Showing papers on "Scalar curvature published in 2022"
TL;DR: In this paper , it was shown that if an η \eta -Einstein para-Kenmotsu manifold admits a conformal Ricci almost soliton and the Reeb vector field leaves the scalar curvature invariant then it is Einstein.
Abstract: Abstract We prove that if an η \eta -Einstein para-Kenmotsu manifold admits a conformal η \eta -Ricci soliton then it is Einstein. Next, we proved that a para-Kenmotsu metric as a conformal η \eta -Ricci soliton is Einstein if its potential vector field V V is infinitesimal paracontact transformation or collinear with the Reeb vector field. Furthermore, we prove that if a para-Kenmotsu manifold admits a gradient conformal η \eta -Ricci almost soliton and the Reeb vector field leaves the scalar curvature invariant then it is Einstein. We also construct an example of para-Kenmotsu manifold that admits conformal η \eta -Ricci soliton and satisfy our results. We also have studied conformal η \eta -Ricci soliton in three-dimensional para-cosymplectic manifolds.
20 citations
TL;DR: In this article , the consequences of extra curvature terms mediated from f(R, T, Q) theory on the formation of scalar functions and their importance in the study of populations who are crowded with regular relativistic objects are explored.
Abstract: The aim of this paper is to explore the consequences of extra curvature terms mediated from f(R, T, Q) (where Q ≡ R μ ν T μ ν ) theory on the formation of scalar functions and their importance in the study of populations who are crowded with regular relativistic objects. For this purpose, we model our system comprising of non-rotating spherical geometry formed due to gravitation of locally anisotropic and radiating sources. After considering a particular f(R, T, Q) model, we form a peculiar relation among Misner-Sharp mass, tidal forces, and matter variables. Through structure scalars, we have modeled shear, Weyl, and expansion evolutions equations. The investigation for the causes of the irregular distribution of energy density is also performed with and without constant curvature conditions. It is deduced that our computed one of the f(R, T, Q) structure scalars (Y T ) has a vital role to play in understanding celestial mechanisms in which gravitational interactions cause singularities to emerge.
18 citations
TL;DR: In this article , the behavior of charged compact stars in the modified f(R,ϕ) theory of gravity was investigated, where R and ϕ denote the Ricci scalar and scalar field respectively.
16 citations
TL;DR: In this article , Chen's inequalities involving Chen's δ-invariant δM, Ricci curvature, Riemannian invariant Θk(2≤k≤m), the scalar curvature and the squared of the mean curvature for submanifolds of generalized Sasakian-space-forms endowed with a quarter-symmetric connection are derived.
Abstract: In this article, we derive Chen’s inequalities involving Chen’s δ-invariant δM, Riemannian invariant δ(m1,⋯,mk), Ricci curvature, Riemannian invariant Θk(2≤k≤m), the scalar curvature and the squared of the mean curvature for submanifolds of generalized Sasakian-space-forms endowed with a quarter-symmetric connection. As an application of the obtain inequality, we first derived the Chen inequality for the bi-slant submanifold of generalized Sasakian-space-forms.
16 citations
TL;DR: In this paper , the Ricci scalar at the center of a compact star is chosen such that it satisfies the asymptotic flatness requirement, and the authors study the hydrostatic equilibrium structure of compact stars with the inclusion of anisotropic pressure.
Abstract:
Within the metric formalism of $f(R)$ theories of gravity, where $R$ is the Ricci scalar, we study the hydrostatic equilibrium structure of compact stars with the inclusion of anisotropic pressure. In particular, we focus on the $f(R)= R^{1+\epsilon}$ model and we examine small deviations from General Relativity (GR) for $\vert \epsilon \vert \ll 1$. A suitable definition of mass function is explicitly formulated from the field equations and the value of the Ricci scalar at the center of each star is chosen such that it satisfies the asymptotic flatness requirement. We find that both the mass and the radius of a compact star are larger with respect to the general relativistic counterpart. Furthermore, we remark that the substantial changes due to anisotropy occur mainly in the high-central-density region.
