Aneta Wojnar
We will briefly discuss the necessary conditions for stability of polytropies in $f(\hat R)$ Palatini gravity and the differences with the General Relativity ones.
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We have derived a modified Lane-Emden equation for the Starobinsky model in Palatini gravity which is numerically solvable. Comparing the results to the ones provided by General Relativity we observe a significant difference depending on the theory parameter for the $M-R$ relations.
We examine static spherically symmetric polytropic spheres in Palatini f(R) gravity and show that no regular solutions to the field equations exist for physically relevant cases such as a monatomic isentropic gas or a degenerate electron gas, thus casting doubt on the validity of Palatini f(R) gravity as an alternative to General Relativity.
After briefly reviewing the results about polytropic stars in Palatini f(R)-theories, we first show how these results rely on the assumption of a regular function f(R). In particular, singular models allow to extend the parameter interval in which no singularity is formed. Furthermore, we present how the conformal metric can be matched smoothly in the cases where the original metric generates a singularity. In fact, the singularity comes from a singular conformal factor which is continuous though not differentiable at the stellar surface. This suggests that the correct metric to be considered …
We investigate spherically symmetric, static matter configurations with polytropic equation of state for a class of f(R) models in Palatini formalism and show that the surface singularities recently reported in the literature are not physical in the case of Planck scale modified lagrangians. In such cases, they are just an artifact of the idealized equation of state used. In fact, we show that for the models f(R)=R\pmλR^2, with λon the order of the Planck length squared, the presence of a single electron in the Universe would be enough to cure all stellar singularities of this type. From our a…
Non-vacuum static spherically-symmetric solutions in Palatini f(R) gravity are examined. It is shown that for generic choices of f(R), there are commonly-used equations of state for which no satisfactory physical solution of the field equations can be found within this framework, apart from in the special case of General Relativity, casting doubt on whether Palatini f(R) gravity can be considered as giving viable alternatives to General Relativity.
We present an analytical model for the evolution of brown dwarfs in quadratic Palatini f(R) gravity. We improve previous studies by adopting a more realistic description of the partially-degenerate state that characterizes brown dwarfs. Furthermore, we take into account the hydrogen metallic-molecular phase transition between the interior of the brown dwarf and its photosphere. For such improved model, we revise the cooling process of sub-stellar objects.
General Relativity yields an analytical prediction of a minimum required mass of roughly $\sim 0.08-0.09 M_{\odot}$ for a star to stably burn sufficient hydrogen to fully compensate photospheric losses and, therefore, to belong to the main sequence. Those objects below this threshold (brown dwarfs) eventually cool down without any chance to stabilize their internal temperature. In this work we consider quadratic Palatini $f(\mathcal{R})$ gravity and show that the corresponding newtonian hydrostatic equilibrium equation contains a new term whose effect is to introduce a weakening/strenghtening …
Covariant Canonical Formalism For Born-Infeld Inspired Gravity in Palatini Formulation
本文在协变正则形式框架下分析了Palatini表述的Born-Infeld启发引力，确定了其协变哈密顿量及相应的运动方程。
A simple cooling model of white dwarf stars is re-analyzed in Palatini $f(R)$ gravity. Modified gravity affects the white dwarf structures and consequently their ages. We find that the resulting super-Chandrasekhar white dwarfs need more time to cool down than sub-Chandrasekhar ones, or when compared to the Newtonian models.
We introduce a new approach to modified gravity which generalizes the recently proposed hybrid metric-Palatini gravity. The gravitational action is taken to depend on a general function of both the metric and Palatini curvature scalars. The dynamical equivalence with a non-minimally coupled bi-scalar field gravitational theory is proved. The evolution of cosmological solutions is studied using dynamical systems techniques.
By establishing that Palatini formulation of $L(R)$ gravity is equivalent to $ω=-3/2$ Brans-Dicke theory, we show that energy-momentum tensor is covariantly conserved in this type of modified gravity theory.
In a previous paper we showed that static spherically symmetric objects which, in the vicinity of their surface, are well-described by a polytropic equation of state with 3/2<Gamma<2 exhibit a curvature singularity in Palatini f(R) gravity. We argued that this casts serious doubt on the validity of Palatini f(R) gravity as a viable alternative to General Relativity. In the present paper we further investigate this characteristic of Palatini f(R) gravity in order to clarify its physical interpretation and consequences.
