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.
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, L ′ = −L, it is possible to establish an exact one-toone mathematical correspondence between the thermodynamic potentials and the new potentials of classical mechanics PACS numbers:
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 [Formula: see text], with [Formula: see text] 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.
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
In this paper, we present the first interior solutions representing compact stars in [Formula: see text] 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 [Formula: see text]. Once arrived at the reduced field equations, we investigate two solutions with [Formula: see text] and [Formula: see text], where [Formula: see text] denotes here another constant that should not be confused with the speed of light. Then, we investigate each solution by determining the thermodynamics variable 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 [Formula: see text] 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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