14 citations
TL;DR: In this article , the Ricci scalar at the center of a compact star is chosen such that it satisfies the asymptotic flatness requirement, and a suitable definition of mass function is explicitly formulated from the field equations.
Abstract: Within the metric formalism of f(R) theories of gravity, where R is the Ricci scalar, we study the hydrostatic equilibrium structure of compact stars with the inclusion of anisotropic pressure. In particular, we focus on the f(R) = R 1+ϵ model and we examine small deviations from general relativity for |ϵ| ≪ 1. A suitable definition of mass function is explicitly formulated from the field equations and the value of the Ricci scalar at the center of each star is chosen such that it satisfies the asymptotic flatness requirement. We find that both the mass and the radius of a compact star are larger with respect to the general relativistic counterpart. Furthermore, we remark that the substantial changes due to anisotropy occur mainly in the high-central-density region.
14 citations
11 Mar 2022
TL;DR: In this paper , the authors used reconstruction methods to obtain cosmological solutions in the recently developed scalar-tensor representation of gravity in the Friedmann-Lema (FLRW) universe, where the energy density, the pressure, and the scalar field associated with the arbitrary dependency of the action in gravity can be expressed as functions of the scale factor.
Abstract: In this work, we use reconstruction methods to obtain cosmological solutions in the recently developed scalar-tensor representation of $f(R,T)$ gravity. Assuming that matter is described by an isotropic perfect fluid and the spacetime is homogeneous and isotropic, i.e., the Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) universe, the energy density, the pressure, and the scalar field associated with the arbitrary dependency of the action in $T$ can be written generally as functions of the scale factor. We then select three particular forms of the scale factor: an exponential expansion with $a(t)\ensuremath{\propto}{e}^{t}$ (motivated by the de Sitter solution); and two types of power-law expansion with $a(t)\ensuremath{\propto}{t}^{1/2}$ and $a(t)\ensuremath{\propto}{t}^{2/3}$ (motivated by the behaviors of radiation- and matter-dominated universes in general relativity, respectively). A complete analysis for different curvature parameters $k={\ensuremath{-}1,0,1}$ and equation of state parameters $w={\ensuremath{-}1,0,1/3}$ is provided. Finally, the explicit forms of the functions $f(R,T)$ associated with the scalar-field potentials of the representation used are deduced.
13 citations
13 citations
TL;DR: In this paper , the authors consider slow-roll inflationary models in a class of modified theories of gravity which contains non-minimal curvature-inflaton couplings, i.e., the f(R,T) gravity, where R is the Ricci scalar and T is the trace of the inflaton energymomentum tensor.
11 citations
TL;DR: It is proved that by imposing that the metric functions are the reciprocal of each other (grr = 1/gtt ), the f(Q) gravity theory reduces to the symmetric teleparallel equivalent of general relativity (plus a cosmological constant), and the metric takes the (Anti)de-Sitter-Schwarzschild form.
Abstract: Symmetric teleparallel gravity is constructed with a nonzero nonmetricity tensor while both torsion and curvature are vanishing. In this framework, we find exact scalarised spherically symmetric static solutions in scalar-tensor theories built with a nonminimal coupling between the nonmetricity scalar and a scalar field. It turns out that the Bocharova-Bronnikov-Melnikov-Bekenstein solution has a symmetric teleparallel analogue (in addition to the recently found metric teleparallel analogue), while some other of these solutions describe scalarised black hole configurations that are not known in the Riemannian or metric teleparallel scalar-tensor case. To aid the analysis we also derive no-hair theorems for the theory. Since the symmetric teleparallel scalar-tensor models also include f(Q) gravity, we shortly discuss this case and further prove a theorem which says that by imposing that the metric functions are the reciprocal of each other (grr = 1/gtt ), the f(Q) gravity theory reduces to the symmetric teleparallel equivalent of general relativity (plus a cosmological constant), and the metric takes the (Anti)de-Sitter-Schwarzschild form.
10 citations
TL;DR: In this article , a compact star in the general F(R) gravity was investigated, and it was shown that an arbitrary relation between the mass M and the radius Rs of the compact star can be realized by adjusting the functional form of F(r).
