arXiv subjects

Alexey Golovnev

Publications and source records attributed to Alexey Golovnev.

At least 37 records · Page 2Linked to original sources

arXiv2023

Static spherically symmetric solutions in New General Relativity

We give a pedagogical introduction to static spherically symmetric solutions in models of New GR, both explaining the basics and showing how all such vacuum solutions can be obtained in elementary functions. In doing so, we coherently introduce the full landscape of these modified teleparallel spacetimes, and find a few special cases. The equations of motion are turned into a very nice and compact form by using the Levi-Civita divergence of the torsion-conjugate; and generalised Bianchi identities are briefly discussed. Another important point we make is that a convenient choice of the radial variable might be instrumental for success of similar studies in other modified gravity models.

gr-qc↗

arXiv2023

On the role of constraints and degrees of freedom in the Hamiltonian formalism

Unfortunately, the Hamiltonian mechanics of degenerate Lagrangian systems is usually presented as a mere recipe of Dirac, with no explanation as to how it works. Then it comes to discussing conjectures of whether all primary constraints correspond to gauge symmetries, and it goes all the way to absolutely wrong claims such as the statement that electrodynamics or gravity have only two physical components each, with others being spurious. One has to be very careful because non-dynamical, or constrained, does not mean unphysical. I give a pedagogical introduction to the degenerate Hamiltonian systems, showing both very simple mechanical examples and general arguments about how it works. For the familiar field theory models, I explain why the gauge freedom there "hits twice" in the sense of producing twice as many first-class constraints as gauge symmetries, and why primary, and only primary, constraints should be put into the total Hamiltonian.

hep-th↗

arXiv2022

Revisiting diagonal tetrads: New Black Hole solutions in $f(T)$ gravity

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.

gr-qc↗

arXiv2022

The Variational principle, Conformal and Disformal transformations, and the degrees of freedom

Conformal and disformal transformations are now being very intensively studied in the context of various modified gravity theories. In particular, some special classes of them can be used for constructing Mimetic Dark Matter models. Recently, it has been shown that many more transformations of this type, if not virtually all of them when the coefficients depend on the scalar kinetic term, can produce new solutions with mimetic properties. The aim of this paper is to explain how it works at the level of the variational principle, and to express some worries about viability of these models.

gr-qc↗

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.

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↗

arXiv2021

Lorentz symmetries and primary constraints in covariant teleparallel gravity

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 Weitzenböck 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.

gr-qc↗

arXiv2021

Foundational issues in f(T) gravity theory

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.

gr-qc↗

arXiv2021

Issues of Lorentz-invariance in f(T) gravity and calculations for spherically symmetric solutions

The f(T) gravity is nowadays being widely used for cosmological model building, as well as for constructing spherically symmetric solutions. In its classical pure tetrad formulation it violates the local Lorentz symmetry in the space of tetrads. By using an appropriate spin connection it can be brought to a formally Lorentz invariant shape. However, despite some mathematical elegance obtained and new options of looking for non-standard couplings to matter probably made possible, it is fully equivalent in itself to the initial formulation. It seems that this fact, that the covariantisation does not in principle change anything, is not understood well by the community. Therefore we give a pedagogical introduction to these topics. And, on top of that, we show that obtaining the explicit equations for spherically symmetric solutions in f(T) gravity is not very difficult computationally and can be easily done even without any computer at hand.

gr-qc↗

arXiv2021

Approaches to spherically symmetric solutions in f(T) gravity

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.

gr-qc↗

arXiv2021

Toward a concordance teleparallel Cosmology I: Background Dynamics

Assuming a spatially flat universe, we study the cosmological viability of an infrared corrected teleparallel gravity model, which accounts for late acceleration by weakening gravity at later times on cosmological distances. The theory does not introduce any additional free parameters into the cosmological model, as is commonly the case with modified gravity based cosmologies. This feature renders the cosmological model statistically comparable, on equal footing, with $Λ$CDM. In this context, using recent cosmological observations -- Pantheon supernova Type Ia, Hubble constant $H_0$, Baryon acoustic oscillation, redshift space distortions, Big Bang nucleosynthesis and the cosmic microwave background constraint on the decoupling acoustic scale -- we show that, although the exponential infrared-corrected gravity and $Λ$CDM are physically different, they are phenomenologically and statistically equivalent. However, the former is more adept at fitting accurately determined observational constraints while decreasing the $H_0$ tension without worsening the $S_8$ tension. This calls for full examination of the empirical viability of the theory at the linear perturbation level, which is the subject of paper II.

astro-ph.CO↗

arXiv2021

Toward a concordance teleparallel Cosmology II: Linear perturbation

Late time cosmic acceleration may be achieved by modifying gravity on large scales. This should also have consequences on the evolution of perturbations. We thus extend our study of exponential infrared $f(T)$ teleparallel gravity to examine the viability of the theory at the linear perturbation level, evaluating the full CMB and matter power spectra. As the theory does not introduce extra free parameters, it fits within the minimal six parameter space of standard $Λ$CDM. Using Planck 2018 CMB (TT+TE+EE+lensing) alone, best fits predict those parameters to be almost identical to $Λ$CDM, with slightly smaller $χ^2_{min}$. The resulting $H_0=72.24\pm 0.64$ km/s/Mpc, which "practically" alleviates the tension with local measurements, due to late time phantom behaviour. Inclusion of BAO data however reduces $H_0$, reflecting furthermore systematic deviations from data that are also present in supernova distances and the growth rate of structure (increasing the apparent tension in the latter case). As the theory, unlike other viable $f(T)$ models, does not reduce to $Λ$CDM through extra free parameters, those conclusions are generic; applying to any modified gravity or dynamical dark energy with phantom behaviour. With best fit parameters, the present scenario produces a CMB spectrum almost identical to $Λ$CDM, with slight deviation at low-multipole $\ell < 30$, where cosmic variance is large. The matter power spectrum is also quite close to $Λ$CDM; with percent level scale free modifications affecting modes significantly smaller than the horizon, arising primarily from modified background evolution. More significant deviations appear on larger scales, and may in principle distinguish modified gravity scenarios of the type studied here from dynamical dark energy.

astro-ph.CO↗

arXiv2021

Non-trivial Minkowski backgrounds in f(T) gravity

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.

gr-qc↗

arXiv2020

Bianchi identities in f(T) gravity: paving the way to confrontation with astrophysics

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.

gr-qc↗

arXiv2020

Minkowski space in $f(T)$ gravity

The full set of solutions of $f(T)$ gravity with the Minkowski metric is considered in this note. At the 4-th order in perturbations around the trivial tetrad solution, a new mode is found explicitly. Its presence signals a strong coupling problem that transcends the Minkowski background and also suggests the pathological nature of cosmological solutions.

gr-qc↗

arXiv2020

Perturbations in f(T) cosmology and the spin connection

In this short paper we explain how the spin connection variables should be introduced into the perturbation theory of the spatially flat cosmology in f(T) gravity with the background tetrad $e^a_μ=a(t)\cdotδ^a_μ$ and zero background spin connection. In passing, we also correct some small mistakes in our previous work on this subject.

gr-qc↗

arXiv2020

Disformal transformations in modified teleparallel gravity

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.

gr-qc↗

arXiv2018

Cosmological perturbations in modified teleparallel gravity models

Cosmological perturbations are considered in $f(T)$ and in scalar-torsion $f(φ)T$ teleparallel models of gravity. Full sets of linear perturbation equations are accurately derived and analysed at the relevant limits. Interesting features of generalisations to other teleparallel models, spatially curved backgrounds, and rotated tetrads are pointed out.

gr-qc↗