This work demonstrates that a complete description of the interaction of matter and all forces, gravitational and non-gravitational, can in fact be realized within a quantum affine algebraic framework. Using the affine group formalism, we construct elements of a physical Hilbert space for full, Lorentzian quantum gravity coupled to the Standard Model in four spacetime dimensions. Affine algebraic quantization of gravitation and matter on equal footing implies a fundamental uncertainty relation which is predicated upon a non-vanishing cosmological constant.
A sketch of the affine quantum gravity program illustrates a different perspective on several difficult issues of principle: metric positivity; quantum anomalies; and nonrenormalizability.
We show how a Metric Affine theory of Dilaton gravity can be reduced to an effective Riemannian Dilaton gravity model. A simple generalization of the Obukhov-Tucker-Wang theorem to Dilaton gravity is then presented.
There is a number of completely integrable gravity theories in two dimensions. We study the metric-affine approach on a 2-dimensional spacetime and display a new integrable model. Its properties are described and compared with the known results of Poincare gauge gravity.
A sketch of a recent approach to quantum gravity is presented which involves several unconventional aspects. The basic ingredients include: (1) Affine kinematical variables; (2) Affine coherent states; (3) Projection operator approach for quantum constraints; (4) Continuous-time regularized functional integral representation without/with constraints; and (5) Hard core picture of nonrenormalizability. Emphasis is given to the functional integral expressions.
Improvement of the classical gravity with the running gravitational coupling obtained from asymptotically safe gravity, is a good way of considering the effects of quantum gravity. This is usually done for metric theories of gravity. Here we investigate the effects of such an improvement for pure affine theories of gravity. To motivate the approach, we first consider the effects of quantum improvement on the connection using metric theory and investigate the effects on the causal structure of black hole solution. Next in the framework of Schrödinger-Eddington affine theory, the general way of …
We present a symmetric hyperbolic formulation of the Einstein equations in affine-null coordinates. Giannakopoulos et. al. (arXiv:2007.06419) recently showed that the most commonly numerically implemented formulations of the Einstein equations in affine-null coordinates (and other single-null coordinate systems) are only weakly-but not strongly-hyperbolic. By making use of the tetrad-based Newman-Penrose formalism, our formulation avoids the hyperbolicity problems of the formulations investigated by Giannakopoulos et. al. We discuss a potential application of our formulation for studying gravi…
Using a semi-empirical approach we show that modified gravity affects the internal properties of terrestrial planets, such as their physical characteristics of a core, mantle, and core-mantle boundary. We also apply these findings for modeling a two-layers exoplanet in Palatini $f(R)$ gravity.
All attempts to quantize gravity face several difficult problems. Among these problems are: (i) metric positivity (positivity of the spatial distance between distinct points), (ii) the presence of anomalies (partial second-class nature of the quantum constraints), and (iii) perturbative nonrenormalizability (the need for infinitely many distinct counterterms). In this report, a relatively nontechnical discussion is presented about how the program of affine quantum gravity proposes to deal with these problems.
We find a class of electrically charged exact solutions for a toy model of metric-affine gravity. Their metric is of the Plebański-Demiański type and their nonmetricity and torsion are represented by a triplet of covectors with dilation, shear, and spin charges.
We consider a (non--Riemannian) metric--affine gravity theory, in particular its nonmetricity--torsion sector ``isomorphic'' to the Einstein--Maxwell theory. We map certain Einstein--Maxwell electrovacuum solutions to it, namely the Plebański--Demiański class of Petrov type D metrics.
Here we consider a metric-affine theory of gravity in which the gravitational Lagrangian is the scalar curvature. The matter action is allowed to depend also on the torsion and the nonmetricity, which are considered as the field variables together with the metric. We find the field equations of the theory and show that they reduce to Einstein equations in vacuum
Above Planck energies, the spacetime might become non--Riemannian, as it is known fron string theory and inflation. Then geometries arise in which nonmetricity and torsion appear as field strengths, side by side with curvature. By gauging the affine group, a metric affine gauge theory emerges as dynamical framework. Here, by using the harmonic map ansatz, a new class of multipole like solutions in the metric affine gravity theory (MAG) is obtained.
