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Dual Effective Field Theory formulation of Metric--Affine and Symmetric Teleparallel Gravity
Authors:
Ginés R. Pérez Teruel
Abstract:
We develop a unified algebraic and effective field theory (EFT) formulation for non--Riemannian extensions of General Relativity with an independent connection. For metric--affine $f(R,Q)$ gravity we show that the connection equations admit an exact matrix solution, whose square--root structure generates a convergent binomial/Neumann expansion in powers of the stress tensor $T_{μν}$. For the Eddin…
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We develop a unified algebraic and effective field theory (EFT) formulation for non--Riemannian extensions of General Relativity with an independent connection. For metric--affine $f(R,Q)$ gravity we show that the connection equations admit an exact matrix solution, whose square--root structure generates a convergent binomial/Neumann expansion in powers of the stress tensor $T_{μν}$. For the Eddington--inspired Born--Infeld (EiBI) theory we show that the connection can be solved algebraically as well, and that its determinantal field equations produce a parallel Neumann expansion with coefficients fixed by the underlying determinant operator. This allows us to rewrite the Einstein--like equations in the auxiliary metric as an effective Einstein equation for $g_{μν}$ with a local algebraic correction $(ΔT)_{μν}$ that follows from a dual EFT built from the invariants $\{T,\,T^2,\,T_{μν}T^{μν},\ldots\}$, organised by a characteristic density scale. We prove a convergence criterion based on the spectral radius of $\hat T^μ_ν$ and interpret EiBI gravity as a determinantal resummation of the same $T$--tower. Extending the framework to symmetric teleparallel $f(Q)$ gravity, we identify the EFT coefficients in terms of $f_Q$ and $f_{QQ}$ and present a background matching for $f(Q)=Q+αQ^2$. The resulting dual EFT provides a common algebraic language for metric--affine, Born--Infeld and non--metricity gravities.
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Submitted 10 December, 2025;
originally announced December 2025.
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Geometric Constraints on Quantum Gravity-Inspired Dispersion Relations
Authors:
Gines R. Perez Teruel
Abstract:
Modified dispersion relations (MDRs) arise in many quantum-gravity approaches, often in non-polynomial or non-analytic form beyond the reach of effective field theory (EFT). Logarithmic, exponential and trigonometric MDRs appear in causal set theory, nonlocal gravity and $κ$-Poincaré models, while Loop Quantum Gravity (LQG) yields polymeric (sine), holonomy, inverse-triad and semiclassical correct…
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Modified dispersion relations (MDRs) arise in many quantum-gravity approaches, often in non-polynomial or non-analytic form beyond the reach of effective field theory (EFT). Logarithmic, exponential and trigonometric MDRs appear in causal set theory, nonlocal gravity and $κ$-Poincaré models, while Loop Quantum Gravity (LQG) yields polymeric (sine), holonomy, inverse-triad and semiclassical corrections. Using the geometric framework of Ref.~\cite{GRP}, we analyse the intrinsic curvature of the associated energy--momentum surfaces, where negative curvature ensures hyperbolic and stable propagation, and curvature sign changes or critical points indicate kinematical instabilities or new invariant scales. We apply this method exhaustively to all major MDRs derived in LQG and find that they remain strictly hyperbolic in the entire phenomenologically relevant regime, with no elliptic patches or critical branching. The same framework provides universal constraints on representative logarithmic, exponential and trigonometric MDRs beyond EFT. Thus, geometric criteria yield a unified and coordinate-independent assessment of stability, thresholds and invariant scales, and demonstrate the robustness of MDRs emerging from LQG.
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Submitted 30 November, 2025;
originally announced December 2025.
