Abstract We establish a correspondence between the Newman–Penrose and 1+1+2 semitetrad covariant formalisms by expressing all Newman–Penrose spin coefficients, Ricci scalars, and Weyl scalars in terms of the scalar, vector, and tensor variables of the 1+1+2 decomposition. In addition, we provide some discussions on the correspondence between the gauge structures of the formalisms. This provides a direct dictionary between two widely used approaches to general relativity and gives a geometrical interpretation of Newman–Penrose quantities in terms of covariantly defined 1+1+2 variables. As a simple demonstration, we use this mapping to derive inequalities on the Newman–Penrose scalars and the cosmological constant, which constrains the existence of future outer trapping horizons in spacetimes exhibiting local rotational symmetry.

Abstract We study static, spherically symmetric stellar configurations in the power-law class of energy-momentum squared gravity defined by F ( R , T ) = R + η T n using the covariant 1 + 1 + 2 semi-tetrad formalism. For perfect physical fluids, we show that the nonlinear matter corrections can be reinterpreted as an effective perfect fluid, so that the stellar equilibrium equations retain the standard Tolman–Oppenheimer–Volkoff (TOV) form when written in terms of effective variables. The resulting covariant structure equations are formulated in both metric and dimensionless variables and, whenever an effective closure relation exists, reduce to an autonomous planar dynamical system. This provides a global qualitative description of the stellar phase space in terms of finite and asymptotic critical points. Specializing to linear physical equations of state, we recover the general relativistic benchmark and identify sectors that are exactly, asymptotically, or piecewise equivalent to general relativity, as well as sectors for which the planar reduction breaks down and the full three-dimensional covariant flow must be considered. We further recover the standard metric TOV equation in terms of effective variables and show that, although the exterior spacetime remains Schwarzschild, the natural matching condition at the stellar surface is p eff ( R ) = 0 , which need not coincide with p ( R ) = 0 for self-bound matter. Finally, in the appendix, we show how our procedure can be applied to a realistic neutron-star equation of state.

We revisit thawing quintessence models with nearly flat scalar-field potentials using a cosmographic framework. Earlier work indicates that the cosmographic reconstruction of the slope λ=-(dV/dϕ)/V of the quintessence potential in the general case requires the knowledge of the cosmographic paremeters up to the jerk parameter j. In this work we show that the slow-roll conditions [(dV/dϕ)/V]^2 ≪ 1 and |(d^2V/dϕ^2)/V| ≪ 1 allow the reconstruction of the slope of a nearly flat potential with knowledge of only the deceleration parameter q (and the density parameter Ω_ϕ). Confronting the assumption of near-flatness with the cosmographic data after DESI DR2, however, reveals possible tension between the two. We further show that these models exhibit attractor behaviour in the w–Ω_ϕ and w–w' phase planes, corresponding to a universal thawing evolution with w ≈ -1 at early times. We also derive the corresponding relation in the cosmographic q–j plane and show that different cosmological expansion histories can produce the same thawing evolution. Nevertheless, all viable trajectories remain close to the ΛCDM limit j=1.

We present a fully covariant and gauge-invariant analysis of linear cosmological perturbations in Energy-Momentum Squared Gravity. Working within the 1+3 formalism, we derive the exact propagation equations for scalar, vector, and tensor modes on FLRW backgrounds, in the case of radiation and dust. Two representative subclasses are examined in detail, in which non-linearity enters through $\mathcal{O}(ηρ^2)$ corrections or modifications in the equation-of-state parameter and the sound speed. For scalar perturbations, the density contrast can be enhanced or reduced relative to General Relativity, depending on the coupling parameter and the wavelength regime. A similar behaviour occurs for vector modes, allowing for a non-trivial vorticity at early-times. Tensor modes, described by the magnetic part of the Weyl tensor and the shear tensor propagate as damped waves with slowly varying effective masses. All sectors reduce continuously to their GR limits as $η\!\to\!0$. The framework isolates robust signatures - early-time scalar tilts, tensor damping shifts, and altered vorticity decay - that can be confronted with CMB and large-scale-structure observations to constrain these theories of gravity.

