Effective Energy-momentum Tensor Research Articles

Cosmological dynamics in f(R) gravity models through cosmographic energy conditions

A proposed f(R) functional form’s constraints caused by energy conditions are presented. Raychaudhuri’s equation and the premise that gravity is attractive are both used to derive null and strong energy conditions for the proposed f(R) gravity model. Furthermore, the weak and dominant energy conditions are established by analysing the energy conditions induced by an effective energy-momentum tensor for the f(R)-theory of gravity. The most recent estimates of the cosmographic parameters that mimic Chaplygin gas-type dark energy are used on the parameters of a pair of f(R) models as a tangible extension of the energy conditions to the Robertson-Walker universe. It is found that under the various values of the coupling parameters the proposed f(R) model satisfy null, weak and dominant energy conditions while strong energy conditions are breached. Further, constraining the coupling parameters as a result of energy conditions, our analysis shows that the proposed model accurately captures the observed cosmic acceleration, as indicated by key parameters such as the effective equation of state (ω eff ), and the deceleration parameter (q). Through a geometric analysis of cosmographic parameters, we observe deviations of f(R) gravity from the ΛCDM model. We identify distinct evolutionary pathways that resemble characteristics of either quintessence or Chaplygin gas dark energy across various epochs, indicating a dynamic rate of cosmic acceleration. Our findings highlight the significant influences of coupling parameters and initial conditions on the cosmic evolution.

Imprints of cloud of strings and quintessence field on compact stellar configurations

This paper looks into how stellar configurations with quintessence and a cloud of string fields behave in general relativity in spherical symmetric spacetime. The goal is to find a stable, stellar model. We compute the unknown constants in the metric using the masses and radii of PSRJ1614 − 2230 stars. We employ the effective energy-momentum tensor in general relativity to analyze field equations. Additionally, we also demonstrate the anisotropic behavior, energy conditions, energy density, quintessence density, pressure profiles, gradients, anisotropic factor, energy conditions, sound speeds, compactification, mass function, EoS components, redshift, and stability of the compact stars. We demonstrate that according to the theory of general relativity, these compact stars exhibit physically plausible structures in the quintessence field with clouds of string.

Gaussian black holes in brane-world model

We present regular black hole solutions in the framework of Brane-world gravity sourced by a Gaussian matter distribution. The black hole metric shares all the common features of regular black holes in the modified General Relativity (GR) with some exciting features. Considering the energy momentum tensor for an isotropic fluid on the brane, the modified Einstein field equation results with an effective energy momentum tensor that describes an anisotropic fluid determined by brane world parameters. Although the effective radial pressure and energy density satisfy the vacuum energy condition, the effective transverse pressure behaves differently. Gaussian black hole (GBH) solutions are obtained from a Gaussian matter distribution. In the paper, a new class of GBH solutions are obtained in the brane-world gravity with effective normal matter in addition to exotic matter distribution. In the brane world gravity, the mass of a GBH depends on the brane tension. The mass of a GBH formed in the brane world is greater than that at low energy (i.e., GR). We study the trajectories of the massive and the massless particles that can be trapped around a GBH for a set of model parameters. The radii of the photon spheres around the GBH and the condition for the stability of the trajectories of the photon spheres are determined. The properties of the GBHs are studied in detail, including their possible observable features.

Traversable wormholes with static spherical symmetry and their stability in higher-curvature gravity

The solutions of traversable wormholes and their geometries are investigated in higher-curvature gravity with boundary terms for each case under the presence of anisotropic, isotropic and barotropic fluids in detail. For each case, the effective energy-momentum tensor violates the null energy condition throughout the wormhole throat. The null and weak energy conditions are also analyzed for ordinary matters. The regions that physically viable wormhole solutions can exist are explicitly shown. Furthermore, it is found that the range of the viable regions exhibits an alternating pattern of expansion and contraction. The present analyses can reveal the regions in which traversable wormholes can be constructed for anisotropic, isotropic and barotropic fluids cases with incorporating realistic matter contents, leading to fundamental physics insights into the feasible construction of wormholes in higher-curvature gravity with boundary term. The main achievements of this work, in contrast to previous studies, are its thorough investigation of traversable wormholes within the framework of higher-curvature gravity with boundary terms, its extensive consideration of various fluid types, and the explicit identification of regions where stable wormhole solutions can exist.