By using our recent generalization of the colliding waves concept to metric-affine gravity theories, and also our generalization of the advanced and retarded time coordinate representation in terms of Jacobi functions, we find a general class of colliding wave solutions with fourth degree polynomials in metric-affine gravity. We show that our general approach contains the standard second degree polynomials colliding wave solutions as a particular case.
We extend the scope of the Raychaudhuri-Komar singularity theorem of General Relativity to affine theories of gravity with and without torsion. We first generalize the existing focusing theorems using time-like and null congruences of curves which are hypersurface orthogonal, showing how the presence of torsion affects the formation of focal points in Lorentzian manifolds. Considering the energy conservation on a given affine gravity theory, we prove new singularity theorems for accelerated curves in the cases of Lorentzian manifolds containing perfect fluids or scalar field matter sources.
We study the well formulation of the initial value problem of f(R)-gravity in the metric-affine formalism. The problem is discussed in vacuo and in presence of perfect-fluid matter, Klein-Gordon and Yang-Mills fields. Adopting Gaussian normal coordinates, it can be shown that the problem is always well-formulated. Our results refute some criticisms to the viability of f(R)-gravity recently appeared in literature.
In the Tucker-Wang approach to Metric Affine gravity we review some particular solutions of the Cartan equation for the non-riemannian part of the connection. As application we show how a quite general non Riemannian model gives a Proca type equation for the trace of the nonmetricity 1-forms Q.
We present an exact stationary {\it axially symmetric} vacuum solution of metric-affine gravity (MAG) which generalises the recently reported spherically symmetric solution. Besides the metric, it carries nonmetricity and torsion as post-Riemannian geometrical structures. The parameters of the solution are interpreted as mass and angular momentum and as dilation, shear and spin charges.
The details are presented of a new evolution algorithm for the characteristic initial-boundary value problem based upon an affine parameter rather than the areal radial coordinate used in the Bondi-Sachs formulation. The advantages over the Bondi-Sachs version are discussed, with particular emphasis on the application to the characteristic extraction of the gravitational waveform from Cauchy simulations of general relativistic astrophysical systems.
A special case of metric-affine gauge theory of gravity (MAG) is equivalent to general relativity with Proca matter as source. We study in detail a corresponding numeric solution of the Reissner-Nordstr"om type. It is static, spherically symmetric, and of electric type. In particular, this solution has no horizon, so it has a naked singularity as its origin.
We show that the coupling of a Dirac spinor field with the gravitational field in the teleparallel equivalent of general relativity is consistent. For an arbitrary SO(3,1) connection there are two possibilities for the coupling of the spinor field with the gravitational field. The problems of consistency raised by Y. N. Obukhov and J. G. Pereira in the paper {\it Metric-affine approach to teleparallel gravity} [gr-qc/0212080] take place only in the framework of one particular coupling. By adopting an alternative coupling the consistency problem disappears.
The improved description of the planets' interior is provided. We examine the modified gravity effects on the Earth-like planets composed of the iron core and silicate mantle. We confirm that the mass-radius relations, as well as density profiles, differ with respect to the commonly adopted Newtonian models.
We generalize the formulation of the colliding gravitational waves to metric-affine theories and present an example of such kind of exact solutions. The plane waves are equipped with five symmetries and the resulting geometry after the collision possesses two spacelike Killing vectors.
We study plane-fronted electrovacuum waves in metric-affine gravity theories (MAG) with cosmological constant. Their field strengths are, on the gravitational side, curvature $R_α{}^β$, nonmetricity $Q_{αβ}$, torsion $T^α$ and, on the matter side, the electromagnetic field strength $F$. Our starting point is the work by Ozsváth, Robinson, and Rózga on type N gravitational fields in general relativity as coupled to null electromagnetic fields.