We derive expressions for the first and second derivatives of the quintessence potential V(ϕ), in terms of λ= -V^'/V and Γ= (V^''/V)/(V^'/V)^2, as functions of the quintessence density fraction Ω_ϕ and the cosmographic parameters q, j, and s. Our mapping is not explicitly a function of the equation of state parameter w. We use these results, along with recent observational data, to derive expansions of V(ϕ) about the present-day value of the scalar field, ϕ_0.

We revisit static, spherically symmetric perfect-fluid stellar models in General Relativity within the framework of the 1+1+2 semi-tetrad formalism. For locally rotationally symmetric static spacetimes, the Tolman-Oppenheimer-Volkoff system can be expressed as a covariant first-order dynamical system and, after suitable normalization, reformulated as a three-dimensional autonomous flow for a general equation of state (EoS). In the case of a linear EoS, the system reduces further to a planar dynamical system whose finite and asymptotic equilibrium points, together with their stability properties, admit a clear geometrical interpretation in terms of covariant variables. For more general equations of state, such as the polytropic case, the dynamics naturally acquire a genuinely three-dimensional character. Beyond providing a compact, covariant, and physically transparent reformulation of the relativistic stellar problem, the present analysis clarifies how the standard metric description is encoded within a global phase-space structure constructed from geometrically meaningful covariant variables.

We present a covariant description of non-vacuum static spherically symmetric spacetimes in f(R) gravity applying the (1+1+2) covariant formalism. The propagation equations are then used to derive a covariant and dimensionless form of the Tolman–Oppenheimer–Volkoff equations. We then give a solution strategy to these equations and obtain some new exact solutions for the particular case , which have the correct thermodynamic properties for standard matter.

ABSTRACT Over the last decade, much attention has been given to the study of modified gravity theories to find a more natural explanation for the late-time acceleration of the Universe. Particular attention has focused on the so-called $f(R)$ dark energy models. Instead of focusing on a particular $f(R)$ model, we present a completely model-independent approach to study the background dynamics and the growth of matter density perturbations for those $f(R)$ models that mimic the Lambda cold dark matter ($\Lambda$CDM) evolution at the background level. We do this by characterizing the dynamics of the gravitational field using a set of dimensionless variables and using cosmography to determine the expansion history. We then illustrate the integrity of this method by fixing the cosmography to be the same as an exact $\Lambda$CDM model, allowing us to test the solution. We compare the exact evolution of the density contrast and growth index with what one obtains from various levels of the quasi-static approximation, without choosing the form of $f(R)$ dark energy.

We present a covariant description of non-vacuum static spherically symmetric spacetimes in f(R) gravity applying the (1+1+2) covariant formalism. The propagation equations are then used to derive a covariant and dimensionless form of the Tolman-Oppenheimer-Volkoff equations. We then give a solution strategy to these equations and obtain some new exact solutions for the particular case f(R)=R+alpha R2, which have the correct thermodynamic properties for standard matter.

In this communication, we address whether or not there is an equivalence between the kinematical and dynamical descriptions of the spatially flat ACDM model. We address this by investigating whether an almost ACDM expansion history [1(z) approximate to 1] corresponds to an almost ACDM model [wDE(z) approximate to -1] by considering two particular explicit examples. At least for the cases considered, this turns out not to be the case. Instead, what we find is that an almost ACDM cosmic evolution rather corresponds to an almost unified dark-fluid model. Considering that one never gets the exact condition 1(z) = 1 from any cosmographic datasets, this raises further questions on whether the ACDM model is the best candidate for the standard model of the evolution of the Universe.

