties of static spherically symmetric solutions in $f(\mathbb T)$ gravity. Based on our previous work on generalising Bianchi identities for this kind of theories, we show how this search of solutions can be reduced to the study of two relatively simple equations. One of them does not depend on the function $f$ and therefore describes the properties of such solutions in any $f(\mathbb T)$ theory. Another equation is the radial one and, if a possible solution is chosen, it allows to find out which function $f$ is suitable for it. We use these equations to find exact and perturbative solutions for arbitrary and specific choices off., Comment: 10 pages, 1 figure; discussion and references added

We give a short review on the status of research on the theoretical foundations of $f(T)$ gravity theories. We discuss recent results on perturbative and non-perturbative approaches, causality and degrees of freedom, and discuss future directions to follow., Comment: 13 pages, no figures, comments welcome; matches the published version

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., Comment: 36 pages, 2 tables, 1 figure; matches the published version

Boosted and rotated tetrad backgrounds for the Minkowski space are studied in $f(T)$ gravity. We perform Lorentzian perturbations at first order around non-trivial backgrounds and show that some Lorentz modes can exhibit non-trivial dynamics and can propagate in time. This remarkable feature gives evidence of additional mode(s) in the Lorentzian sector which have no precedent in Lorentz-violating modified gravities, however they can cast doubts onto even theoretical viability of these models., Comment: 10 pages, no figures, comments welcome; additional discussion added

We introduce a novel procedure for studying the Hamiltonian formalism of new general relativity (NGR) based on the mathematical properties encoded in the constitutive tensor defined by the premetric approach. We derive the canonical momenta conjugate to the tetrad field and study the eigenvalues of the Hessian tensor, which is mapped to a Hessian matrix with the help of indexation formulas. The properties of the Hessian matrix heavily rely on the possible values of the free coefficients $c_i, i=1,2,3$ appearing in the NGR Lagrangian. We find four null eigenvalues associated with trivial primary constraints in the temporal part of the momenta. The remaining eigenvalues are grouped in four sets, which have multiplicity 3, 1, 5 and 3, and can be set to zero depending on different choices of the coefficients $c_i$. There are nine possible different cases when one, two, or three sets of eigenvalues are imposed to vanish simultaneously. All cases lead to a different number of primary constraints, which are consistent with previous work on the Hamiltonian analysis of NGR by Blixt et al. (2018)., Comment: 13 pages, 2 tables, no figures, comments welcome; title changed, discussion added

Theories of $f(T)$ gravity are being actively confronted with cosmological observations, and are being studied for their potential to solve famous problems of cosmology. A necessary step is to extend these studies to astrophysical settings. However, to this end one must understand the structure of spherically symmetric solutions. We show that two different known approaches to these solutions are actually fully equivalent from the point of view of Lorentz-covariant formalism. Moreover, we explain Bianchi identities in $f(T)$ gravity and apply them to show that the corresponding equations are always compatible. It puts these efforts on much firmer grounds than before., Comment: 7 pages, no figures, comments welcome; minor changes, references added, matches the published version

The increasing demand of dedicated accelerators to improve energy efficiency and performance has highlighted FPGAs as a promising option to deliver both. However, programming FPGAs in hardware description languages requires long time and effort to achieve optimal results, which discourages many programmers from adopting this technology. High Level Synthesis tools improve the accessibility to FPGAs, but the optimization process is still time expensive due to the large compilation time, between minutes and days, required to generate a single bitstream. Whereas placing and routing take most of this time, the RTL pipeline and memory organization are known in seconds. This early information about the organization of the upcoming bitstream is enough to provide an accurate and fast performance model. This paper presents a performance analytical model for HLS designs focused on memory bound applications. With a careful analysis of the generated memory architecture and DRAM organization, the model predicts the execution time with a maximum error of 9.2% for a set of representative applications. Compared with previous works, our predictions reduce on average at least $2\times$ the estimation error.