Emergence of cosmic space with Barrow entropy, in non-equilibrium thermodynamic conditions

Recently, Barrow proposed a modified area–entropy relation S=(A/A0)1+Δ/2, where the exponent Δ, ranges 0≤Δ≤1, by taking account of the quantum gravitational deformation effects to the black hole’s surface. In recent literature, this horizon entropy has been adopted to the cosmological context. Following this, we obtained the law of emergence, which describes the dynamics of the universe, with Barrow entropy in the context of equilibrium thermodynamics (unified first law and Clausius relation). However, when considering Barrow entropy (a non-Bekenstein entropy), an additional entropy generation arises owing to the non-equilibrium thermodynamics. The corresponding field equation bears an effective coupling strength, which connects the geometry with an effective energy–momentum tensor. We derived the law of emergence by using the non-equilibrium description of the thermodynamic principle, which accounts for the addition entropy production term. We compared it with that of the equilibrium description. In addition, we checked the consistency of the modified law in the context of entropy maximization. Interestingly, we found that the non-equilibrium entropy generation rate decreases gradually, and the universe evolves to an equilibrium state of maximum entropy corresponding to the de Sitter epoch.

Boson mixing and flavor vacuum in the expanding Universe: A possible candidate for the dark energy

We analyze the boson mixing in curved spacetime and compute the expectation value of the energy-momentum tensor of bosons on the flavor vacuum in spatially flat Friedmann-Lemaître-Robertson-Walker metrics. We show that the energy-momentum tensor of the flavor vacuum behaves as the effective energy-momentum tensor of a perfect fluid. Assuming a fixed de Sitter background, we show that the equation of state can assume values in the interval [−1,1], and, in the flat space-time limit has a value −1, which is the one of the dark energy. The results here presented show that vacuum of mixed bosons like neutrino super-partners, can represent a possible component of the dark energy of the Universe.

A new test of dynamical dark energy models and cosmic tensions in Hořava gravity

ABSTRACT Hořava gravity has been proposed as a renormalizable, higher derivative, Lorentz-violating quantum gravity model without ghost problems. A Hořava gravity-based dark energy (HDE) model for dynamical dark energy has also been proposed earlier by identifying all the extra (gravitational) contributions from the Lorentz-violating terms as an effective energy–momentum tensor in Einstein equation. We consider a complete cosmic microwave background, baryon acoustic oscillation (BAO), and supernova Ia data test of the HDE model by considering general perturbations over the background perfect HDE fluid. Except from BAO, we obtain the preference of non-flat universes for all other data set combinations. We obtain a positive result on the cosmic tensions between the Hubble constant H0 and the cosmic shear S8, because we have a shift of H0 towards a higher value, though not enough for resolving the H0 tension, but the value of S8 is unaltered. This is in contrast to a rather decreasing H0 but increasing S8 in a non-flat Lambda cold dark matter (LCDM). For all other parameters, like Ωm and $\Omega _\Lambda$, we obtain quite comparable results with those of LCDM for all data sets, especially with BAO, so that our results are close to a cosmic concordance between the data sets, contrary to the standard non-flat LCDM. We also obtain some undesirable features, like an almost null result on Ωk, which gives back the flat LCDM, if we do not predetermine the sign of Ωk, but we propose several promising ways for improvements by generalizing our analysis.

Quest for realistic non-singular black-hole geometries: regular-center type

We propose seven criteria to single out physically reasonable non-singular black-hole models and adopt them to four different spherically symmetric models with a regular center and their rotating counterparts. In general relativity, all such non-singular black holes are non-generic with a certain matter field including a class of nonlinear electromagnetic fields. According to a criterion that the effective energy-momentum tensor should satisfy all the standard energy conditions in asymptotically flat regions, the well- known Bardeen and Hayward black holes are discarded. In contrast, the Dymnikova and Fan-Wang black holes respect the dominant energy condition everywhere. Although the rotating Fan-Wang black hole contains a curvature singularity, the rotating Dymnikova black hole is free from scalar polynomial curvature singularities and closed timelike curves. In addition, the dominant energy condition is respected on and outside the event horizons in the latter case. The absence of parallelly propagated curvature singularities remains an open question.

Second-order energy-momentum tensor of a scalar field

We investigate the second-order effective energy-momentum tensor (2EMT) constructed by the quadratic terms of the linear scalar cosmological perturbations while the universe is dominated by a scalar field. We show that 2EMT is gauge dependent. We then study 2EMT in three (longitudinal, spatially flat, and comoving) gauge conditions in the slow-roll stage of inflation. We find that 2EMT exhibits an effective fluid of $w=\ensuremath{-}1/3$ on superhorizon scales in all of those gauge conditions.

Quantum flavor vacuum in the expanding universe: A possible candidate for cosmological dark matter?

We analyze fermion mixing in the framework of field quantization in curved spacetime. We compute the expectation value of the energy momentum tensor of mixed fermions on the flavor vacuum. We consider spatially flat Friedmann-Lemaitre-Robertson-Walker metrics, and we show that the energy momentum tensor of the flavor vacuum is diagonal and conserved. Therefore it can be interpreted as the effective energy momentum tensor of a perfect fluid. In particular, assuming a fixed De Sitter background, the equation of state of the fluid is consistent with that of dust and cold dark matter. Our results establish a new link between quantum effects and classical fluids, and indicate that the flavor vacuum of mixed fermions may represent a new component of dark matter.