TL;DR: In this article , the stable behavior of axial symmetrical compact fluid configuration with anisotropic conditions was investigated under the influence of f(R,T) gravity in which the Lagrangian is taken as a varying function of Ricci scalar invariant (R) and trace of energy tensor (T).
TL;DR: In this article , the Ricci scalar curvature and the Holst invariant are coupled non-minimally to a scalar field, and the spectral index can either decrease or increase depending on the position in parameter space.
Abstract: In the general framework of Metric-Affine theories of gravity, where the metric and the connection are independent variables, we consider actions quadratic in the Ricci scalar curvature and the Holst invariant (the contraction of the Riemann curvature with the Levi-Civita antisymmetric tensor) coupled non-minimally to a scalar field. We study the profile of the equivalent effective metric theory, featuring an extra dynamical pseudoscalar degree of freedom, and show that it reduces to an effective single-field inflationary model. We analyze in detail the inflationary predictions and find that they fall within the latest observational bounds for a wide range of parameters, allowing for an increase in the tensor-to-scalar ratio. The spectral index can either decrease or increase depending on the position in parameter space.
TL;DR: In this article , the geometric composition of a perfect fluid spacetime with torse-forming vector field ξ in connection with conformal Ricci-Yamabe metric and conformal η-Ricci-yamabe soliton was studied.
Abstract: The present paper aims to deliberate the geometric composition of a perfect fluid spacetime with torse-forming vector field ξ in connection with conformal Ricci–Yamabe metric and conformal η-Ricci–Yamabe metric. We delineate the conditions for conformal Ricci–Yamabe soliton to be expanding, steady or shrinking. We also discuss conformal Ricci–Yamabe soliton on some special types of perfect fluid spacetime such as dust fluid, dark fluid and radiation era. Furthermore, we design conformal η-Ricci–Yamabe soliton to find its characteristics in a perfect fluid spacetime and lastly acquired Laplace equation from conformal η-Ricci–Yamabe soliton equation when the potential vector field ξ of the soliton is of gradient type. Overall, the main novelty of the paper is to study the geometrical phenomena and characteristics of our newly introduced conformal Ricci–Yamabe and conformal η-Ricci–Yamabe solitons to apply their existence in a perfect fluid spacetime.
TL;DR: In this paper , a non-metricity scalar non-minimally coupled to the trace of stress-energy tensor is investigated. And the authors obtained the Hubble parameter analytically and constrain free parameters of the model through the MCMC sampling of 57 recent Hubble parameter observations.
Abstract: In the General Theory of Relativity (GR) gravitational interactions are described by the scalar Ricci curvature. But there exists another class of modified gravity theories equivalent to GR, described by the torsion tensor or non-metricity scalar. One of such theories, investigated in this paper is f ( Q , T ) gravity, built from the arbitrary function of non-metricity scalar non-minimally coupled to the trace of stress-energy tensor. Current work is aimed on the linear f ( Q , T ) = α Q + β T gravity, where α and β are free MOG parameters to be varied. As well, we assume that the fluid is bulk-viscous with pressure p ‾ = p − 3 ζ H and the bulk viscosity parameter ζ = ζ 0 + ζ 1 H + ζ 2 ( H ˙ / H + H ) . From the modified Einstein Field Equations (EFE's) we obtain the Hubble parameter analytically and constrain free parameters of the model through the MCMC sampling of 57 recent Hubble parameter observations. We found that computed Hubble rate for our model from MCMC sampling converges with the observational data at the ± 1 σ confidence level. To examine the current accelerated expansion rate of the universe in details we use the statefinder diagnostics. Besides, to distinguish Λ CDM and our model we use Om ( z ) analysis.
TL;DR: In this article , the authors extend the Kronheimer-Mrowka characterization of the Thurston norm to any closed, oriented 3-manifold with no nonseparating spheres and show that it admits no metric of positive scalar curvature.
