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Register a new userThe first non-static inhomogeneous exact solution in $f(T,B)$ gravity
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Sebasti\\'an N\\'ajera Valencia
Publication date
2021
fields
Physics
and research's language is
English
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We examine in this paper the possibility of finding exact solutions for Teleparallel Gravity (TG) of the type of spherically symmetric Lema^i tre-Tolman-Bondi (LTB) dust models. We apply to the LTB metric, as obtained from the Schwarzschild solution in General Relativity, the formalism of Teleparallel Gravity in its extension to $f(T,B)$ models. An exact LTB solution is obtained that is compatible with a specific $f(T,B)$ model that seems to be appropriate to fit observations when applied to standard spatially flat Robertson-Walker geometry.
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We analyse the vacuum static spherically symmetric space-time for a specific class of non-conservative theories of gravity based on the Rastalls theory. We obtain a new vacuum solution which has the same structure as the Schwarzschild-de Sitter solution in the General Relativity theory obtained with a cosmological constant playing the r^ole of source. We further discuss the structure (in particular, the coupling to matter fields) and some cosmological aspects of the underline non-conservative theory
The article presents modeling of inflationary scenarios for the first time in the $f(R,T)$ theory of gravity. We assume the $f(R,T)$ functional from to be $R + eta T$, where $R$ denotes the Ricci scalar, $T$ the trace of the energy-momentum tensor and $eta$ the model parameter (constant). We first investigated an inflationary scenario where the inflation is driven purely due to geometric effects outside of GR. We found the inflation observables to be independent of the number of e-foldings in this setup. The computed value of the spectral index is consistent with latest Planck 2018 dataset while the scalar to tensor ratio is a bit higher. We then proceeded to analyze the behavior of an inflation driven by $f(R,T)$ gravity coupled with a real scalar field. By taking the slow-roll approximation, we generated interesting scenarios where a Klein Gordon potential leads to observationally consistent inflation observables. Our results makes it clear-cut that in addition to the Ricci scalar and scalar fields, the trace of energy momentum tensor also play a major role in driving inflationary scenarios.
The evolution of the configurational entropy of the universe relies on the growth rate of density fluctuations and on the Hubble parameter. In this work, I present the evolution of configurational entropy for the power-law $f(T)$ gravity model of the form $f(T) = zeta (-T)^ b$, where, $zeta = (6 H_{0}^{2})^{(1-s)}frac{Omega_{P_{0}}}{2 s -1}$ and $b$ a free parameter. From the analysis, I report that the configurational entropy in $f(T)$ gravity is negative and decreases with increasing scale factor and therefore consistent with an accelerating universe. The decrease in configurational entropy is the highest when $b$ vanishes since the effect of dark energy is maximum when $b=0$. Additionally, I find that as the parameter $b$ increases, the growth rate, growing mode, and the matter density parameter evolve slowly whereas the Hubble parameter evolves rapidly. The rapid evolution of the Hubble parameter in conjunction with the growth rate for the $b=0$ may provide an explanation for the large dissipation of configurational entropy.
[Abridged] In its standard formulation, the $f(T)$ field equations are not invariant under local Lorentz transformations, and thus the theory does not inherit the causal structure of special relativity. A locally Lorentz covariant $f(T)$ gravity theory has been devised recently, and this local causality problem has been overcome. The nonlocal question, however, is left open. If gravitation is to be described by this covariant $f(T)$ gravity theory there are a number of issues that ought to be examined in its context, including the question as to whether its field equations allow homogeneous Godel-type solutions, which necessarily leads to violation of causality on nonlocal scale. Here, to look into the potentialities and difficulties of the covariant $f(T)$ theories, we examine whether they admit Godel-type solutions. We take a combination of a perfect fluid with electromagnetic plus a scalar field as source, and determine a general Godel-type solution, which contains special solutions in which the essential parameter of Godel-type geometries, $m^2$, defines any class of homogeneous Godel-type geometries. We extended to the context of covariant $f(T)$ gravity a theorem, which ensures that any perfect-fluid homogeneous Godel-type solution defines the same set of Godel tetrads $h_A^{~mu}$ up to a Lorentz transformation. We also shown that the single massless scalar field generates Godel-type solution with no closed timelike curves. Even though the covariant $f(T)$ gravity restores Lorentz covariance of the field equations and the local validity of the causality principle, the bare existence of the Godel-type solutions makes apparent that the covariant formulation of $f(T)$ gravity does not preclude non-local violation of causality in the form of closed timelike curves.
With the advent of gravitational wave astronomy and first pictures of the shadow of the central black hole of our milky way, theoretical analyses of black holes (and compact objects mimicking them sufficiently closely) have become more important than ever. The near future promises more and more detailed information about the observable black holes and black hole candidates. This information could lead to important advances on constraints on or evidence for modifications of general relativity. More precisely, we are studying the influence of weak teleparallel perturbations on general relativistic vacuum spacetime geometries in spherical symmetry. We find the most general family of spherically symmetric, static vacuum solutions of the theory, which are candidates for describing teleparallel black holes which emerge as perturbations to the Schwarzschild black hole. We compare our findings to results on black hole or static, spherically symmetric solutions in teleparallel gravity discussed in the literature, by comparing the predictions for classical observables such as the photon sphere, the perihelion shift, the light deflection, and the Shapiro delay. On the basis of these observables, we demonstrate that among the solutions we found, there exist spacetime geometries that lead to much weaker bounds on teleparallel gravity than those found earlier. Finally, we move on to a discussion of how the teleparallel perturbations influence the Hawking evaporation in these spacetimes.
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