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Manuel Hohmann - One of the best experts on this subject based on the ideXlab platform.
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Post-Newtonian Limit of Teleparallel Horndeski gravity
arXiv: General Relativity and Quantum Cosmology, 2020Co-Authors: Sebastian Bahamonde, Manuel Hohmann, Konstantinos F. Dialektopoulos, Jackson Levi SaidAbstract:We consider the newly proposed Bahamonde-Dialektopoulos-Levi Said (BDLS) theory, that is the Horndeski analog in the teleparallel framework and thus contains a non-minimally coupled scalar field, including higher order derivatives, that leads however to second order field equations both for the tetrad and the scalar field. This theory was mostly constructed to revive those models that were severely constrained in the scalar-tensor version of the theory from the GW170817, but includes also much richer phenomenology because of the nature of the torsion tensor. For this theory we determine the parametrized post-Newtonian Limit, calculate the full set of post-Newtonian parameters and highlight some special cases.
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Post-Newtonian Limit of scalar-torsion theories of gravity as analogue to scalar-curvature theories
Physical Review D, 2020Co-Authors: Elena Dmitrievna Emtsova, Manuel HohmannAbstract:We consider a recently proposed class of extended teleparallel theories of gravity, which entail a scalar field which is non-minimally coupled to the torsion of a flat, metric-compatible connection. This class of scalar-torsion theories of gravity is constructed in analogy to and as a direct extension of the well-studied class of scalar-curvature gravity theories, and has various common features, such as the conformal frame freedom. For this class we determine the parametrized post-Newtonian Limit, both for a massive and a massless scalar field. In the massive case, we determine the effective gravitational constant and the post-Newtonian parameter $\gamma$, both of which depend on the distance between the gravitating and test masses. In the massless case, we calculate the full set of parameters and find that only $\gamma$ and $\beta$ potentially deviate from their general relativity values. In particular, we find that for a minimally coupled scalar field the theory becomes indistinguishable from general relativity at this level of the post-Newtonian approximation.
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Post-Newtonian Limit of generalized scalar-torsion theories of gravity
Physical Review D, 2020Co-Authors: Kai Flathmann, Manuel HohmannAbstract:In this article we derive the post-Newtonian Limit of a class of teleparallel theories of gravity, where the action is a free function $L(T,X,Y,\phi)$ of the Torsion scalar $T$ and scalar quantities $X$ and $Y$ built from the dynamical scalar field $\phi$. We restrict the analysis to a massless scalar field in order to use the parameterized post-Newtonian formalism without modifications, such as introducing an effective gravitational constant which depends on the distance between the interacting masses. In particular the results show a class of fully-conservative theories of gravity, where the only non-vanishing parameters are $\gamma$ and $\beta$. For a particular choice of the function $L(T,X,Y,\phi)$ the theory cannot be distinguished from General Relativity in its post-Newtonian approximation.
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Parametrized post-Newtonian Limit of general teleparallel gravity theories
Physical Review D, 2019Co-Authors: Ulbossyn Ualikhanova, Manuel HohmannAbstract:We derive the post-Newtonian Limit of a general class of teleparallel gravity theories, whose action is given by a free function of three scalar quantities obtained from the torsion of the teleparallel connection. This class of theories is chosen to be sufficiently generic in order to include the $f(T)$ class of theories as well as new general relativity as subclasses. To derive its post-Newtonian Limit, we first impose the Weitzenb\"ock gauge, and then introduce a post-Newtonian approximation of the tetrad field around a Minkowski background solution. Our results show that the class of theories we consider is fully conservative, with only the parameters $\beta$ and $\gamma$ potentially deviating from their general relativity values. In particular, we find that the post-Newtonian Limit of any $f(T)$ theory is identical to that of general relativity, so that these theories cannot be distinguished by measurements of the post-Newtonian parameters alone.
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Parametrized post-Newtonian Limit of Horndeski’s gravity theory
Physical Review D, 2015Co-Authors: Manuel HohmannAbstract:We discuss the parameterized post-Newtonian (PPN) Limit of Horndeski's theory of gravity, also known under the name generalized G-inflation or $\text{G}^2$-inflation, which is the most general scalar-tensor theory of gravity with at most second order field equations in four dimensions. We derive conditions on the action for the validity of the post-Newtonian Limit. For the most general class of theories consistent with these conditions we calculate the PPN parameters $\gamma(r)$ and $\beta(r)$, which in general depend on the interaction distance $r$ between the gravitating mass and the test mass. For a more restricted class of theories, in which the scalar field is massless, we calculate the full set of PPN parameters. It turns out that in this restricted case all parameters are constants and that the only parameters potentially deviating from observations are $\gamma$ and $\beta$. We finally apply our results to a number of example theories, including galileons and different models of Higgs inflation.