Inflation in energy-momentum squared gravity in light of Planck2018

We study cosmological dynamics of the energy-momentum squared gravity. By adding the squared of the matter field’s energy-momentum tensor (\(\zeta \, \mathbf{T} ^{2}\)) to the Einstein–Hilbert action, we obtain the Einstein’s field equations and study the conservation law. We show that, the presence of \(\zeta \, \mathbf{T} ^{2}\) term, breaks the conservation of the energy-momentum tensor of the matter fields. However, an effective energy-momentum tensor in this model is conserved in time. By considering the FRW metric as the background, we find the Friedmann equations and by which we explore the cosmological inflation in \(\zeta \,\mathbf{T} ^{2}\) model. We perform a numerical analysis on the perturbation parameters and compare the results with Planck2018 different data sets at \(68\%\) and \(95\%\) CL, to obtain some constraints on the coupling parameter \(\zeta \). We show that, for \(0< \zeta \le 2.1\times 10^{-5}\), the \(\zeta \, \mathbf{T} ^{2}\) gravity is an observationally viable model of inflation.

Generalised Ellis–Bronnikov wormholes in f(R) gravity

In this manuscript, we construct generalized Ellis–Bronnikov wormholes in the context of f(R) modified theories of gravity. We consider that the matter driving the wormhole satisfies the energy conditions so that it is the effective energy–momentum tensor containing the higher-order derivatives of curvature terms that violate the null energy condition. Thus, the gravitational fluid is interpreted by the higher-order derivatives of curvature terms to represent the wormhole geometries and is fundamentally different from its counter representation in general relativity. In particular, we explore the wormhole geometries by presuming various well-known forms of Lagrangian f(R). In addition, for the seek of completeness, we discuss modified Tolman–Oppenheimer–Volkov, volume integral quantifier, and total gravitational energy.

Hyperbolically symmetric static charged cosmological fluid models

ABSTRACT In this work, the study on static fluid distributions under the influence of electromagnetism has been carried out with an emphasis on the hyperbolically symmetric metric. For this purpose, modified gravitational formulations in the presence of charge are used to calculate the effective energy–momentum tensor, which is then further refined by taking into account tetrad field components in the Minkowski coordinate system. Also, we compute the Tolman mass and a suitable formulation of the mass function. It exhibits that the hyperbolically symmetrical source has a negative effective matter density in all stellar formulations. This demonstrates that the quantum processes together with certain excessive constraints are deemed important to explain any physical implementations under the effects of the electromagnetic field. Additionally, we assessed the structure scalars and implemented the orthogonal splitting of the structure scalars and Riemann tensor in this modified gravity. Subsequently, various explicit precise cosmological solutions and their generating functions are developed.

Wormhole solutions and energy conditions in f(R,G) gravity

In this manuscript, the traversable wormhole solutions have been explored in modified gravity by taking into consideration the model , where R is the Ricci curvature scalar and G is the Gauss–Bonnet term. An acceptable form of the redshift function has been incorporated which is a non-constant in nature along with the implementation of those already defined in literature, the two shape functions namely and . It is shown by studying the energy condition and through the graphical analysis that the null energy bounds for the effective energy-momentum tensor are generally violated for the presence of the ordinary matter in modified gravity. Energy conditions associated with the matter content threading the wormhole geometries are evaluated and in general are found to favor the null energy conditions in the vicinity of the wormhole throat, the existence of the non-exotic wormhole geometries threaded by the matter has been confirmed under this gravity.

Gravastars in modified Gauss–Bonnet gravity

This paper aims to discuss the viable and analytic solution of the spherically symmetric gravastar model under the influence of modification of Gauss–Bonnet gravity, i.e., f(G) gravity, where G is the Gauss–Bonnet curvature term. For this purpose, we evaluate the field equations in corresponding theory and conservation equation with the help of an effective energy–momentum tensor. A mathematical formalism of the gravastar’s three regions, i.e., interior de-Sitter region, thin shell, and the exterior Schwarzschild vacuum region have been discussed. We, then analyze different realistic features, in particular energy, entropy, and length of the shell. The viability of these physical features is then examined through the graphical representations separately. Within the framework of an alternative theory, we have obtained the exact and singularity free model of gravastar.