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A Modified Gravitational Theory of the Matter Sector of the Type $φ(R,T)\mathcal{L}_{m}$
Authors:
Gines R. Pérez Teruel,
Antonio Peña Peña
Abstract:
We investigate a modified gravity framework where the geometric Einstein--Hilbert sector remains untouched while the matter Lagrangian is weighted by a nontrivial function $φ(T)$ of the energy--momentum trace. Unlike $f(R,T)$ or $f(R,\mathcal L_m)$ theories, this construction alters how matter curves spacetime without introducing extra geometric degrees of freedom, thereby remaining consistent wit…
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We investigate a modified gravity framework where the geometric Einstein--Hilbert sector remains untouched while the matter Lagrangian is weighted by a nontrivial function $φ(T)$ of the energy--momentum trace. Unlike $f(R,T)$ or $f(R,\mathcal L_m)$ theories, this construction alters how matter curves spacetime without introducing extra geometric degrees of freedom, thereby remaining consistent with local tests of gravity. Physically, the factor $φ(T)\mathcal L_m$ can be interpreted as an effective renormalization of the matter sector, relevant at high densities and smoothly reducing to GR at low densities. Within this setup we identify a robust window in parameter space leading to a smooth and nonsingular cosmological bounce, with bounded density, finite $\dot H>0$ at the bounce, and preservation of the infrared limit where $Λ$CDM is recovered. This mechanism provides a natural route to singularity resolution while retaining the empirical successes of standard cosmology.
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Submitted 10 November, 2025;
originally announced November 2025.
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Energy-Momentum Surfaces: A Differential Geometric Framework for Dispersion Relations
Authors:
Gines R. Perez Teruel
Abstract:
We propose a geometric framework where dispersion relations are viewed as parametric surfaces in energy-momentum space. Within this picture, the presence and type of critical points of the surface emerge as clear geometric signatures of kinematical restrictions. The Newtonian relation corresponds to a developable surface with no critical points, reflecting the absence of invariant limits. Special…
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We propose a geometric framework where dispersion relations are viewed as parametric surfaces in energy-momentum space. Within this picture, the presence and type of critical points of the surface emerge as clear geometric signatures of kinematical restrictions. The Newtonian relation corresponds to a developable surface with no critical points, reflecting the absence of invariant limits. Special Relativity generates a saddle point and globally negative curvature, encoding the universal light cone. Modified dispersion relations may introduce additional critical points, signaling new invariant energy scales or thresholds. This unifying approach not only recasts known results in a transparent geometric language but also provides a simple diagnostic tool for exploring departures from Lorentz invariance and their physical implications.
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Submitted 18 October, 2025;
originally announced October 2025.
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Conservative wormholes in generalized $κ(\mathcal{R},\mathcal{T})$-function
Authors:
Ksh. Newton Singh,
G. R. P. Teruel,
S. K. Maurya,
Tanmoy Chowdhury,
Farook Rahaman
Abstract:
We present an exhaustive study of wormhole configurations in $κ(\mathcal{R},\mathcal{T})$ gravity with linear and non-linear functions. The model assumed Morrison-Thorne spacetime where the redshift and shape functions linked with the matter contain and geometry of the spacetime through non-covariant conservation equation of the stress-energy tensor. The first solution was explored assuming a cons…
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We present an exhaustive study of wormhole configurations in $κ(\mathcal{R},\mathcal{T})$ gravity with linear and non-linear functions. The model assumed Morrison-Thorne spacetime where the redshift and shape functions linked with the matter contain and geometry of the spacetime through non-covariant conservation equation of the stress-energy tensor. The first solution was explored assuming a constant redshift function that leads to a wormhole (WH) which is asymptotically non-flat. The remaining solutions were explored in two cases. Firstly, assuming a linear equation of state $p(r)=ωρ(r)$ along with different forms of $κ(\mathcal{R},\mathcal{T})-$function. This proved enough to derive a shape function of the form $b(r)=r_{0}\left(\frac{r_{0}}{r}\right)^{1/ω}$. Secondly, by assuming specific choices of the shape function consistent with the wormhole configuration requirements. All the solutions fulfill flare-out condition, asymptotically flat and supported by phantom energy. Further, the embedding surface and its revolution has been generated using numerical method to see how the length of the throat is affected of the coupling parameters through $κ(\mathcal{R},\mathcal{T})$ function. At the end, we have also calculated the average null energy condition, which is satisfied by all the WH models signifying minimum exotic matter is required to open the WH throats.
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Submitted 11 October, 2024; v1 submitted 28 March, 2024;
originally announced March 2024.
