arXiv subjects

Martin Krššák

Publications and source records attributed to Martin Krššák.

16 recordsLinked to original sources

arXiv2026

Teleparallel Regularization of Gravitational Action

We study the gravitational action in the teleparallel equivalent of general relativity, where the spin connection contributes to the action through a surface term and, when chosen appropriately, regularizes the action by effectively playing the role of a counterterm. We resolve several apparent ambiguities in this procedure using the Schwarzschild spacetime as an example. We show that the apparent discrepancy between bulk and quasilocal actions originates from contributions associated with spacetime singularities, and that the quasilocal action agrees with the standard results obtained in general relativity. We further clarify the role of the tetrad choice in determining the corresponding spin connection, showing that the proper diagonal and canonical frames give the same Euclidean action, while only the proper diagonal frame reproduces the expected Lorentzian action on the Wheeler--DeWitt patch. Finally, we establish the uniqueness of the regularization scheme and show that imposing an appropriate fall-off behavior of the torsion tensor removes the remaining ambiguity and fixes the Euclidean action uniquely.

gr-qc↗

arXiv2026

Teleparallel gravity from the principal bundle viewpoint

We examine whether the Teleparallel Equivalent of General Relativity (TEGR) can be formulated as a gauge theory in the language of connections on principal bundles. We argue in favor of using either the affine bundle with the Poincaré group or, equivalently, the orthonormal frame bundle with the Lorentz group as the structure group. Following the framework of Trautman--where gauge symmetries are determined using the absolute elements--we set to identify the absolute elements and gauge symmetries of TEGR. The problem of a non-dynamical teleparallel connection raises the question of whether it should be treated as an absolute element. If so, the gauge group of TEGR is potentially some undetermined subgroup of the diffeomorphism group. On the other hand, if the connection is allowed to be non-dynamical but the only absolute element is taken to be the canonical 1-form of the frame bundle, we recover the whole diffeomorphism group as the gauge group of TEGR.

gr-qc↗

arXiv2025

Self-Excited Gravitational Instantons

We present a novel approach to constructing gravitational instantons based on the observation that the gravitational action of general relativity in its teleparallel formulation can be expressed as a product of the torsion and excitation forms. We introduce a new class of solutions where these two forms are equal, which we term the self-excited instantons, and advocate for their use over the self-dual instantons of Eguchi and Hanson. These new self-excited instantons exhibit striking similarities to BPST instantons in Yang-Mills theory, as their action reduces to a topological Nieh-Yan term, which allows us to identify the axial torsion as a topological current and show that the gravitational action is given by a topological charge.

gr-qc↗

arXiv2025

Einstein gravity from the Einstein action: Counterterms and covariance

The field equations of general relativity can be derived from the Einstein action, which is quadratic in connection coefficients, rather than the standard action involving the Gibbons-Hawking-York term and counterterm. We show that it is possible to construct a new counterterm directly for the Einstein action, which removes divergences and naturally introduces a flat reference spacetime. The total action is then covariant under simultaneous transformation of both the spacetime and reference tetrads, and argue that this is analogous to the Gibbons-Hawking action. We then explore different perspectives arising naturally from different uses of the reference tetrad, and explore implications of viewing gravity as fundamentally described in terms of non-covariant connection coefficients.

gr-qc↗

arXiv2024

Lowering the strong coupling mode of modified teleparallel gravity theories

We investigate the strong coupling problem in modified teleparallel gravity theories using the effective field theory (EFT) approach, demonstrating that it is possible to shift the emergence of new degrees of freedom (DoFs) to lower orders in perturbation theory. We first focus on the case of $f(T)$ gravity, and we show that in its conformally equivalent form the scalar perturbations are non-dynamical up to the cubic action. We then propose a simple modification of the theory, which lowers the appearance of new DoFs to cubic order, compared to the quartic order in standard $f(T)$ gravity. Our work opens a new avenue to address the issue of strong coupling in modified teleparallel gravity, and suggests a new classification scheme of these theories based on the perturbative order at which new DoFs appear.