In this paper, we review modified $f(R)$ theories of gravity in Palatini formalism. In this framework, , we use the Raychaudhuri's equation along with the requirement that the gravity is attractive, which holds for any geometrical theory of gravity to discuss the energy conditions. Then, to derive these conditions, we obtain an expression for effective pressure and energy density by considering FLRW metric. Energy conditions derived in Palatini version of $f(R)$ Gravity differ from those derived in GR. We will see that the WEC (weak energy condition) derived in Palatini formalism has exactly t…
We consider several physical scenarios where black holes within classical gravity theories including $R^2$ and Ricci-squared corrections and formulated à la Palatini can be analytically studied.
We derive the dynamical equations for a non-local gravity model in the Palatini formalism and we discuss some of the properties of this model. We have shown that, in some specific cases, the vacuum solutions of general relativity are also vacuum solutions of the non-local model, so we conclude that, at least in this case, the singularities of Einstein's gravity are not removed.
In this paper, the hybrid metric-Palatini gravity is an approach to modified gravity in which is added to the usual Einstein-Hilbert action a supplementary term containing a Palatini-type correction of the form $f({\cal R},T)$. Here, ${\cal R}$ is the Palatini curvature scalar, which is constructed from an independent connection and $T$ is the trace of the energy-momentum tensor. This theory describes a non-minimal coupling between matter and geometry. The modified Einstein field equations in this hybrid metric-Palatini approach are obtained. Then, it is investigated whether this modified theo…
We study nonlinear gravity theories in both the metric and the Palatini (metric-affine) formalisms. The nonlinear character of the gravity lagrangian in the metric formalism causes the appearance of a scalar source of matter in Einstein's equations that can be interpreted as a quintessence field. However, in the Palatini case no new energy sources appear, though the equations of motion get modified in such a way that usual matter can lead to repulsive gravity at very low densities. Thus, the Palatini formalism could provide a mechanism to explain the recent acceleration of the universe without…
Recent observations of several peculiar over- and under-luminous type Ia supernovae infer indirect evidence for the violation of the Chandrasekhar mass-limit by suggesting the existence of super- and sub-Chandrasekhar limiting mass white dwarfs. In an attempt to explain these phenomena in the context of general relativistic extensions, we study these objects in Palatini $f(R)$ gravity. We obtain the super- and sub-Chandrasekhar limiting masses as well as the dynamical instability criteria for white dwarfs in the given gravitational theory. We further demonstrate that the conventional positivit…
We consider the Palatini formalism of gravity with cosmological constant $Λ$ coupled to a scalar field $ϕ$ in $n$-dimensions. The $n$-dimensional Einstein equations with $Λ$ can be derived by the variation of the coupled Palatini action provided $n>2$. The Hamiltonian analysis of the coupled action is carried out by a $1+(n-1)$ decomposition of the spacetime. It turns out that both Palatini action and Hilbert action lead to the same geometric dynamics in the presence of $Λ$ and $ϕ$. While, the $n$-dimensional Palatini action could not give a connection dynamics formalism directly.
The question of the correspondence between the number of degrees of freedom and the number of polarization states in hybrid metric-Palatini f(R)-gravity is considered. It is shown that the scalar transverse breathing and longitudinal modes are a mixture of one polarization state. The speed of gravitational waves propagation in hybrid f(R)-gravity is calculated.
By using the equivalence between metric and Palatini f(R) (or "modified") gravities with omega=0, -3/2 Brans-Dicke theories, it is shown that the Ehlers-Geren-Sachs theorem of general relativity is extended to modified gravity. In the case of metric f(R) gravity previously studied, this agrees with previous literature.