We study the existence of gradient conformal Killing vectors (CKVs) in the class of locally rotationally symmetric (LRS) spacetimes which generalizes spherically symmetric spacetimes, and investigate some implications for the evolutionary character of marginally outer trapped surfaces. We first study existence of gradient CKVs via the obtention of a relationship between the Ricci curvature and the gradient of the divergence of the CKV. This provides an alternative set of equations, for which the integrability condition is obtained, to analyze the existence of gradient CKVs. A uniqueness result is obtained in the case of perfect fluids, where it is demonstrated that the Robertson-Walker solution is the unique perfect fluid solution with a nonvanishing pressure, admitting a timelike gradient CKV. The constant mean curvature condition for LRS spacetimes is also obtained, characterized by three distinct conditions which are specified by a set of three scalars. Linear combinations of these scalars, whose vanishing define the constant mean curvature condition, turn out to be related to the evolutions of null expansions of 2-spheres along their null normal directions. As such, some implications for the existence of black holes and the character of the associated horizons are obtained. It is further shown that dynamical black holes of increasing area, with a non-vanishing heat flux across the horizon, will be in equilibrium, with respect to the frame of the conformal observers.

We consider a double polytropic cosmological fluid and demonstrate that, when one constituent resembles a bare cosmological constant while the other emulates a generalized Chaplygin gas, a good description of the Universe’s large-scale dynamics is obtained. In particular, our double polytropic reduces to the Murnaghan equation of state, whose applications are already well established in solid state physics and classical thermodynamics. Intriguingly, our model approximates the conventional ΛCDM paradigm while reproducing the collective effects of logotropic and generalized Chaplygin fluids across different regimes. To check the goodness of our fluid description, we analyze first order density perturbations, refining our model through various orders of approximation, utilizing σ8 data alongside other cosmological data sets. Encouraging results suggest that our model, based on the Murnaghan equation of state, outperforms the standard cosmological background within specific approximate regimes and, on the whole, surpasses the standard phenomenological reconstruction of dark energy.

We present a dynamical system formulation for inhomogeneous LRS-II spacetimes using the covariant 1+1+2 decomposition approach. Our approach describes the LRS-II dynamics from the point of view of a comoving observer. Promoting the covariant radial derivatives of the covariant dynamical quantities to new dynamical variables and utilizing the commutation relation between the covariant temporal and radial derivatives, we were able to construct an autonomous system of first-order ordinary differential equations along with some purely algebraic constraints. Using our dynamical system formulation we found several interesting features in the LRS-II phase space with dust, one of them being that the homogeneous solutions constitute an invariant submanifold. For the particular case of LTB, we were also able to recover the previously known result that an expanding LTB tends to Milne in the absence of a cosmological constant, providing a potential validation of our formalism.

We study the causal dynamics of an embedded null horizon foliated by marginally outer trapped surfaces (MOTS) for a locally rotationally symmetric background spacetime subjected to linear perturbations. We introduce a simple procedure which characterizes the transition of the causal character of the null horizon. We apply our characterization scheme to non-dissipative perturbations of the Schwarzschild and spatially homogeneous backgrounds. For the latter, a linear equation of state was imposed. Assuming a harmonic decomposition of the linearized field equations, we clarify the variables of a formal solution to the linearized system that determine how the null horizon evolves. For both classes of backgrounds, the shear and vorticity 2-vectors are essential to the characterization, and their roles are made precise. Finally, we discuss aspects of the relationship between the characterizing conditions. Various properties related to the self-adjointness of the MOTS stability operator are extensively discussed.