We present the generalized Reissner-Nordström solution of the field equations of metric-affine gravity (MAG), endowed with electric and magnetic charges, as well as with gravito-electric and gravito-magnetic charges and a cosmological constant term. Moreover, the case $M=e_o$, i.e. mass equal to electric charge and $λ=0$, corresponds to an electrically and magnetically charged monopole. Also further multipole solutions are obtained. The charge assignments of the solutions is discussed.
We show that almost all metric--affine theories of gravity yield Einstein equations with a non--null cosmological constant $Λ$. Under certain circumstances and for any dimension, it is also possible to incorporate a Weyl vector field $W_μ$ and therefore the presence of an anisotropy. The viability of these field equations is discussed in view of recent astrophysical observations.
Geometrical structure of homogeneous isotropic models in the frame of the metric-affine gauge theory of gravity (MAGT) is analyzed. By using general form of gravitational Lagrangian including both a scalar curvature and various invariants quadratic in the curvature, torsion and nonmetricity tensors, gravitational equations of MAGT for homogeneous isotropic models are deduced. It is shown, that obtained gravitational equations lead to generalized cosmological Friedmann equation for the metrics by certain restrictions on indefinite parameters of gravitational Lagrangian. Isotropic models in the …
We derive the equations of motion of extended deformable bodies in metric-affine gravity. The conservation laws which follow from the invariance of the action under the general coordinate transformations are used as a starting point for the discussion of the dynamics of extended deformable test bodies. By means of a covariant approach, based on Synge's world function, we obtain the master equation of motion for an arbitrary system of coupled conserved currents. This unified framework is then applied to metric-affine gravity. We confirm and extend earlier findings; in particular, we once again …
In a teleparallel theory of (2+1)-dimensional gravity developed in a previous paper, we examine generators of internal Lorentz transformations and of general affine coordinate transformations for static circularly symmetric exact solutions of gravitational field equation. The \lq \lq spin" angular momentum, the energy-momentum and the \lq \lq extended orbital angular momentum" are explicitly given for each solution. Also, we give a critical comment on Deser's claim that neither momentum nor boosts are definable for finite energy solutions of three-dimensional Einstein gravity.
The role of torsion in f(R) gravity is considered in the framework of metric-affine formalism. We discuss the field equations in empty space and in presence of perfect fluid matter taking into account the analogy with the Palatini formalism. As a result, the extra curvature and torsion degrees of freedom can be dealt as an effective scalar field of fully geometric origin. From a cosmological point of view, such a geometric description could account for the whole Dark Side of the Universe.
It is shown how consistent histories quantum cosmology can be realised through Isham's Histories Projection Operator consistent histories scheme. This is done by using an affine algebra instead of a canonical one and also by using cocycle representations. A regularisation scheme allows us to find a history Hamiltonian which exists as a proper self-adjoint operator. The role of a cocycle choice is also discussed.
Affine variational principle for General Relativity, proposed in 1978 by one of us (J.K.), is a good remedy for the non-universal properties of the standard, metric formulation, arising when the matter Lagrangian depends upon the metric derivatives. Affine version of the theory cures the standard drawback of the metric version, where the leading (second order) term of the field equations depends upon matter fields and its causal structure violates the light cone structure of the metric. Choosing the affine connection (and not the metric one) as the gravitational configuration, simplifies consi…
Generalization of an idea may lead to very interesting result. Learning how torsion influences on tidal force reveals similarity between tidal equation for geodesic and the Killing equation of second type. The relationship between tidal acceleration, curvature and torsion gives an opportunity to measure torsion.