The Palatini $f(R,T)$ gravity theory is considered. The standard Einstein-Hilbert action is replaced by an arbitrary function of the Ricci scalar $R$ and of the trace $T$ of the energy-momentum tensor. In the Palatini approach, the Ricci scalar is a function of the metric and the connection. These two quantities, metric and connection, are taken as independents variables. Then, it is examined whether Palatini $f(R,T)$ gravity theory allows solutions in which lead to violation of causality. The Gödel and Gödel-type space-times are considered. In addition, a critical radius, which permits to exa…
We consider compact binary systems in f(R) gravity theories in the Palatini approach and calculate the post-Newtonian parameters to the 1.5PN order using the method of Direct Integration of the Relaxed Einstein equations (DIRE). The Palatini-type modifications of gravity can be formulated as Einsteins gravity with modified response to matter sources, and it is shown in detail how to treat these correctly within the DIRE formalism. Our results explicitly confirm the expectation that for binary black holes the new effects can be absorbed into redefinitions of the binary masses, rendering such sy…
We work out the junction conditions for $f(R)$ gravity formulated in metric-affine (Palatini) spaces using a tensor distributional approach. These conditions are needed for building consistent models of gravitating bodies with an interior and exterior regions matched at some hypersurface. Some of these conditions depart from the standard Darmois-Israel ones of General Relativity and from their metric $f(R)$ counterparts. In particular, we find that the trace of the stress-energy momentum tensor in the bulk must be continuous across the matching hypersurface, though its normal derivative need n…
In Palatini $f(R)$ gravity, the parameters of the Schwarzschild - de Sitter solution as well as the whole interior solutions of compact objects are expected to change when compared to general relativity. We solve the Palatini field equations numerically in the case of the models $f(R) = R + αR^2$ and $f(R) = R - μ^4/R$, and using the equation of state of Fermi gas. We show how the density profiles and the prediction for the maximum masses of white dwarfs (the Chandrasekhar limit) and neutron stars (the Tolman-Oppenheimer-Volkoff limit) are altered, and thereby conclude that observations on com…
We consider a Palatini variation on a general $N$-Dimensional second order, torsion-free dilaton gravity action and determine the resulting equations of motion. Consistency is checked by considering the restraint imposed due to invariance of the matter action under simple coordinate transformations, and the special case of N=2 is examined. We also examine a sub-class of theories whereby a Palatini variation dynamically coincides with that of the "ordinary" Hilbert variational principle; in particular we examine a generalized Brans-Dicke theory and the associated role of conformal transformatio…
This paper aims to analyze the generalization of Lema\^ıtre-Tolman-Bondi (LTB) spacetime for dissipative dust under the influence of Palatini $f(R)$ gravity. We explore the modified field equations, kinematical variables, and mass function in this scenario. We construct Bianchi identities using conservation and differential equations for shear, expansion, and curvature scalar in the background of Palatini $f(R)$ gravity. We calculated the scalar functions coming from the orthogonal decomposition of the Riemann tensor in this framework. These scalar functions known as structure scalars have bee…
In this paper by deriving the Modified Friedmann equation in the Palatini formulation of $R^2$ gravity, first we discuss the problem of whether in Palatini formulation an additional $R^2$ term in Einstein's General Relativity action can drive an inflation. We show that the Palatini formulation of $R^2$ gravity cannot lead to the gravity-driven inflation as in the metric formalism. If considering no zero radiation and matter energy densities, we obtain that only under rather restrictive assumption about the radiation and matter energy densities there will be a mild power-law inflation $a(t)\sim…
In the frame work of Palatini approach to modified $f(R)$ theories of gravity, we attempt to investigate the thermodynamic behavior of time-dependent wormhole geometries. By considering an evolving wormhole spacetime, we find the field equations in Palatini $f(R)$ gravity. The energy density and pressure are redefined in order to satisfy the continuity equation. To discuss the thermodynamic behavior, an expression for the variation of total entropy is obtained. Then, we extend our discussions to apparent and event horizons of evolving wormholes. We employ the radius of apparent and event horiz…
We discuss recent results on the cosmology of extended theories of gravity formulated in the Palatini approach, i.e., assuming that metric and connection are independent fields. In particular, we focus on the attempts to explain the cosmic speedup with f(R) theories and on models that avoid the big bang singularity. The field equations for gravity Lagrangians of the form f(g_{μν},{R^α}_{βμν}) (including torsion) are explicitly derived and discussed.
In this paper, we explicitly prove the presymplectic forms of the Palatini and Ashtekar gravity to be zero along gauge orbits of the Lorentz and diffeomorphism groups, which ensures the diffeomorphism invariance of these theories.