Abstract: For a harmonic map $u : M^3 \to S^1$ on a closed, oriented $3$-manifold, we establish the identity \[ 2 \pi \int_{\theta \in S^1} \chi (\Sigma _\theta) \geq \frac{1}{2} \int_{\theta \in S^1} \int_{\Sigma_\theta} \left( {\lvert du \rvert}^{-2} {\lvert \mathit{Hess} (u) \rvert}^2 + R_M \right) \] relating the scalar curvature $R_M$ of $M$ to the average Euler characteristic of the level sets $\Sigma_\theta = u^{-1} {\lbrace \theta \rbrace}$. As our primary application, we extend the Kronheimer–Mrowka characterization of the Thurston norm on $H_2 (M; \mathbb{Z})$ in terms of ${\lVert R^{-}_M \rVert}_{L^2}$ and the harmonic norm to any closed $3$-manifold containing no nonseparating spheres. Additional corollaries include the Bray–Brendle–Neves rigidity theorem for the systolic inequality $(\min R_M) \mathit{sys}_2 (M) \leq 8\pi$, and the well-known result of Schoen and Yau that $T^3$ admits no metric of positive scalar curvature.
TL;DR: In this article , it was shown that the Ricci soliton of the Reeb vector field leaves the scalar curvature invariants and the potential vector field is collinear with Reeb vectors.
Abstract: The aim of this paper is to find some important classes of Einstein manifolds using conformal [Formula: see text]-Ricci solitons and conformal [Formula: see text]-Ricci almost solitons. We prove that a Kenmotsu metric as conformal [Formula: see text]-Ricci soliton is Einstein if it is [Formula: see text]-Einstein or the potential vector field [Formula: see text] is infinitesimal contact transformation or collinear with the Reeb vector field [Formula: see text]. Next, we prove that a Kenmotsu metric as gradient conformal [Formula: see text]-Ricci almost soliton is Einstein if the Reeb vector field leaves the scalar curvature invariants. Finally, we construct some examples to illustrate the existence of conformal [Formula: see text]-Ricci soliton, gradient almost conformal [Formula: see text]-Ricci soliton on Kenmotsu manifold.
TL;DR: In this paper , extensions of General Relativity based on the nonlocal function f(R,□−1R), where R is the Ricci curvature scalar and the non-locality is due to the term □− 1R, are considered.
07 Oct 2022
TL;DR: In this article , the authors investigated the field equations of the conformally invariant models of gravity with curvature-matter coupling, constructed in Weyl geometry, using the Palatini formalism.
Abstract: Abstract We investigate the field equations of the conformally invariant models of gravity with curvature-matter coupling, constructed in Weyl geometry, using the Palatini formalism. We consider the case in which the Lagrangian is given by the sum of the square of the Weyl scalar, the strength of the field associated to the Weyl vector, and a conformally invariant geometry-matter coupling term, constructed from the matter Lagrangian and the Weyl scalar. After substituting the Weyl scalar in terms of its Riemannian counterpart, the quadratic action is defined in Riemann geometry and involves a nonminimal coupling between the Ricci scalar and the matter Lagrangian. For the sake of generality, a more general Lagrangian, in which the Weyl vector is nonminimally coupled with an arbitrary function of the Ricci scalar, is also considered. By varying the action independently with respect to the metric and the connection, the independent connection can be expressed as the Levi-Civita connection of an auxiliary Ricci scalar- and Weyl vector-dependent metric, which is related to the physical metric by means of a conformal transformation. The field equations are obtained in both the metric and the Palatini formulations. The cosmological implications of the Palatini field equations are investigated for three distinct models corresponding to different forms of the coupling functions. A comparison with the standard $$\Lambda $$ Λ CDM model is also performed, and we find that the Palatini type cosmological models can give an acceptable description of the observations.
TL;DR: In this article , a semi-classical description of quantum fluctuations embedded in a Riemannian spacetime can be effectively recast as classical back reactions and manifest themselves in the form of non-minimal couplings between matter and curvature.
TL;DR: In this paper , it was shown that the noncollapsed Gromov-Hausdorff limits of polarized Kähler manifolds, with Ricci curvature bounded below, are normal projective varieties, and the metric singularities of the limit space are precisely given by a countable union of analytic subvarieties.