Investigating new forms of gravity-matter couplings in the gravitational field equations

This paper proposes a toy model where, in the Einstein equations, the right-hand side is modified by the addition of a term proportional to the symmetrized partial contraction of the Ricci tensor with the energy-momentum tensor, while the left-hand side remains equal to the Einstein tensor. Bearing in mind the existence of a natural length scale given by the Planck length, dimensional analysis shows that such a term yields a correction linear in $\ensuremath{\hbar}$ to the classical term that is instead just proportional to the energy-momentum tensor. One then obtains an effective energy-momentum tensor that consists of three contributions: pure energy part, mechanical stress, and thermal part. The pure energy part has the appropriate property for dealing with the dark sector of modern relativistic cosmology. Such a theory coincides with general relativity in vacuum, and the resulting field equations are here solved for a Dunn and Tupper metric, for departures from an interior Schwarzschild solution as well as for a Friedmann-Lemaitre-Robertson-Walker universe.

An anisotropic version of Tolman VII solution in f(R, T) gravity via gravitational decoupling MGD approach

In this work, we have adopted gravitational decoupling by Minimal Geometric Deformation (MGD) approach and have developed an anisotropic version of well-known Tolman VII isotropic solution in the framework of $f(R, T)$ gravity, where $R$ is Ricci scalar and $T$ is trace of energy momentum tensor. The set of field equations has been developed with respect to total energy momentum tensor, which combines effective energy momentum tensor in $f(R,T)$ gravity and additional source $\phi_{ij}$. Following MGD approach, the set of field equations has been separated into two sections. One section represents $f(R, T)$ field equations, while the other is related to the source $\phi_{ij}$. The matching conditions for inner and outer geometry have also been discussed and an anisotropic solution has been developed using mimic constraint for radial pressure. In order to check viability of the solution, we have considered observation data of three different compact star models, named PSR J1614-2230, PSR 1937+21 and SAX J1808.4-3658 and have discussed thermodynamical properties analytically and graphically. The energy conditions are found to be satisfied for the three compact stars. The stability analysis has been presented through causality condition and Herrera's cracking concept, which ensures physical acceptability of the solution.

Second-order effective energy-momentum tensor of gravitational scalar perturbations with perfect fluid

We investigate the second-order gravitational scalar perturbations for a barotropic fluid. We derive the effective energy-momentum tensor described by the quadratic terms of the gravitational and the matter perturbations. We show that the second-order effective energy-momentum tensor is gauge dependent. We impose three gauge conditions (longitudinal, spatially-flat, and comoving gauges) for dust and radiation. The resulting energy-momentum tensor is described only by a gauge invariant variable, but the functional form depends on the gauge choice. In the matter-dominated epoch with dust-like fluid background, the second-order effective energy density and pressure of the perturbations evolve as 1/a^2 in all three gauge choices, like the curvature density of the Universe, but they do not provide the correct equation of state. The value of this parameter depends also on the gauge choice. In the radiation-dominated epoch, the perturbations in the short-wave limit behave in the same way as the radiation-like fluid in the longitudinal and the spatially-flat gauges. However, they behave in a different way in the comoving gauge. As a whole, we conclude that the second-order effective energy-momentum tensor of the scalar perturbation is strictly gauge dependent.

Ringing of rotating black holes in higher-derivative gravity

We compute scalar quasinormal mode (QNM) frequencies in rotating black hole solutions of the most general class of higher-derivative gravity theories, to quartic order in the curvature, that reduce to General Relativity for weak fields and are compatible with its symmetries. The wave operator governing the QNMs is not separable, but we show one can extract the QNM frequencies by a projection onto the set of spheroidal harmonics. We have obtained accurate results for the quasinormal frequency corrections relative to Kerr for rotating black holes with dimensionless spins up to $\sim 0.7$. We also discuss to what extent our results carry over to the phenomenologically more relevant case of gravitational QNMs. Finally we provide an ancillary computational package that allows one to generalize our calculations to any effective energy-momentum tensor arising from higher-derivative terms in the effective action.

Stealth spontaneous spinorization of relativistic stars

We investigate the behavior of the Dirac spinor fields in general relativistic high density stellar backgrounds and the possibility of spontaneous spinorization which is analogous to spontaneous scalarization. We consider the model with the modified kinetic term of the Dirac field by the insertion of the fifth gamma matrix ${\hat \gamma}^5$ and the conformal coupling of the Dirac spinor field to the matter sector, which would lead to the tachyonic growth of the Dirac spinor field in the high density compact stellar backgrounds. In order to obtain the static and spherically symmetric solutions, we have to consider the two Dirac fields at the same time. We show that in the constant density stellar backgrounds our model gives rise to the nontrivial solutions of the Dirac spinor fields with any number of nodes, where one mode has one more nodes than the other. We also show that at the leading order all the components of the effective energy-momentum tensor of the Dirac spinor fields, after the summation over the two fields, vanish for any separable time-dependent ansatz of the Dirac spinor fields in any static and spherically symmetric spacetime backgrounds, indicating that spontaneous spinorization takes place as a stealth process in the static and spherically symmetric spacetime with any number of nodes, which would be quenched by nonlinear effects and leave no observable effects.