General Relativity has so far passed almost all the ground-based and solar-system experiments. Any reasonable extended gravity models should consistently reduce to it at least in the weak field approximation. In this work we derive the gravitational potential for the Palatini formulation of the modified gravity of the L(R) type which admits a de Sitter vacuum solution. We conclude that the Newtonian limit is always obtained in those class of models and the deviations from General Relativity is very small for a slowly moving source.
We consider static spherically symmetric stellar configurations in Palatini theories of gravity in which the Lagrangian is an unspecified function of the form $f(R,R_{μν}R^{μν})$. We obtain the Tolman-Oppenheimer-Volkov equations corresponding to this class of theories and show that they recover those of $f(R)$ theories and General Relativity in the appropriate limits. We show that the exterior vacuum solutions are of Schwarzschild-de Sitter type and comment on the possible expected modifications, as compared to GR, of the interior solutions.
Hybrid metric-Palatini gravity is a recent and novel approach to modified theories of gravity, which consists of adding to the metric Einstein-Hilbert Lagrangian an f(R) term constructed a la Palatini. It was shown that the theory passes local tests even if the scalar field is very light, and thus implies the existence of a long-range scalar field, which is able to modify the dynamics in galactic and cosmological scales, but leaves the Solar System unaffected. In this work, motivated by the possibility that the Universe may have started out in an asymptotically Einstein static state in the inf…
We formulate the generalized Tolman-Oppenheimer-Volkoff equations for the $f(\hat{R})$ Palatini gravity in the case of static and spherical symmetric geometry. We also show that a neutron star is a stable system independently of the form of the functional $f(\hat{R})$
We developed the parameterized post-Keplerian formalism for hybrid metric-Palatini $f(R)$-gravity. We obtained analytical expressions in the generel eccentric case for four PPK parameters: $\dotω$, $\dot P_{\rm b}$, $r$ and $s$. Using observational data of PSR J0737-3039 and PSR J1903+0327 we imposed restrictions on the parameters of hybrid f(R)-gravity and showed that this theory is not ruled out by the observations in strong field regime. In addition we obtained predictions for masses of systems components and found that considered astrophysical objects will be heavier than in GR.
Some parts of the substellar evolution, such as fragmentation of a gaseous cloud and Jupiter-like planet's cooling, are demonstrated to be impacted by Palatini $f(\bar R)$ gravity. Using simple models describing those processes we show that the opacity mass limit as well as cooling time of jovian planets differ in modified gravity.
In this paper we generalize the off-shell Abbott-Deser-Tekin (ADT) conserved charge formalism to Palatini theory of gravity with torsion and non-metricity. Our construction is based on the coordinate formalism and the independent dynamic fields are the metric and the affine connection. For a general Palatini theory of gravity, which is diffeomorphism invariant up to a boundary term, we obtain the most general expression for off-shell ADT potential. As explicit examples, we derive the off-shell ADT potentials for Einstein-Hilbert action, the most general $L(g_{μν}, R^λ{}_{ναμ}, T^λ{}_{αβ}, Q_{α…
Thin accretion disk signatures in hybrid metric-Palatini gravity
该研究采用Novikov-Thorne模型，数值计算混合度规-Palatini引力下静态球对称黑洞薄吸积盘的相关物理量，对比Schwarzschild黑洞结果，发现该引力框架下吸积盘温度更低、光度更弱，为模型可行性分析提供依据。
I review recent results obtained for extensions of general relativity formulated within the Palatini formalism, an approach in which metric and connection are treated as independent geometrical entities. The peculiar dynamics of these theories, governed by second-order equations and having no new degrees of freedom, makes them specially suitable to address certain aspects of quantum gravity phenomenology, construct nonsingular bouncing cosmologies, and explore black hole interiors, which in the Reissner-Nordstrom case develop a compact core of finite density instead of a point-like singularity…
We analyse the most general connection allowed by Einstein-Hilbert theory in Palatini formalism. We also consider a matter lagrangian independent of the affine connection. We show that any solution of the equation of the connection is essentially Levi-Civita up to a term that contains an undetermined 1-form. Finally, it is proved that these connections and Levi-Civita describe a completely equivalent physics.
We consider static spherically symmetric stellar configurations in Palatini theories of gravity in which the Lagrangian is an unspecified function of the form f(R,R_{μν}R^{μν}). We obtain the Tolman-Oppenheimer-Volkov equations corresponding to this class of theories and show that they recover those of f(R) theories and General Relativity in the appropriate limits. We compute exterior vacuum solutions and comment on the possible expected modifications, as compared to GR, of the interior solutions.