Salvatore Capozziello - One of the best experts on this subject based on the ideXlab platform.
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Comparing scalar-tensor gravity and f(R)-gravity in the Newtonian Limit
Physics Letters B, 2010Co-Authors: Salvatore Capozziello, Arturo Stabile, A TroisiAbstract:Abstract Recently, a strong debate has been pursued about the Newtonian Limit (i.e. small velocity and weak field) of fourth order gravity models. According to some authors, the Newtonian Limit of f ( R ) -gravity is equivalent to the one of Brans–Dicke gravity with ω BD = 0 , so that the PPN parameters of these models turn out to be ill-defined. In this Letter, we carefully discuss this point considering that fourth order gravity models are dynamically equivalent to the O'Hanlon Lagrangian. This is a special case of scalar–tensor gravity characterized only by self-interaction potential and that, in the Newtonian Limit, this implies a non-standard behavior that cannot be compared with the usual PPN Limit of General Relativity. The result turns out to be completely different from the one of Brans–Dicke theory and in particular suggests that it is misleading to consider the PPN parameters of this theory with ω BD = 0 in order to characterize the homologous quantities of f ( R ) -gravity. Finally the solutions at Newtonian level, obtained in the Jordan frame for an f ( R ) -gravity, reinterpreted as a scalar–tensor theory, are linked to those in the Einstein frame.
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The Newtonian Limit of metric gravity theories with quadratic Lagrangians
Classical and Quantum Gravity, 2009Co-Authors: Salvatore Capozziello, Arturo StabileAbstract:The Newtonian Limit of fourth-order gravity is worked out discussing its viability with respect to the standard results of general relativity. We investigate the Limit in the metric approach which, with respect to the Palatini formulation, has been much less studied in the recent literature, due to the higher order of the field equations. In addition, we refrain from exploiting the formal equivalence of higher-order theories considering the analogy with specific scalar–tensor theories, i.e. we work in the so-called Jordan frame in order to avoid possible misleading interpretations of the results. Explicit solutions are provided for several different types of Lagrangians containing powers of the Ricci scalar as well as combinations of the other curvature invariants. In particular, we develop the Green's function method for fourth-order theories in order to find out solutions. Finally, the consistency of the results with respect to general relativity is discussed.
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Newtonian Limit of f r gravity
Physical Review D, 2007Co-Authors: Salvatore Capozziello, Arturo Stabile, A TroisiAbstract:A general analytic procedure is developed to deal with the Newtonian Limit of f(R) gravity. A discussion comparing the Newtonian and the post-Newtonian Limit of these models is proposed in order to point out the differences between the two approaches. We calculate the post-Newtonian parameters of such theories without any redefinition of the degrees of freedom, in particular, without adopting some scalar fields and without any change from Jordan to Einstein frame. Considering the Taylor expansion of a generic f(R) theory, it is possible to obtain general solutions in terms of the metric coefficients up to the third order of approximation. In particular, the solution relative to the g{sub tt} component gives a gravitational potential always corrected with respect to the Newtonian one of the linear theory f(R)=R. Furthermore, we show that the Birkhoff theorem is not a general result for f(R) gravity since time-dependent evolution for spherically symmetric solutions can be achieved depending on the order of perturbations. Finally, we discuss the post-Minkowskian Limit and the emergence of massive gravitational wave solutions.
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The Newtonian Limit of F(R) gravity
Physical Review D, 2007Co-Authors: Salvatore Capozziello, Arturo Stabile, A TroisiAbstract:A general analytic procedure is developed to deal with the Newtonian Limit of $f(R)$ gravity. A discussion comparing the Newtonian and the post-Newtonian Limit of these models is proposed in order to point out the differences between the two approaches. We calculate the post-Newtonian parameters of such theories without any redefinition of the degrees of freedom, in particular, without adopting some scalar fields and without any change from Jordan to Einstein frame. Considering the Taylor expansion of a generic $f(R)$ theory, it is possible to obtain general solutions in term of the metric coefficients up to the third order of approximation. In particular, the solution relative to the $g_{tt}$ component gives a gravitational potential always corrected with respect to the Newtonian one of the linear theory $f(R)=R$. Furthermore, we show that the Birkhoff theorem is not a general result for $f(R)$-gravity since time-dependent evolution for spherically symmetric solutions can be achieved depending on the order of perturbations. Finally, we discuss the post-Minkowskian Limit and the emergence of massive gravitational wave solutions.
