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Register a new userInvestigating new forms of gravity-matter couplings in the gravitational field equations
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Added by
Giampiero Esposito Dr.
Publication date
2021
fields
Physics
and research's language is
English
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This paper proposes a toy model where, in the Einstein equations, the right-hand side is modified by the addition of a term proportional to the symmetrized partial contraction of the Ricci tensor with the energy-momentum tensor, while the left-hand side remains equal to the Einstein tensor. Bearing in mind the existence of a natural length scale given by the Planck length, dimensional analysis shows that such a term yields a correction linear in h to the classical term, that is instead just proportional to the energy-momentum tensor. One then obtains an effective energy-momentum tensor that consists of three contributions: pure energy part, mechanical stress and thermal part. The pure energy part has the appropriate property for dealing with the dark sector of modern relativistic cosmology. Such a theory coincides with general relativity in vacuum, and the resulting field equations are here solved for a Dunn and Tupper metric, for departures from an interior Schwarzschild solution as well as for a Friedmann-Lemaitre-Robertson-Walker universe.
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In this paper we analyze the gravitational field of a global monopole in the context of $f(R)$ gravity. More precisely, we show that the field equations obtained are expressed in terms of $F(R)=frac{df(R)}{dR}$. Since we are dealing with a spherically symmetric system, we assume that $F(R)$ is a function of the radial coordinate only. Moreover, adopting the weak field approximation, we can provide all components of the metric tensor. A comparison with the corresponding results obtained in General Relativity and in the Brans-Dicke theory is also made.
We give a self-contained introduction into the metric-affine gauge theory of gravity. Starting from the equivalence of reference frames, the prototype of a gauge theory is presented and illustrated by the example of Yang-Mills theory. Along the same lines we perform a gauging of the affine group and establish the geometry of metric-affine gravity. The results are put into the dynamical framework of a classical field theory. We derive subcases of metric-affine gravity by restricting the affine group to some of its subgroups. The important subcase of general relativity as a gauge theory of translations is explained in detail.
We deal with quadratic metric-affine gravity (QMAG), which is an alternative theory of gravity and present a new explicit representation of the field equations of this theory. In our previous work we found new explicit vacuum solutions of QMAG, namely generalised pp-waves of parallel Ricci curvature with purely tensor torsion. Here we do not make any assumptions on the properties of torsion and write down our field equations accordingly. We present a review of research done thus far by several authors in finding new solutions of QMAG and different approaches in generalising pp-waves. We present two conjectures on the new types of solutions of QMAG which the ansatz presented in this paper will hopefully enable us to prove.
We propose gravitational microlensing as a way of testing the emergent gravity theory recently proposed by Eric Verlinde~cite{Verlinde:2016toy}. We consider two limiting cases: the dark mass of maximally anisotropic pressures (Case I) and of isotropic pressures (Case II). Our analysis of perihelion advancement of a planet shows that only Case I yields a viable theory. In this case the metric outside a star of mass $M_*$ can be modeled by that of a point-like global monopole whose mass is $M_*$ and a deficit angle $Delta = sqrt{(2GH_0M_*)/(3c^3)}$, where $H_0$ is the Hubble rate and $G$ the Newton constant. This deficit angle can be used to test the theory since light exhibits additional bending around stars given by, $alpha_Dapprox -piDelta/2$. This angle is independent on the distance from the star and it affects equally light and massive particles. The effect is too small to be measurable today, but should be within reach of the next generation of high resolution telescopes. Finally we note that the advancement of periastron of a planet orbiting around a star or black hole, which equals $piDelta$ per period, can be also used to test the theory.
Deviations from relativity are tightly constrained by numerous experiments. A class of unmeasured and potentially large violations is presented that can be tested in the laboratory only via weak gravity couplings. Specialized highly sensitive experiments could achieve measurements of the corresponding effects. A single constraint of 1 x 10^{-11} GeV is extracted on one combination of the 12 possible effects in ordinary matter. Estimates are provided for attainable sensitivities in existing and future experiments.
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