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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 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 to define a topological charge.

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., Comment: 12 pages; an earlier version was submitted to Gravity Research Foundation 2024 Awards for Essays on Gravitation

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., Comment: 6 pages, 1 Figure; journal version

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., Comment: 14 pages

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., Comment: 6 pages, 1 figure, talk delivered at the AT1 parallel session, "Hamiltonian Analysis In New General Relativity", at the 15th Marcel Grossmann Meeting 2018. Corrections of great importance have been implemented, which lead to changes in Fig. 1

Teleparallel geometry utilizes Weitzenb\"ock 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 $f(T,\phi)$ 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., Comment: minor clarifications and references added; 14 pages, no figures; contributed to the special issue "Selected Papers from Teleparallel Universes in Salamanca 2018"

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., Comment: 27 pages, no figures; final version accepted by Physical Review D

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., Comment: 11 pages, 1 figure; updated references to match published version. arXiv admin note: substantial text overlap with arXiv:1808.02894

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., Comment: 13 pages, no figures; journal version

New classes of modified teleparallel theories of gravity are introduced. The action of this theory is constructed to be a function of the irreducible parts of torsion $f(T_{\rm ax},T_{\rm ten},T_{\rm vec})$, where $T_{\rm ax},T_{\rm ten}$ and $T_{\rm vec}$ are squares of the axial, tensor and vector components of torsion, respectively. This is the most general (well-motivated) second order teleparallel theory of gravity that can be constructed from the torsion tensor. Different particular second order theories can be recovered from this theory such as new general relativity, conformal teleparallel gravity or $f(T)$ gravity. Additionally, the boundary term $B$ which connects the Ricci scalar with the torsion scalar via $R=-T+B$ can also be incorporated into the action. By performing a conformal transformation, it is shown that the two unique theories which have an Einstein frame are either the teleparallel equivalent of general relativity or $f(-T+B)=f(R)$ gravity, as expected., Comment: v2: 10 pages, accepted for publication in PLB; for a detailed derivation of the field equations see Appendix A in v1

We consider the variational principle in the covariant formulation of modified teleparallel theories with second order field equations. We vary the action with respect to the spin connection and obtain a consistency condition relating the spin connection with the tetrad. We argue that since the spin connection can be calculated using an additional reference tetrad, modified teleparallel theories can be interpreted as effectively bigravity theories. We conclude with discussion about the relation of our results and those obtained in the usual, non-covariant, formulation of teleparallel theories and present the solution to the problem of choosing the tetrad in $f(T)$ gravity theories., Comment: 15 pages, v3: significantly updated version including new results

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., Comment: 12 pages, version published in CQG

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., Comment: 9 pages, v3: Extended discussion on reference tetrads. Matches the published version

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., Comment: v2: 13 pages, minor corrections, new section about solving the field equations included

In this thesis, we study the physics of the quark gluon plasma (QGP) using holographic methods borrowed from string theory. We start our discussion by motivating the use of such machinery, explaining how recent experimental results from the LHC and RHIC colliders suggests that the created QGP should be described as a strongly coupled liquid with small but nonvanishing bulk and shear viscosities. We argue that holographic dualities are a very efficient framework for studying transport properties in such a medium. Next, we introduce the underlying physics behind all holographic dualities, the AdS/CFT correspondence, and then motivate the necessity of implementing conformal invariance breaking in them. After this, we present the phenomenologically most successful holographic model of the strong interactions - Improved Holographic QCD (IHQCD). Working within IHQCD, we next move on to calculate energy momentum tensor correlators in the bulk and shear channels of large-Nc Yang-Mills theory. In the shear channel, we confront our results with those derived in strongly coupled N=4 Super Yang-Mills theory as well as weakly interacting ordinary Yang-Mills theory. Close to the critical temperature of the deconfinement transition, we observe significant effects of conformal invariance breaking. In the bulk channel, where the conformal result is trivial, we make comparisons with both perturbative and lattice QCD. We observe that lattice data seem to favor our holographic prediction over the perturbative one over a wide range of temperatures., Comment: 107 pages, 14 figures, PhD thesis

We study a bottom-up holographic model of large-Nc Yang-Mills theory, in which conformal invariance is broken through the introduction of a dilaton potential on the gravity side. We use the model to calculate the spectral densities of the shear and bulk channels at finite temperature. In the shear channel, we compare our results to those derived in strongly coupled N=4 Super Yang-Mills theory as well as in weakly coupled ordinary Yang-Mills. In the bulk channel, where the conformal result is trivial, we make comparisons with both perturbative and lattice QCD. In both channels, we pay particular attention into the effects of conformal invariance breaking in the IHQCD model., Comment: 10 pages, 8 figures. To appear in the proceedings of the "Barcelona Postgrad Encounters on Fundamental Physics", University of Barcelona, October 17-19, 2012

We investigate the behavior of energy momentum tensor correlators in strongly coupled large-N_c Yang-Mills theory at nonzero temperature, working within the Improved Holographic QCD model. In particular, we determine the spectral functions and corresponding imaginary time correlators in the bulk and shear channels, and compare the results to recent perturbative and lattice calculations where available. For the bulk channel imaginary time correlator, for which all three results exist, lattice data is seen to favor the holographic prediction over the perturbative one over a wide range of temperatures., Comment: 14 pages, 5 figures; v2: minor modifications, accepted for publication in JHEP

In this talk, we discuss a number of recent calculations aimed at determining the spectral functions corresponding to various components of the energy momentum tensor in high-temperature SU(N) Yang-Mills theory. The computations reviewed include applications of both weak coupling and gauge/gravity techniques, and thus enable one to access different limits of the quantities. The motivation for the work is twofold: On one hand, the results are hoped to aid the eventual nonperturbative extraction of the bulk and shear viscosities from lattice data, while on the other hand they also enable an immediate comparison of the lattice, perturbative and holographic predictions for certain Euclidean correlators., Comment: 8 pages, 5 figures. To appear in the proceedings of the workshop 'Xth Quark Confinement and the Hadron Spectrum', TUM Campus Garching, Munich, October 8-12, 2012

We use AdS/QCD duality to compute the finite temperature Green's function G(omega,k;T) of the shear operator T_12 for all omega,k in hot Yang-Mills theory. The goal is to assess how the existence of scales like the transition temperature and glueball masses affects the correlator computed in the scalefree conformal N=4 supersymmetric Yang-Mills theory. We observe sizeable effects for T close to T_c which rapidly disappear with increasing T. Quantitative agreement of these predictions with future lattice Monte Carlo data would suggest that QCD matter in this temperature range is strongly interacting., Comment: 27 pages, 20 figures