We study how higher-order gravity affects Higgs inflation in the Palatini formulation. We first review the metric and Palatini formulations in comparative manner and discuss their differences. Next cosmic inflation driven by a scalar field and inflationary observables are discussed. After this we review the Higgs inflation and compute the inflationary observables both in the metric and Palatini formulations. We then consider adding higher-order terms of the curvature to the action. We derive the equations of motion for the most general action quadratic in the curvature that does not violate pa…
A Palatini-type action for Einstein and Gauss-Bonnet gravity with non-trivial torsion is proposed. Three-form flux is incorporated via a deformation of the Riemann tensor, and consistency of the Palatini variational principle requires the flux to be covariantly constant and to satisfy a Jacobi identity. Studying gravity actions of third order in the curvature leads to a conjecture about general Palatini-Lovelock-Cartan gravity. We point out potential relations to string-theoretic Bianchi identities and, using the Schouten-Nijenhuis bracket, derive a set of Bianchi identities for the non-geomet…
We investigate the efficiency of screening mechanisms in the hybrid metric-Palatini gravity. The value of the field is computed around spherical bodies embedded in a background of constant density. We find a thin shell condition for the field depending on the background field value. In order to quantify how the thin shell effect is relevant, we analyze how it behaves in the neighborhood of different astrophysical objects (planets, moons or stars). We find that the condition is very well satisfied except only for some peculiar objects. Furthermore we establish bounds on the model using data fro…
We consider cosmological scalar field evolving under exponential potential of the Non-minimal Derivative Coupling (NMDC) gravity model in Palatini formalism. Slow-roll regime is assumed. GR and metric formalism NMDC cases are compared in this study. Phase portraits show that Palatini NMDC effect restricts acceleration phase into smaller region in the phase space. NMDC effect of the Palatini case suppresses expansion rate than that of the GR while the metric NMDC enhances rate of expansion of the GR case.
We estimate the parameters of Hybrid Palatini gravity model with the Schwarzschild precession of S-stars, specifically of S2, S38 and S55 stars. We also take into account case of bulk mass distribution near Galactic Center. We assume that the Schwarzschild orbital precession of mentioned S-stars is the same like in General Relativity (GR) in all studied cases. In 2020 the GRAVITY Collaboration detected the orbital precession of the S2 star around the supermassive black hole (SMBH) at the Galactic Center and showed that it is close to the GR prediction. The astronomical data analysis of S38 and…
The generalized hybrid metric-Palatini theory of gravity admits a scalar-tensor representation in terms of two interacting scalar fields. We show that, upon an appropriate choice of the interaction potential, one of the scalar fields behaves like dark energy, inducing a late-time accelerated expansion of the universe, while the other scalar field behaves like pressureless dark matter that, together with ordinary baryonic matter, dominates the intermediate phases of cosmic evolution. This unified description of dark energy and dark matter gives rise to viable cosmological solutions, which repro…
We study the generalized version of energy-momentum squared gravity (EMSG) in the Palatini formalism. This theory allows the existence of a scalar constructed with energy-momentum tensor as $T_{αβ}T^{αβ}$ in the generic action of the theory. We study the most general form of this theory in the Palatini framework and present the underlying field equations. The equations of motion of a massive test particle have been derived. The weak field limit of the theory is explored and the generalized version of the Poisson equation is obtained. Moreover, we explore the cosmological behavior of the theory…
The possibility of testing gravity theories with the help of gravitational wave detections has become an interesting arena of recent research. In this paper, we follow this direction by investigating the quasinormal modes (QNMs) of the axial perturbations for charged black holes in the Palatini-type theories of gravity, specifically ($i$) the Palatini $f(R)$ gravity coupled with Born-Infeld nonlinear electrodynamics and ($ii$) the Eddington-inspired-Born-Infeld gravity (EiBI) coupled with Maxwell electromagnetic fields. The coupled master equations describing perturbations of charged black hol…
