The analysis of teleparallel f(T,∇μ1T,…,∇μn⋯∇μ1T) gravity in the Jordan and Einstein frames is presented. The equivalence between f(T,∇μ1T,…,∇μn⋯∇μ1T) gravity and a scalar-multitensor theory is ...proved in both frames for systems with a regular Hessian matrix. For each order of derivative an auxiliary tensor of the same order is introduced. As a consequence, the order of the differential equation for the tetrad field is reduced to an equation of order two, but the price to be paid is the analysis of a system of coupled equations for the auxiliary fields.
Bopp–Podolsky black holes and the no-hair theorem Cuzinatto, R. R.; de Melo, C. A. M.; Medeiros, L. G. ...
The European physical journal. C, Particles and fields,
2018/1, Letnik:
78, Številka:
1
Journal Article
Recenzirano
Odprti dostop
Bopp–Podolsky electrodynamics is generalized to curved space-times. The equations of motion are written for the case of static spherically symmetric black holes and their exterior solutions are ...analyzed using Bekenstein’s method. It is shown that the solutions split up into two parts, namely a non-homogeneous (asymptotically massless) regime and a homogeneous (asymptotically massive) sector which is null outside the event horizon. In addition, in the simplest approach to Bopp–Podolsky black holes, the non-homogeneous solutions are found to be Maxwell’s solutions leading to a Reissner–Nordström black hole. It is also demonstrated that the only exterior solution consistent with the weak and null energy conditions is the Maxwell one. Thus, in the light of the energy conditions, it is concluded that only Maxwell modes propagate outside the horizon and, therefore, the no-hair theorem is satisfied in the case of Bopp–Podolsky fields in spherically symmetric space-times.
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Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
In Cuzinatto et al. Phys. Rev. D 93, 124034 (2016), it has been demonstrated that theories of gravity in which the Lagrangian includes terms depending on the scalar curvature R and its derivatives up ...to order n, i.e., f(R,∇μR,∇μ1∇μ2R,…,∇μ1⋯∇μnR) theories of gravity, are equivalent to scalar-multitensorial theories in the Jordan frame. In particular, in the metric and Palatini formalisms, this scalar-multitensorial equivalent scenario shows a structure that resembles that of the Brans-Dicke theories with a kinetic term for the scalar field with ω0=0 or ω0=−3/2, respectively. In the present work, the aforementioned analysis is extended to the Einstein frame. The conformal transformation of the metric characterizing the transformation from Jordan's to Einstein's frame is responsible for decoupling the scalar field from the scalar curvature and also for introducing a usual kinetic term for the scalar field in the metric formalism. In the Palatini approach, this kinetic term is absent in the action. Concerning the other tensorial auxiliary fields, they appear in the theory through a generalized potential. As an example, the analysis of an extension of the Starobinsky model (with an extra term proportional to ∇μR∇μR) is performed and the fluid representation for the energy-momentum tensor is considered. In the metric formalism, the presence of the extra term causes the fluid to be an imperfect fluid with a heat flux contribution; on the other hand, in the Palatini formalism the effective energy-momentum tensor for the extended Starobinsky gravity is that of a perfect fluid type. Finally, it is also shown that the extra term in the Palatini formalism represents a dynamical field which is able to generate an inflationary regime without a graceful exit.
Neutron stars in modified teleparallel gravity Vilhena, S.G.; Duarte, S.B.; Dutra, M. ...
Journal of cosmology and astroparticle physics,
04/2023, Letnik:
2023, Številka:
4
Journal Article
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Abstract
We investigate compact objects in modified teleparallel gravity with realistic equations
of state. We propose a modification of Teleparallel Equivalent to General Relativity, then an
...appropriate tetrad is applied to the field equations. A specific set of relations showing an
equivalency between our gravitational model and the New General Relativity is found. The
conservation equation implies that our Tolman-Oppenheimer-Volkoff equations are presented with an
effective gravitational coupling constant. Numerical analysis using realistic equations of state
is made, and the behavior of mass, radius, and the relation mass-radius as functions of a free
parameter of our model is also investigated.
An extension of the Starobinsky model is proposed. Besides the usual Starobinsky Lagrangian, a term proportional to the derivative of the scalar curvature, ∇μR∇μR, is considered. The analyzis is done ...in the Einstein frame with the introduction of a scalar field and a vector field. We show that inflation is attainable in our model, allowing for a graceful exit. We also build the cosmological perturbations and obtain the leading-order curvature power spectrum, scalar and tensor tilts and tensor-to-scalar ratio. The tensor and curvature power spectrums are compared to the most recent observations from BICEP2/Keck collaboration. We verify that the scalar-to-tensor rate r can be expected to be up to three times the values predicted by Starobinsky model.
Second-order teleparallel gauge theory Assencio, E M B; Caraça, R S; Vilhena, S G ...
Classical and quantum gravity,
10/2023, Letnik:
40, Številka:
20
Journal Article
Recenzirano
Abstract
In this work, we analyze second-order extensions of teleparallel theories of gravity as gauge theories for the translation group. We use Utiyama’s approach to gauge theories and show that it ...is possible to include second-order derivative terms in the Lagrangian of the gauge potential and preserve gauge invariance. Besides the usual field strength, a new object has to be introduced in order to preserve both gauge and diffeomorphism invariances. From this new object, we obtain a set of fourteen independent invariants which leads to equations that are linear in the fourth derivative of the tetrad field. We analyze a particular example with one of these invariants and evaluate the weak field limit, showing that the effective gravitational potential is a combination of Newton and Yukawa potentials.
Abstract In this work we analyze, in the context of modified teleparallel gravity, the equivalence between scalar-vector-tensor theories and geometrical theories of the type f T , B , ∇ μ T , ∇ μ B , ...where T and B are respectively the scalar torsion and the boundary scalar. This analysis is performed in the Jordan and Einstein frames. In particular, in the latter frame, two distinct cases are analyzed, where the role of surface terms is discussed. The equivalence between the geometrical and the scalar-vector-tensor approaches is verified for regular systems, i.e. for systems that present a regular Hessian matrix. An example is presented and the analysis of the Cauchy problem is made for the different approaches. An extension for systems that include higher-order derivatives of T and B is briefly presented, showing the equivalence between the geometrical and scalar-multi tensor theories.
A massive gauge theory à la Utiyama Cuzinatto, R R; Pimentel, B M; Pompeia, P J ...
Physica scripta,
08/2023, Letnik:
98, Številka:
8
Journal Article
Recenzirano
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Abstract
Utiyama’s method is a deductive approach of building gauge theories for semi-simple groups of local transformations, including the Abelian U(1) case, the non-Abelian SU(N) group, and the ...gravitational interaction. Gauge theories
à la
Utiyama typically predict a massless gauge potential. This work brings a mass generation mechanism and Utiyama’s method together thus giving mass to the interaction boson without breaking the gauge symmetry. Herein we devote our attention to the Abelian case. Two gauge potentials are introduced: a vetor field
A
μ
and a scalar field
B
. The associated gauge-invariant field strengths
F
μ
ν
and
G
μ
are built from Utiyama’s technique. Gauge invariance requirement upon the total Lagrangian (including matter fields and gauge fields) yields the conserved currents. Finally, we study the simplest type of Lagrangian involving the field strengths and obtain the related field equation. By imposing appropriate constraints on this particular example, Stueckelberg model is recovered.
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