We explore a generalised unified dark energy model that incorporates a non-minimal interaction between a tachyonic fluid and an additional scalar field. Specifically, we require that the second field possesses a vacuum energy, introducing an ineliminable offset due to a symmetry-breaking mechanism. After the transition (occurring as due to the symmetry-breaking mechanism of the second field), the corresponding equation of state (EoS) takes the form of a combination between a generalised Chaplygin gas (GCG) component and a cosmological constant contribution. We reinterpret this outcome by drawing parallels to the so-called Murnaghan EoS, widely-employed in the realm of solid-state physics to characterise fluids that, under external pressure, counteract the pressure's effect. We examine the dynamic behaviour of this model and highlight its key distinctions compared to the GCG model. We establish parameter bounds that clarifies the model's evolution across cosmic expansion history, showing that it, precisely, exhibits behaviour akin to a logotropic fluid that eventually converges to the $\Lambda$CDM model in the early universe, while behaving as a logotropic or Chaplygin gas at intermediate and late times respectively. We explain our findings from a thermodynamic perspective, and determine the small perturbations in the linear regime. At very early times, the growth factor flattens as expected while the main departures occur at late times, where the Murnagham EoS results in a more efficient growth of perturbations. We discuss this deviation in view of current observations and conclude that our model is a suitable alternative to the standard cosmological paradigm, introducing the concept of a matter-like field with non-zero pressure.

Using the dynamical systems approach together with the cosmographic parameters, we present a model-independent dynamical system formulation for cosmology in f(R) gravity. The formulation is model-independent in the sense that one needs to specify not a particular functional form of f(R) a-priori, but rather a particular cosmological evolution, which fixes the cosmography. In a sense, our approach is the way around the reconstruction method. This is shown using both non-compact and compact dynamical variables. The focus in this paper is on the compact analysis since we demonstrate the applicability of this formulation using examples of bouncing and cyclic cosmology. In particular, our analysis reveals, in a model-independent manner, the problem of achieving such cosmologies when the universe is globally spatially flat and devoid of matter.

We perform a detailed dynamical system analysis for the behavior of a Dirac-Born-Infeld (DBI) field in a spatially closed Friedmann-Lema & icirc;tre-Robertson-Walker (FLRW) cosmology. The DBI field is characterized by a potential and brane tension. We study power-law or exponential functions for the potential and tension. We find that in a spatially closed FLRW cosmology, a DBI field in the ultrarelativistic limit allows for a broader range of initial conditions resulting in a bouncing universe than in the nonrelativistic limit. We further note that the range of initial conditions allowing for a bounce is larger if we consider power-law functions for the potential and tension, compared to the exponential case. Our dynamical analysis shows that a DBI field does not exhibit stable cyclical behavior, including the case in which a negative cosmological constant is present.

We study a quintessence model for which the scalar field is disformally coupled to dark matter. The background mimics the LCDM cosmological evolution and the quintessence potential is not specified. A disformal effect due to the quintessential mass is seen in the growth rate of the cosmological structure on large scales. The disformal parameter renders no appreciable effect on the evolution of the total matter perturbation. An analysis of the conformal parameter and quintessential mass is investigated using the Redshift Space Distortion data to find the best-fit values that might explain the well-known sigma-8 tension.

In this paper, we study the stability of marginally outer trapped surfaces (MOTSs), foliating horizons of the form r=X(τ) , embedded in locally rotationally symmetric class II perfect fluid spacetimes. An upper bound on the area of stable MOTS is obtained. It is shown that any stable MOTS of the types considered in these spacetimes must be strictly stably outermost, that is, there are no MOTS ‘outside’ of and homologous to . Aspects of the topology of the MOTS, as well as the case when an extension is made to imperfect fluids, are discussed. Some non-existence results are also obtained. Finally, the ‘growth’ of certain matter and curvature quantities on certain unstable MOTS are provided under specified conditions.

Non-singular bouncing cosmologies are well-motivated models for the early uni-verse. Recent observational data are consistent with positive spatial curvature and allow for a natural collapsing and bouncing phase in the very early universe. Additionally, bouncing cosmologies have the potential to rectify conceptual shortcomings identified in the theory of inflation, such as the singularity problem. In this paper we present a classical bouncing model in the context of modified gravity, including an R2-term in the action. We show that after the bounce, the universe enters naturally a period of inflation, driven by the R2-term. We analyse the stability of the model and find that the scalaron assists the stability of the model.