gr-qc↗

arXiv2024

Bulk Action Growth for Holographic Complexity

The action growth proposal relates the holographic complexity to the value of the action on the Wheeler-de Witt patch. We introduce a new method of calculating the gravitational action using the "bulk" term, i.e. the part of the Einstein-Hilbert action quadratic in connection coefficients. We demonstrate how to address the issue of non-covariance of the bulk action and evaluate it using the tetrad formalism. Due to the boundary term-free nature of the bulk action, we can gain further insights into the spatial structure of the action on the Wheeler-de Witt patch. We then argue that our entire scheme can be naturally covariantized within the framework of teleparallel geometry.

hep-th↗

arXiv2024

Teleparallel Gravity, Covariance and Their Geometrical Meaning

We explore the geometrical meaning of teleparallel geometries and the role of covariance in their definition. We argue that pure gauge connections are a necessary ingredient for describing geometry and gravity in terms of torsion and non-metricity. We show the other viable alternative is using the Einstein and Moller Lagrangians, but these are defined through the Riemannian connection coefficients and hence do not involve torsion nor non-metricity. We argue that the teleparallel geometries can be defined on the manifold without introducing any additional structures and that they naturally provide the covariant framework for the Einstein and Moller Lagrangians. We explore some consequences of this viewpoint for the modified theories of gravity as well.

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↗

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↗

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.

gr-qc↗

arXiv2019

Conformal Gravity and Transformations in the Symmetric Teleparallel Framework

Conformal symmetries appear in many parts of physics and play a unique role in exploring the Universe. In this work, we consider the possibility of constructing conformal theories of gravity in the Symmetric Teleparallel Gravity framework, where gravitation is expressed through non-metricity rather than curvature or torsion. We demonstrate that it is possible to formulate a family of conformal theories with second-order field equations and have the metric tensor as the fundamental variable. Moreover, we consider the addition of a scalar field to the theory, and compare the results to the Teleparallel Gravity setting. Finally, we present the scalar-tensor representation of modified symmetric teleparallel theories, and amongst others, we show that there is an interesting sub-case that has the possibility of playing the role of dark energy.

gr-qc↗

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.

gr-qc↗

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.

gr-qc↗

arXiv2017

Holographic Renormalization in Teleparallel Gravity

We consider the problem of IR divergences of the action in the covariant formulation of teleparallel gravity in asymptotically Minkowski spacetimes. We show that divergences are caused by inertial effects and can be removed by adding an appropriate surface term, leading to the renormalized action. This process can be viewed as a teleparallel analogue of holographic renormalization. Moreover, we explore the variational problem in teleparallel gravity and explain how the variation with respect to the spin connection should be performed.

gr-qc↗

arXiv2016

The covariant formulation of f(T) gravity

We show that the well-known problem of frame dependence and violation of local Lorentz invariance in the usual formulation of $f(T)$ gravity is a consequence of neglecting the role of spin connection. We re-formulate $f(T)$ gravity starting, instead of the "pure-tetrad" teleparallel gravity, from the covariant teleparallel gravity, using both the tetrad and the spin connection as dynamical variables, resulting in the fully covariant, consistent, and frame-independent, version of $f(T)$ gravity, which does not suffer from the notorious problems of the usual, pure-tetrad, $f(T)$ theory. We present the method to extract solutions for the most physically important cases, such as the Minkowski, the FRW and the spherically-symmetric ones. We show that in the covariant $f(T)$ gravity we are allowed to use an arbitrary tetrad in an arbitrary coordinate system along with the corresponding spin connection, resulting always to the same physically relevant field equations.

gr-qc↗

arXiv2015

Spin Connection and Renormalization of Teleparallel Action

In general relativity, inertia and gravitation are both included in the Levi-Civita connection. As a consequence, the gravitational action, as well as the corresponding energy-momentum density, are in general contaminated by spurious contributions coming from inertial effects. In teleparallel gravity, on the other hand, because the spin connection represents inertial effects only, it is possible to separate inertia from gravitation. Relying on this property, it is shown that to each tetrad there is naturally associated a spin connection that locally removes the inertial effects from the action. The use of the appropriate spin connection can be viewed as a renormalization process in the sense that the computation of energy and momentum naturally yields the physically relevant values. A self-consistent method for solving field equations and determining the appropriate spin connection is presented.

gr-qc↗