Nonlinear generalizations of teleparallel gravity entail the modification of a Lagrangian that is pseudoinvariant under local Lorentz transformations of the tetrad field. This procedure consequently leads to the loss of the local pseudoinvariance and the appearance of additional degrees of freedom (d.o.f.). The constraint structure of f(T) gravity suggests the existence of one extra d.o.f. when compared with GR, which should describe some aspect of the orientation of the tetrad. The purpose of this article is to better understand the nature of this extra d.o.f. by means of a toy model that mimics essential features of f(T) gravity. We find that the nonlinear modification of a Lagrangian L possessing a local rotational pseudoinvariance produces two types of solutions. In one case the original gauge-invariant variables -- the analogue of the metric in teleparallelism -- evolve like when governed by the (nondeformed) Lagrangian L; these solutions are characterized by a (selectable) constant value of its Lagrangian, which is the manifestation of the extra d.o.f. In the other case, the solutions do contain new dynamics for the original gauge-invariant variables, but the extra d.o.f. does not materialize because the Lagrangian remains invariant on-shell. Coming back to f(T) gravity, the first case includes solutions where the torsion scalar T is a constant, to be chosen at the initial conditions (extra d.o.f.), and no new dynamics for the metric is expected. The latter case covers those solutions displaying a genuine modified gravity; T is not a constant, but it is (on-shell) invariant under Lorentz transformations depending only on time. Both kinds of f(T) solutions are exemplified in a flat FLRW universe. Finally, we present a toy model for a higher-order Lagrangian with rotational invariance [analogous to f(R) gravity] and derive its constraint structure and number of d.o.f., Comment: 22 pages, 2 tables, no figures, comments welcome; matches the published version

In this work, we explore disformal transformations in the context of the teleparallel equivalent of general relativity and modified teleparallel gravity. We present explicit formulas in components for disformal transformations of the main geometric objects in these theories such as torsion tensor, torsion vector and contortion. Most importantly, we consider the boundary term which distinguishes the torsion scalar from the Ricci scalar. With that we show for $f(T)$ gravity that disformal transformations from the Jordan frame representation are unable to straightforwardly remove local Lorentz breaking terms that characterize it. However, we have shown that disformal transformations have interesting properties, which can be useful for future applications in scalar-torsion gravity models, among others., Comment: 12 pages, no figures; prepared for proceedings of the 10th Mathematical Physics Meeting: School and Conference on Modern Mathematical Physics, 9 - 14 September 2019, Belgrade, Serbia, in which one of us (AG) participated; matches the published version

The existence of an extra degree of freedom (d.o.f.) in $f(T)$ gravity has been recently proved by means of the Dirac formalism for constrained Hamiltonian systems. We will show a toy model displaying the essential feature of $f(T)$ gravity, which is the pseudoinvariance of T under a local symmetry, to understand the nature of the extra d.o.f., Comment: 4 pages, no figures, to appear in the conference proceedings of the 10th Alexander Friedmann International Seminar on Gravitation and Cosmology, International Journal of Modern Physics A, World Scientific Publishing Company

We review the current status of the Lorentz covariance in teleparallel and modified teleparallel theories of gravity, and discuss the controversial features of the different approaches. We also revisit the issue of the remnant Lorentz gauge symmetries in $f(T)$ gravity., Comment: 12 pages, no figures; contribution to the proceedings of the workshop "Teleparallel Universes in Salamanca"

f(T) gravity is a generalization of the teleparallel equivalent of general relativity (TEGR), where T is the torsion scalar made up of the Weitzenb\"{o}ck connection. This connection describes a spacetime with zero curvature but with nonvanishing torsion, which fully encodes the gravitational phenomena. We will present recent results in f(T) gravity related with the issue of the degrees of freedom of the theory. In particular, we discuss the recent finding that f(T) gravity has one extra degree of freedom compared with TEGR, which was concluded through a detailed Hamiltonian analysis of the constraint structure of the theory. The physical interpretation of this result at the level of the trace of the equations of motion and its comparison with the f(R) case is discussed., Comment: 6 pages, talk delivered at the AT1 parallel session, "Extended Theories of Gravity and Quantum Cosmology", of the 15th Marcel Grossmann Meeting 2018

It has recently been shown that $f(T)$ gravity has $\frac{n(n-3)}{2}+1$ physical degrees of freedom (d.o.f.) in $n$ dimensions, contrary to previous claims. The simplest physical interpretation of this fact is that the theory possesses a scalar d.o.f. This is the case of $f(R)$ gravity, a theory that can be understood in the Einstein frame as general relativity plus a scalaron. The scalar field that represents the extra d.o.f. in $f(T)$ gravity encodes information about the parallelization of the spacetime, which is detected through a reinterpretation of the equations of motion in both the teleparallel Jordan and Einstein frames. The trace of the equations of motion in $f(T)$ gravity shows the propagation of the scalar d.o.f., giving an accurate proof of its existence. We also provide a simple toy model of a physical system with rotational pseudoinvariance, like $f(T)$ gravity, which gives insights into the physical interpretation of the extra d.o.f. We discuss some implications and unusual features of the previously worked out Hamiltonian formalism for $f(T)$ gravity. Finally we show some mathematical tools to implement the Hamiltonian formulation in the Einstein frame of $f(T)$ gravity, which exhibits some problems that should be addressed in future works., Comment: 18 pages, no figures, comments welcome; v2: references added, typos corrected, additional discussion in Sec. IV and VI; v3: matches the published version