Exact Spherically Symmetric Solutions in Modified Teleparallel Gravity

Bahamonde, Sebastián; Camcı, Uğur

doi:10.3390/sym11121462

“…The latter theories have been studied in particular detail in regard on their consequences in cosmology [22,[24][25][26][27] and astrophysics [28][29][30], as well as their degrees of freedom [31,32]. Further generalizations have also been considered in the literature, including ones explicitly involving the boundary term in f (T, B)-gravity [33], or, involving three terms, T ax , T vec , T ten ; these are a specific decomposition of the torsion scalar T, which feature in so-called f (T ax , T vec , T ten )-gravity [34].…”

Section: Introductionmentioning

confidence: 99%

Static Spherically Symmetric Black Holes in Weak f(T)-Gravity

Pfeifer

¹

,

Schuster

²

2021

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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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“…We have to introduce both boundary term B = 2∇ μ (T μ ), depending on the derivatives of the torsion vector T μ and terms like T , k T in the teleparallel Lagrangian [8,9]. We can therefore start from f (R) gravity, and find its teleparallel equivalent after observing that the boundary term is B = −T − R and then restore the f (T, B) gravity [10]. The teleparallel theory of gravity f (T, B) is the teleparallel equivalent of f (R) as the TEGR is the teleparallel equivalent of GR as we will show below by considering the weak field limit and the gravitational wave modes.…”

Section: Introductionmentioning

confidence: 99%

Weak field limit and gravitational waves in f(T, B) teleparallel gravity

Capozziello

¹

,

Capriolo

²

,

Caso

³

2020

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We derive the gravitational waves for f (T, B) gravity which is an extension of teleparallel gravity and demonstrate that it is equivalent to f (R) gravity by linearized the field equations in the weak field limit approximation. f (T, B) gravity shows three polarizations: the two standard of general relativity, plus and cross, which are purely transverse with two-helicity, massless tensor polarization modes, and an additional massive scalar mode with zero-helicity. The last one is a mix of longitudinal and transverse breathing scalar polarization modes. The boundary term B excites the extra scalar polarization and the mass of scalar field breaks the symmetry of the TT gauge by adding a new degree of freedom, namely a single mixed scalar polarization.

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“…In the context of f (G, T ) gravity, where G represents the Gauss-Bonnet term and T is the energy-momentum tensor trace, Shamir and Ahmad [62,63] have applied Noether symmetries approach to explore some exact cosmologically viable solutions using both isotropic and anisotropic geometries. Bahamonde and Capozziello [64,65] have adopted the Noether symmetry approach to study the related dynamical systems and to find cosmological solutions using FRW and static spherically symmetric metrics. In another study, Fazlollahi [66] have discussed the behavior of effective EoS parameter for the obtained cosmology by exploring existence of Noether gauge symmetries in f (R) theory.…”

Section: Introductionmentioning

confidence: 99%

Isotropic exact solutions in $$F(R,Y,\phi )$$ gravity via Noether symmetries

Waheed

¹

,

Nawazish

²

,

Zubair

³

2021

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The present article investigates the existence of Noether and Noether gauge symmetries of flat Friedman–Robertson–Walker universe model with perfect fluid matter ingredients in a generalized scalar field formulation namely $$f(R,Y,\phi )$$ f ( R , Y , ϕ ) gravity, where R is the Ricci scalar and Y denotes the curvature invariant term defined by $$Y=R_{\alpha \beta }R^{\alpha \beta }$$ Y = R α β R α β , while $$\phi $$ ϕ represents scalar field. For this purpose, we assume different general cases of generic $$f(R,Y,\phi )$$ f ( R , Y , ϕ ) function and explore its possible forms along with field potential $$V(\phi )$$ V ( ϕ ) by taking constant and variable coupling function of scalar field $$\omega (\phi )$$ ω ( ϕ ) . In each case, we find non-trivial symmetry generator and its related first integrals of motion (conserved quantities). It is seen that due to complexity of the resulting system of Lagrange dynamical equations, it is difficult to find exact cosmological solutions except for few simple cases. It is found that in each case, the existence of Noether symmetries leads to power law form of scalar field potential and different new types of generic function. For the acquired exact solutions, we discuss the cosmology generated by these solutions graphically and discuss their physical significance which favors the accelerated expanding eras of cosmic evolution.

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Exact Spherically Symmetric Solutions in Modified Teleparallel Gravity

Cited by 49 publications

References 87 publications

Static Spherically Symmetric Black Holes in Weak f(T)-Gravity

Static Spherically Symmetric Black Holes in Weak f(T)-Gravity

Weak field limit and gravitational waves in f(T, B) teleparallel gravity

Isotropic exact solutions in $$F(R,Y,\phi )$$ gravity via Noether symmetries

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