The teleparallel gravity theory, treated physically as a gauge theory of translations, naturally represents a particular case of the most general gauge-theoretic model based on the general affine group of spacetime. On the other hand, geometrically, the Weitzenboeck spacetime of distant parallelism is a particular case of the general metric-affine spacetime manifold. These physical and geometrical facts offer a new approach to the teleparallelism. We present a systematic treatment of the teleparallel gravity within the framework of the metric-affine theory. The symmetries, conservation laws an…
The Minkowski space of special relativity can be understood as a flat 4-dimensional affine space enriched by a constant Minkowski metric. If we gauge the general affine group and `superimpose' the metric, then we arrive at the metric-affine theory of gravity (MAG). The gravitational potentials are the spacetime coframe, the metric, and the linear connection. The material energy-momentum is coupled to the coframe (and the metric), a hypothetical hypermomentum current to the connection. The hypermomentum splits in a spin, a dilation, and a shear piece. We collect some evidence in favor of the ex…
Affine gravity is a connection-based formulation of gravity that does not involve a metric. After a review of basic properties of affine gravity, we compute the tree-level scattering amplitude of scalar particles interacting gravitationally via the connection in a curved spacetime. We find that, while classically equivalent to general relativity, affine gravity differs from metric quantum gravity.
Within the context of the Ashtekar variables, the Hamiltonian constraint of four-dimensional pure General Relativity with cosmological constant, $Λ$, is reexpressed as an affine algebra with the commutator of the imaginary part of the Chern-Simons functional, $Q$, and the positive-definite volume element. This demonstrates that the affine algebra quantization program of Klauder can indeed be applicable to the full Lorentzian signature theory of quantum gravity with non-vanishing cosmological constant; and it facilitates the construction of solutions to all of the constraints. Unitary, irreduci…
We construct new explicit vacuum solutions of quadratic metric-affine gravity. The approach of metric-affine gravity in using an independent affine connection produces a theory with 10+64 unknowns, which implies admitting torsion and possible nonmetricity. Our spacetimes are generalisations of classical pp-waves, four-dimensional Lorentzian spacetimes which admit a nonvanishing parallel spinor field. We generalize this definition to metric compatible spacetimes with pp-metric and purely axial torsion. It has been suggested that one can interpret that the axial component of torsion as the Hodge…
A new geometric interpretation for General Relativity (GR) is proposed. We show that in the presence of an arbitrary affine connection, the gravitational field is described as nonmetricity of the affine connection. An affine connection can be interpreted as induced by a frame of reference (FR). Although the gravitational field equations are identical to Einstein's equations of GR, this formulation leads to a covariant tensor (instead of the pseudotensor) of energy-momentum of the gravitational field and covariant conservation laws. We further develop a geometric representation of FR as a metri…
We study f(R,T) theories of gravity, where T is the trace of the energy-momentum tensor T_{μν}, with independent metric and affine connection (metric-affine theories). We find that the resulting field equations share a close resemblance with their metric-affine f(R) relatives once an effective energy-momentum tensor is introduced. As a result, the metric field equations are second-order and no new propagating degrees of freedom arise as compared to GR, which contrasts with the metric formulation of these theories, where a dynamical scalar degree of freedom is present. Analogously to its metric…
Affine quantum gravity, which differs notably from either string theory or loop quantum gravity, is briefly reviewed. Emphasis in this article is placed on the use of affine coherent states in this program.
This work provides a short but comprehensible overview of some relevant aspects of metric-affine theories of gravity in relation to the physics and astrophysics of compact objects. We shall highlight the pertinence of this approach to supersede General Relativity on its strong-field regime, as well as its advantages and some of its difficulties. Moreover, we shall reflect on the present and future opportunities to testing its predictions with relativistic and non-relativistic stars, black holes, and other exotic horizonless compact objects.
We investigate spherically symmetric and static gravitational fields representing black hole configurations in the framework of metric-affine gauge theories of gravity (MAG) in the presence of different matter fields. It is shown that in the triplet ansatz sector of MAG, black hole configurations in the presence of non-Abelian matter fields allow the existence of black hole hair. We analyze several cases of matter fields characterized by the presence of hair and for all of them we show the validity of the no short hair conjecture.