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Newtonian Limit of Extended Theories of Gravity
arXiv: General Relativity and Quantum Cosmology, 2004Co-Authors: Salvatore CapozzielloAbstract:Newtonian Limit of Extended Theories of Gravity (in particular, higher--order and scalar--tensor theories) is theoretically discussed taking into account recent observational and experimental results.
Hohmann Manuel - One of the best experts on this subject based on the ideXlab platform.
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Post-Newtonian Limit of Teleparallel Horndeski gravity
2020Co-Authors: Bahamonde Sebastian, Dialektopoulos, Konstantinos F., Hohmann Manuel, Said, Jackson LeviAbstract:We consider the newly proposed Bahamonde-Dialektopoulos-Levi Said (BDLS) theory, that is the Horndeski analog in the teleparallel framework and thus contains a non-minimally coupled scalar field, including higher order derivatives, that leads however to second order field equations both for the tetrad and the scalar field. This theory was mostly constructed to revive those models that were severely constrained in the scalar-tensor version of the theory from the GW170817, but includes also much richer phenomenology because of the nature of the torsion tensor. For this theory we determine the parametrized post-Newtonian Limit, calculate the full set of post-Newtonian parameters and highlight some special cases.Comment: LaTeX, 22 pages, no figure
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Post-Newtonian Limit of generalized scalar-torsion theories of gravity
'American Physical Society (APS)', 2020Co-Authors: Flathmann Kai, Hohmann ManuelAbstract:In this article we derive the post-Newtonian Limit of a class of teleparallel theories of gravity, where the action is a free function $L(T,X,Y,\phi)$ of the Torsion scalar $T$ and scalar quantities $X$ and $Y$ built from the dynamical scalar field $\phi$. We restrict the analysis to a massless scalar field in order to use the parameterized post-Newtonian formalism without modifications, such as introducing an effective gravitational constant which depends on the distance between the interacting masses. In particular the results show a class of fully-conservative theories of gravity, where the only non-vanishing parameters are $\gamma$ and $\beta$. For a particular choice of the function $L(T,X,Y,\phi)$ the theory cannot be distinguished from General Relativity in its post-Newtonian approximation.Comment: LaTeX, 10 pages, no figures; corrected matter action; published version, references updated. arXiv admin note: text overlap with arXiv:1909.0935
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Post-Newtonian Limit of scalar-torsion theories of gravity as analogue to scalar-curvature theories
'American Physical Society (APS)', 2020Co-Authors: Emtsova, Elena D., Hohmann ManuelAbstract:We consider a recently proposed class of extended teleparallel theories of gravity, which entail a scalar field which is non-minimally coupled to the torsion of a flat, metric-compatible connection. This class of scalar-torsion theories of gravity is constructed in analogy to and as a direct extension of the well-studied class of scalar-curvature gravity theories, and has various common features, such as the conformal frame freedom. For this class we determine the parametrized post-Newtonian Limit, both for a massive and a massless scalar field. In the massive case, we determine the effective gravitational constant and the post-Newtonian parameter $\gamma$, both of which depend on the distance between the gravitating and test masses. In the massless case, we calculate the full set of parameters and find that only $\gamma$ and $\beta$ potentially deviate from their general relativity values. In particular, we find that for a minimally coupled scalar field the theory becomes indistinguishable from general relativity at this level of the post-Newtonian approximation.Comment: LaTeX, 17 pages, no figures; published version, references update
A Troisi - One of the best experts on this subject based on the ideXlab platform.
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Comparing scalar-tensor gravity and f(R)-gravity in the Newtonian Limit
Physics Letters B, 2010Co-Authors: Salvatore Capozziello, Arturo Stabile, A TroisiAbstract:Abstract Recently, a strong debate has been pursued about the Newtonian Limit (i.e. small velocity and weak field) of fourth order gravity models. According to some authors, the Newtonian Limit of f ( R ) -gravity is equivalent to the one of Brans–Dicke gravity with ω BD = 0 , so that the PPN parameters of these models turn out to be ill-defined. In this Letter, we carefully discuss this point considering that fourth order gravity models are dynamically equivalent to the O'Hanlon Lagrangian. This is a special case of scalar–tensor gravity characterized only by self-interaction potential and that, in the Newtonian Limit, this implies a non-standard behavior that cannot be compared with the usual PPN Limit of General Relativity. The result turns out to be completely different from the one of Brans–Dicke theory and in particular suggests that it is misleading to consider the PPN parameters of this theory with ω BD = 0 in order to characterize the homologous quantities of f ( R ) -gravity. Finally the solutions at Newtonian level, obtained in the Jordan frame for an f ( R ) -gravity, reinterpreted as a scalar–tensor theory, are linked to those in the Einstein frame.