In metric formalism, Noether symmetry of F(R) theory of gravity in vacuum and in the presence of pressureless dust yields $F(R)\propto R^\frac{3}{2}$ along with the conserved current $\frac{d}{dt} (a\sqrt R)$ in Robertson-Walker metric and nothing else. However, Roshan et.al. had claimed in $\mathrm{Phys. Lett. \textbf{B668}, 238 (2008)}$ \cite{o} that Noether symmetry in the context of Palatini $F(\Re)$ theory of gravity admits $F(\Re)\propto \Re^{s}$, (where $s$ is an arbitrary constant) in matter domain era in Friedmann- Robertson-Walker universe. But, it has been shown that the conserved c…
Primordial Gravitational Waves in Generalized Palatini Gravity
本文研究扩展 Palatini 引力中几何 Proca 场对原初引力波的影响，发现其会留下显著信号且能量密度足以被下一代引力波探测器探测，从而为引力的非黎曼本质提供观测判据。
In this work we discuss the exact solution to the algebraic equation associated to the Ricci tensor in the quadratic $f(R,Q)$ extension of Palatini gravity. We show that an exact solution always exists, and in the general case it can be found by a simple matrix diagonalization. Furthermore, the general implications of the solution are analysed in detail, including the generation of an effective cosmological constant, and the recovery of the $f(R)$ and $f(Q)$ theories as particular cases in their corresponding limit. In addition, it is proposed a power series expansion of the solution which is …
We study Palatini f(R) cosmology using Noether symmetry approach for the matter dominated universe. In order to construct a point-like Lagrangian in the flat FRW space time, we use the dynamical equivalence between f(R) gravity and scalar-tensor theories. The existence of Noether symmetry of the cosmological f(R) Lagrangian helps us to find out the form of f(R) and the exact solutions for cosmic scale factor. We show that this symmetry always exist for f(R)~R^n and the Noether constant is a function of the Newton's gravitational constant and the current matter content of the universe.
4D Palatini-Cartan Gravity in Hamiltonian Form
本文研究Palatini-Cartan形式下四维引力的哈密顿化问题，通过消去联络中包含的辅助场，重新得到其哈密顿表述。
We analyze the cosmological implementation of Palatini $f(R)$ theories, constructed with a Nieh-Yan term and solved with respect to the torsion. We consider the relevant case of the quadratic correction to the Hilbert-Palatini action in the Ricci scalar, mimicking the Starobinsky model of the metric formulation. We point out the emergence of peculiar cosmological scenarios, depending on the sign of such correction, able to reproduce bouncing settings and to restore the standard Universe dynamics in the late asymptotic limit. Furthermore, we outline the settling of Little-Rip dynamics, which ca…
To write down a path integral for the Ashtekar gravity one must solve three fundamental problems. First, one must understand rules of complex contour functional integration with holomorphic action. Second, one should find which gauges are compatible with reality conditions. Third, one should evaluate the Faddeev-Popov determinant produced by these conditions. In the present paper we derive the BRST path integral for the Hilbert-Palatini gravity. We show, that for certain class of gauge conditions this path integral can be re-written in terms of the Ashtekar variables. Reality conditions define…
In the present work, we study linear, torsion-free metric-Palatini gravity, extended by the quadratics of the antisymmetric part of the Ricci tensor and extended also by the presence of the affine connection in the matter sector. We show that this extended metric-Palatini gravity reduces dynamically to the general relativity plus a geometrical massive vector field corresponding to non-metricity of the connection. We also show that this geometric Proca field couples to fermions universally. We derive static, spherically symmetric field equations of this Einstein-geometric Proca theory. We study…
In an accelerated expanding universe, one can expect the existence of an event horizon. It may be interesting to study the thermodynamics of the Friedmann-Robertson-Walker (FRW) universe at the event horizon. Considering the usual Hawking temperature, the first law of thermodynamics does not hold on the event horizon. To satisfy the first law of thermodynamics, it is necessary to redefine Hawking temperature. In this paper, using the redefinition of Hawking temperature and applying the first law of thermodynamics on the event horizon, the Friedmann equations are obtained in f(R) gravity from t…
Some parts of the accretion model of the jovian planets' formation are studied in the context of Palatini gravity. We mainly focus on the critical core mass, that is, a mass for which there is no hydrostatic equilibrium solution for the planet's envelope, which is a starting point of the runaway accretion. We also discuss the conditions needed to be satisfied by a planet such that it can posses a massive gaseous envelope around a solid core.
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