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Possible existence of stable compact stars in $κ(\mathcal{R},\mathcal{T})-$gravity
Authors:
Ginés R. Pérez Teruel,
Ksh. Newton Singh,
Farook Rahaman,
Tanmoy Chowdhury
Abstract:
We present the first interior solutions representing compact stars in $κ(\mathcal{R},\mathcal{T})$ gravity, by solving the modified field equations in isotropic coordinates. Further, we have assumed the metric potentials in Schwarzschild's form and a few parameters along with the isotropic condition of pressure. For solving, we use specific choice of the running gravitational constant as…
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We present the first interior solutions representing compact stars in $κ(\mathcal{R},\mathcal{T})$ gravity, by solving the modified field equations in isotropic coordinates. Further, we have assumed the metric potentials in Schwarzschild's form and a few parameters along with the isotropic condition of pressure. For solving, we use specific choice of the running gravitational constant as $κ(\mathcal{R},\mathcal{T})=8π-λ\mathcal{T} ~~(G=\tilde{c}=1)$. Once arrived at the reduced field equations, we investigate two solutions with $c=1$ and $c \neq 1$, where $c$ denotes here another constant that should not be confused with the speed of light. Then, we investigate each solution by determining the thermodynamics variable {\it viz} pressure, density, speed of sound, and adiabatic index. We found that these solutions satisfy the Bondi criterion, causality condition, and energy conditions. We also found that the $M-R$ curves generated from these solutions satisfy the stringent constraints provided by the gravitational wave observations due to the neutron star merger GW 170817.
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Submitted 30 November, 2022;
originally announced December 2022.
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$κ(R,T)$ gravity
Authors:
Ginés R. Pérez Teruel
Abstract:
In this note we explore a modified theory of gravitation that is not based on the least action principle, but on a natural generalization of the original Einstein's field equations. This approach leads to the non-covariant conservation of the stress-energy tensor, a feature shared with other Lagrangian theories of gravity such as the $f(R,T)$ case. We consider the cosmological implications of a pa…
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In this note we explore a modified theory of gravitation that is not based on the least action principle, but on a natural generalization of the original Einstein's field equations. This approach leads to the non-covariant conservation of the stress-energy tensor, a feature shared with other Lagrangian theories of gravity such as the $f(R,T)$ case. We consider the cosmological implications of a pair of particular models within this theory, and we show that they have some interesting properties. In particular, for some of the studied models we find that the density is bounded from above, and cannot exceed a maximum value that depends on certain physical constants. In the last part of the work we compare the theory to the $f(R,T)$ case and show that they lead to different predictions for the motion of test particles.
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Submitted 18 August, 2018; v1 submitted 31 December, 2017;
originally announced January 2018.
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Non-linear energy conservation theorem in the framework of Special Relativity
Authors:
Ginés R. Pérez Teruel
Abstract:
In this work we revisit the study of the gravitational interaction in the context of the Special Theory of Relativity. It is found that, as long as the equivalence principle is respected, a relativistic non-linear energy conservation theorem arises in a natural way. We interpret that this non-linear conservation law stresses the non-linear character of the gravitational interaction.The theorem rep…
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In this work we revisit the study of the gravitational interaction in the context of the Special Theory of Relativity. It is found that, as long as the equivalence principle is respected, a relativistic non-linear energy conservation theorem arises in a natural way. We interpret that this non-linear conservation law stresses the non-linear character of the gravitational interaction.The theorem reproduces the energy conservation theorem of Newtonian mechanics in the corresponding low energy limit, but also allows to derive some standard results of post-Newtonian gravity, such as the formula of the gravitational redshift. Guided by this conservation law, we develop a Lagrangian formalism for a particle in a gravitational field. We realize that the Lagrangian can be written in an explicit covariant fashion, and turns out to be the geodesic Lagrangian of a curved Lorentzian manifold. Therefore, any attempt to describe gravity within the Special Theory, leads outside their own domains towards a curved space-time. Thus, the pedagogical content of the paper may be useful as a starting point to discuss the problem of Gravitation in the context of the Special Theory, as a preliminary step before introducing General Relativity.
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Submitted 3 May, 2015;
originally announced May 2015.