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Newtonian Limit of f r gravity
Physical Review D, 2007Co-Authors: Salvatore Capozziello, Arturo Stabile, A TroisiAbstract:A general analytic procedure is developed to deal with the Newtonian Limit of f(R) gravity. A discussion comparing the Newtonian and the post-Newtonian Limit of these models is proposed in order to point out the differences between the two approaches. We calculate the post-Newtonian parameters of such theories without any redefinition of the degrees of freedom, in particular, without adopting some scalar fields and without any change from Jordan to Einstein frame. Considering the Taylor expansion of a generic f(R) theory, it is possible to obtain general solutions in terms of the metric coefficients up to the third order of approximation. In particular, the solution relative to the g{sub tt} component gives a gravitational potential always corrected with respect to the Newtonian one of the linear theory f(R)=R. Furthermore, we show that the Birkhoff theorem is not a general result for f(R) gravity since time-dependent evolution for spherically symmetric solutions can be achieved depending on the order of perturbations. Finally, we discuss the post-Minkowskian Limit and the emergence of massive gravitational wave solutions.
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The Newtonian Limit of F(R) gravity
Physical Review D, 2007Co-Authors: Salvatore Capozziello, Arturo Stabile, A TroisiAbstract:A general analytic procedure is developed to deal with the Newtonian Limit of $f(R)$ gravity. A discussion comparing the Newtonian and the post-Newtonian Limit of these models is proposed in order to point out the differences between the two approaches. We calculate the post-Newtonian parameters of such theories without any redefinition of the degrees of freedom, in particular, without adopting some scalar fields and without any change from Jordan to Einstein frame. Considering the Taylor expansion of a generic $f(R)$ theory, it is possible to obtain general solutions in term of the metric coefficients up to the third order of approximation. In particular, the solution relative to the $g_{tt}$ component gives a gravitational potential always corrected with respect to the Newtonian one of the linear theory $f(R)=R$. Furthermore, we show that the Birkhoff theorem is not a general result for $f(R)$-gravity since time-dependent evolution for spherically symmetric solutions can be achieved depending on the order of perturbations. Finally, we discuss the post-Minkowskian Limit and the emergence of massive gravitational wave solutions.
Raafat Talhouk - One of the best experts on this subject based on the ideXlab platform.
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Newtonian Limit for weakly viscoelastic fluid flows of Olroyds' type
arXiv: Analysis of PDEs, 2008Co-Authors: Luc Molinet, Raafat TalhoukAbstract:This paper is concerned with regular flows of incompressible weakly viscoelastic fluids which obey a differential constitutive law of Oldroyd type. We study the Newtonian Limit for weakly viscoelastic fluid flows in $\R^N$ or $\T^N$ for $N=2, 3$, when the Weissenberg number (relaxation time measuring the elasticity effect in the fluid) tends to zero. More precisely, we prove that the velocity field and the extra-stress tensor converge in their existence spaces (we examine the Sobolev-$H^s$ theory and the Besov-$B^{s,1}_2$ theory to reach the critical case $s= N/2$) to the corresponding Newtonian quantities. These convergence results are established in the case of "ill-prepared"' data.We deduce, in the two-dimensional case, a new result concerning the global existence of weakly viscoelastic fluids flow. Our approach makes use of essentially two ingredients : the stability of the null solution of the viscoelastic fluids flow and the damping effect,on the difference between the extra-stress tensor and the tensor of rate of deformation, induced by the constitutive law of the fluid.
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Newtonian Limit for Weakly Viscoelastic Fluid Flows of Oldroyd Type
SIAM Journal on Mathematical Analysis, 2008Co-Authors: Luc Molinet, Raafat TalhoukAbstract:This paper is concerned with regular flows of incompressible weakly viscoelastic fluids which obey a differential constitutive law of Oldroyd type. We study the Newtonian Limit for weakly viscoelastic fluid flows in $\Bbb {R}^N$ or $\Bbb{T}^N$ for $N=2, 3$, when the Weissenberg number (relaxation time measuring the elasticity effect in the fluid) tends to zero. More precisely, we prove that the velocity field and the extrastress tensor converge in their existence spaces (we examine the Sobolev-$H^s$ theory and the Besov-$B^{s,1}_2$ theory to reach the critical case $s= N/2$) to the corresponding Newtonian quantities. This convergence results are established in the case of “ill-prepared" data. We deduce, in the two-dimensional case, a new result concerning the global existence of weakly viscoelastic fluid flow. Our approach makes use of essentially two ingredients: the stability of the null solution of the viscoelastic fluid flow and the damping effect, on the difference between the extrastress tensor and ...