Abstract: We show that non-collapsed Gromov–Hausdorff limits of polarized Kähler manifolds, with Ricci curvature bounded below, are normal projective varieties, and the metric singularities of the limit space are precisely given by a countable union of analytic subvarieties. This extends a fundamental result of Donaldson–Sun, in which 2-sided Ricci curvature bounds were assumed. As a basic ingredient we show that, under lower Ricci curvature bounds, almost Euclidean balls in Kähler manifolds admit good holomorphic coordinates. Further applications are integral bounds for the scalar curvature on balls, and a rigidity theorem for Kähler manifolds with almost Euclidean volume growth.
TL;DR: In this paper , the interplay of geometry and positive scalar curvature on a complete, non-compact manifold with non-negative Ricci curvature was studied and a minimal volume growth was obtained.
Abstract: Abstract In this paper, we study the interplay of geometry and positive scalar curvature on a complete, non-compact manifold with non-negative Ricci curvature. On three-dimensional manifold, we prove a minimal volume growth, an estimate of integral of scalar curvature and width. On higher-dimensional manifold, we obtain a volume growth with a stronger condition.
TL;DR: For any G $G$ -invariant metric on a compact homogeneous space M = G / K $M=G/K$ , a formula for the Lichnerowicz Laplacian restricted to the space of symmetric 2-tensors in terms of structural constants was given in this article .
Abstract: For any G $G$ -invariant metric on a compact homogeneous space M = G / K $M=G/K$ , we give a formula for the Lichnerowicz Laplacian restricted to the space of all G $G$ -invariant symmetric 2-tensors in terms of the structural constants of G / K $G/K$ . As an application, we compute the G $G$ -invariant spectrum of the Lichnerowicz Laplacian for all the Einstein metrics on most generalized Wallach spaces and any flag manifold with b 2 ( M ) = 1 $b_2(M)=1$ . This allows to deduce the G $G$ -stability and critical point types of each of such Einstein metrics as a critical point of the scalar curvature functional.
TL;DR: In this article , the authors studied the scalar curvature of a complete gradient Yamabe soliton and proved that it is a Yamabe metric and becomes rotationally symmetric under a linear growth of the potential function.
Abstract: The aim of this short note is the study of the scalar curvature of a complete gradient Yamabe solitons. In particular we show an integral inequality for a gradient Yamabe soliton and as a consequence we proved that under a linear growth of the potential function f the gradient Yamabe soliton has constant scalar curvature. Also, with natural conditions and non-positive Ricci curvature, any complete Yamabe soliton has constant scalar curvature, namely, it is a Yamabe metric and become rotationally symmetric.
TL;DR: In this article , the authors study a theory of gravity called mimetic f ( R , T ) in the presence of swampland dS conjecture and introduce several inflation solutions of the Hubble parameter H ( N ) from f (R, T ) = R + δ T gravity model, in which R is Ricci scalar, and T denotes the trace of the energymomentum tensor.
Abstract: Abstract In this paper, we study a theory of gravity called mimetic f ( R , T ) in the presence of swampland dS conjecture. For this purpose, we introduce several inflation solutions of the Hubble parameter H ( N ) from f ( R , T ) = R + δ T gravity model, in which R is Ricci scalar, and T denotes the trace of the energy–momentum tensor. Also, δ and N are the free parameter and a number of e-fold, respectively. Then we calculate quantities such as potential, Lagrange multiplier, slow-roll, and some cosmological parameters such as n s and r . Then we challenge the mentioned inflationary model from the swampland dS conjecture. We discuss the stability of the model and investigate the compatibility or incompatibility of this inflationary scenario with the latest Planck observable data.
TL;DR: In this paper , an action of a scalar field coupled non-minimally to gravity in the metric formulation of General Relativity has been constructed, and its implications for Higgs inflation have been discussed.
Abstract: General Relativity (GR) exists in different formulations. They are equivalent in pure gravity but generically lead to distinct predictions once matter is included. After a brief overview of various versions of GR, we focus on metric-affine gravity, which avoids any assumption about the vanishing of curvature, torsion or non-metricity. We use it to construct an action of a scalar field coupled non-minimally to gravity. It encompasses as special cases numerous previously studied models. Eliminating non-propagating degrees of freedom, we derive an equivalent theory in the metric formulation of GR. Finally, we give a brief outlook to implications for Higgs inflation.