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Implications of nonsymmetric metric theories for particle physics. New interpretation of the Pauli coupling
Authors:
Ginés R. Pérez Teruel
Abstract:
In this work we provide a possible geometrical interpretation of the spin of elementary particles. In particular, it is investigated how the wave equations of matter are altered by the addition of an antisymmetric contribution to the metric tensor. In this scenario the explicit form of the matter wave equations is investigated in a general curved space-time, and then the equations are particulariz…
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In this work we provide a possible geometrical interpretation of the spin of elementary particles. In particular, it is investigated how the wave equations of matter are altered by the addition of an antisymmetric contribution to the metric tensor. In this scenario the explicit form of the matter wave equations is investigated in a general curved space-time, and then the equations are particularized to the flat case. Unlike traditional approaches of NGT, in which the gravitational field is responsible for breaking the symmetry of the flat Minkowski metric, we find more natural to consider that, in general, the metric of the space-time could be nonsymmetric even in the flat case. The physical consequences of this assumption are explored in detail. Interestingly enough, it is found that the metric tensor splits into a bosonic and a fermionic; the antisymmetric part of the metric is very sensitive to the spin and turns out to be undetectable for spinless scalar particles. However, fermions couple to it in a non-trivial way (only when there are interactions). In addition, the Pauli coupling is derived automatically as a consequence of the nonsymmetric nature of the metric
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Submitted 20 June, 2014;
originally announced June 2014.
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Analytic solution of the algebraic equation associated to the Ricci tensor in extended Palatini gravity
Authors:
Ginés R. Pérez Teruel
Abstract:
In this work we discuss the exact solution to the algebraic equation associated to the Ricci tensor in the quadratic $f(R,Q)$ extension of Palatini gravity. We show that an exact solution always exists, and in the general case it can be found by a simple matrix diagonalization. Furthermore, the general implications of the solution are analysed in detail, including the generation of an effective co…
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In this work we discuss the exact solution to the algebraic equation associated to the Ricci tensor in the quadratic $f(R,Q)$ extension of Palatini gravity. We show that an exact solution always exists, and in the general case it can be found by a simple matrix diagonalization. Furthermore, the general implications of the solution are analysed in detail, including the generation of an effective cosmological constant, and the recovery of the $f(R)$ and $f(Q)$ theories as particular cases in their corresponding limit. In addition, it is proposed a power series expansion of the solution which is successfully applied to the case of the electromagnetic field. We show that this power series expansion may be useful to deal perturbatively with some problems in the context of Palatini gravity.
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Submitted 16 July, 2014; v1 submitted 1 October, 2013;
originally announced October 2013.
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An alternative formulation of Classical Mechanics based on an analogy with Thermodynamics
Authors:
Ginés R. Pérez Teruel
Abstract:
We study new Legendre transforms in classical mechanics and investigate some of their general properties. The behaviour of the new functions is analyzed under coordinate transformations.When invariance under different kinds of transformations are considered, the new formulation is found to be completly equivalent to the usual Lagrangian formulation, recovering well established results like the con…
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We study new Legendre transforms in classical mechanics and investigate some of their general properties. The behaviour of the new functions is analyzed under coordinate transformations.When invariance under different kinds of transformations are considered, the new formulation is found to be completly equivalent to the usual Lagrangian formulation, recovering well established results like the conservation of the angular momentum. Furthermore, a natural generalization of the Poisson Bracket is found to be inherent to the formalism introduced. On the other hand, we find that with a convenient redefinition of the Lagrangian, $\mathcal{L}^{\prime}=-\mathcal{L}$, it is possible to establish an exact one-to-one mathematical correspondence between the thermodynamic potentials and the new potentials of classical mechanics
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Submitted 21 September, 2013;
originally announced September 2013.
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Generalized Einstein-Maxwell field equations in the Palatini formalism
Authors:
Ginés R. Pérez Teruel
Abstract:
We derive a new set of field equations within the framework of the Palatini formalism.These equations are a natural generalization of the Einstein-Maxwell equations which arise by adding a function $\mathcal{F}(\mathcal{Q})$, with $\mathcal{Q}\equiv F^{αβ}F_{αβ}$ to the Palatini Lagrangian $f(R,Q)$.The result we obtain can be viewed as the coupling of gravity with a nonlinear extension of the elec…
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We derive a new set of field equations within the framework of the Palatini formalism.These equations are a natural generalization of the Einstein-Maxwell equations which arise by adding a function $\mathcal{F}(\mathcal{Q})$, with $\mathcal{Q}\equiv F^{αβ}F_{αβ}$ to the Palatini Lagrangian $f(R,Q)$.The result we obtain can be viewed as the coupling of gravity with a nonlinear extension of the electromagnetic field.In addition,a new method is introduced to solve the algebraic equation associated to the Ricci tensor.
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Submitted 14 February, 2013; v1 submitted 26 January, 2013;
originally announced January 2013.