Torsion and curvature could play a fundamental role in explaining cosmological dynamics. f(R)-gravity with torsion is an approach aimed to encompass in a comprehensive scheme all the Dark Side of the Universe (Dark Energy and Dark Matter). We discuss the field equations in empty space and in presence of perfect fluid matter taking into account the analogy with the metric-affine formalism. The result is that the extra curvature and torsion degrees of freedom can be dealt under the standard of an effective scalar field of fully geometric origin. The initial value problem for such theories is als…
We discuss the presence of ghostly instabilities for metric-affine theories constructed with higher order curvature terms. We mainly focus on theories containing only the Ricci tensor and show the crucial role played by the projective symmetry. The pathological modes arise from the absence of a pure kinetic term for the projective mode and the non-minimal coupling of a 2-form field contained in the connection, and which can be related to the antisymmetric part of the metric in non-symmetric gravity theories. The couplings to matter are considered at length and cannot be used to render the theo…
One of the most appealing results of metric-affine gauge theory of gravity is a close parallel between the Riemann curvature two-form and the Cartan torsion two-form: While the former is the field strength of the Lorentz-group connection one-form, the latter can be understood as the field strength of the coframe one-form. This parallel, unfortunately, is not fully established until one adopts Trautman's idea of introducing an affine-vector-valued zero-from, the meaning of which has not been satisfactorily clarified. This paper aims to derive this parallel from first principles without any ad h…
The approach of metric-affine gravity initially distinguishes it from Einstein's general relativity. Using an independent affine connection produces a theory with 10+64 unknowns. We write down the Yang-Mills action for the affine connection and produce the Yang-Mills equation and the so called complementary Yang-Mills equation by independently varying with respect to the connection and the metric respectively. We call this theory the Yang-Mielke theory of gravity. We construct explicit spacetimes with pp-metric and purely axial torsion and show that they represent a solution of Yang-Mills theo…
Metric-affine geometry provides a non-trivial extension of the general relativity where the metric and connection are treated as the two independent fundamental quantities in constructing the space-time (with non-vanishing torsion and non-metricity). In this paper we study the generic form of action in this formalism, and then construct the Weyl-invariant version of this theory. It is shown that in Weitzenbock space, the obtained Weyl-invariant action can cover the conformally invariant teleparallel action. Finally the related field equations are obtained in the general case.
The metric-affine gauge theory of gravity provides a broad framework in which gauge theories of gravity can be formulated. In this article we fit metric-affine gravity into the covariant BRST--antifield formalism in order to obtain gauge fixed quantum actions. As an example the gauge fixing of a general two-dimensional model of metric-affine gravity is worked out explicitly. The result is shown to contain the gauge fixed action of the bosonic string in conformal gauge as a special case.
One of the virtues of the Ashtekar variables is the simplification of the initial value constraints for gravity. In the case of self-dual variables this entails a complexification of the phase space which comes at the expense of having to implement reality conditions in the Lorentzian signature case. A reformulation of the theory in terms of real variables eliminates this difficulty, albeit at the expense of having to deal with a more complicated Hamiltonian constraint. The set of available gravitational theories classically equivalent to Einstein's is parametrized by a parameter $β$, known as…
Loop Quantum Gravity is widely developed using canonical quantization in an effort to find the correct quantization for gravity. Affine quantization, which is like canonical quantization augmented bounded in one orientation, e.g., a strictly positive coordinate. We open discussion using canonical and affine quantizations for two simple problems so each procedure can be understood. That analysis opens a modest treatment of quantum gravity gleaned from some typical features that exhibit the profound differences between aspects of seeking the quantum treatment of Einstein's gravity.
This work mainly focuses to unveil the optical features of a black hole. For this objective, we utilize the metric-affine black hole geometry with the inclusion of dilation, spin, and shear charge. The Lagrangian coefficients $f_1$ and $d_1$ are the main parameters, where $f_1<0$, which differentiate the solutions by $d_1=8f_1,\;d_1=-8f_1,\;\&\;d_1=\pm8f_1$. Based on these parameters, we carry out this work in two cases, i.e., $d_1=8f_1,\;\&\;d_1=-8f_1$. We forecast the detailed impact of dilation, spin, and shear charges on the optical properties of the black holes in both cases. To unreveal …