TL;DR: In this article , a curvature-matter coupling between an arbitrary function of the scalar curvature and the Lagrangian density of matter has been studied, which implies non-geodesic motion and leads to the appearance of an extra force.
Abstract: In this proceeding, we review modified theories of gravity with a curvature-matter coupling between an arbitrary function of the scalar curvature and the Lagrangian density of matter. This explicit nonminimal coupling induces a non-vanishing covariant derivative of the energy-momentum tensor, that implies non-geodesic motion and consequently leads to the appearance of an extra force. Here, we explore the physical and cosmological implications of the nonconservation of the energy-momentum tensor by using the formalism of irreversible thermodynamics of open systems in the presence of matter creation/annihilation. The particle creation rates, pressure, and the expression of the comoving entropy are obtained in a covariant formulation and discussed in detail. Applied together with the gravitational field equations, the thermodynamics of open systems lead to a generalization of the standard $\Lambda$CDM cosmological paradigm, in which the particle creation rates and pressures are effectively considered as components of the cosmological fluid energy-momentum tensor. Furthermore, we also briefly present the coupling of curvature to geometry in conformal quadratic Weyl gravity, by assuming a coupling term of the form $L_m\tilde{R}^2$, where $L_m$ is the ordinary matter Lagrangian, and $\tilde{R}$ is the Weyl scalar. The coupling explicitly satisfies the requirement of the conformal invariance of the theory. Expressing $\tilde{R}^2$ with the use of an auxiliary scalar field and of the Weyl scalar, the gravitational action can be linearized in the Ricci scalar, leading in the Riemann space to a conformally invariant $f\left(R,L_m\right)$ type theory, with the matter Lagrangian nonminimally coupled to geometry.
TL;DR: In this article , a generalization of the ADM mass for weighted asymptotically Euclidean (AE) manifolds is defined; on manifolds with nonnegative weighted scalar curvature, it satisfies a weighted Witten formula and thereby a positive weighted mass theorem.
Abstract: Abstract This paper generalizes classical spin geometry to the setting of weighted manifolds (manifolds with density) and provides applications to the Ricci flow. Spectral properties of the naturally associated weighted Dirac operator, introduced by Perelman, and its relationship with the weighted scalar curvature are investigated. Further, a generalization of the ADM mass for weighted asymptotically Euclidean (AE) manifolds is defined; on manifolds with nonnegative weighted scalar curvature, it satisfies a weighted Witten formula and thereby a positive weighted mass theorem. Finally, on such manifolds, Ricci flow is the gradient flow of said weighted ADM mass, for a natural choice of weight function. This yields a monotonicity formula for the weighted spinorial Dirichlet energy of a weighted Witten spinor along Ricci flow.
TL;DR: In this paper , the Euler-Heisenberg anti-de Sitter black hole was studied in the extended phase space and the Ruppeiner geometry was constructed for both the small/large black hole phase transition and reentrant phase transition cases.
Abstract:
Taking the quantum electrodynamics (QED) effect into account, we study the black hole phase transition and Ruppeiner geometry for the Euler-Heisenberg anti-de Sitter black hole in the extended phase space. For negative and small positive QED parameter, we observe a small/large black hole phase transition and reentrant phase transition, respectively. While a large positive value of the QED parameter ruins the phase transition. The phase diagrams for each case are explicitly exhibited. Then we construct the Ruppeiner geometry in the thermodynamic parameter space. Different features of the corresponding scalar curvature are shown for both the small/large black hole phase transition and reentrant phase transition cases. Of particular interest is that an additional region of positive scalar curvature indicating dominated repulsive interaction among black hole microstructure is present for the black hole with a small positive QED parameter. Furthermore, the universal critical phenomena are also observed for the scalar curvature of the Ruppeiner geometry. These results indicate that the QED parameter has a crucial influence on the black hole phase transition and microstructure.