Effective Energy Momentum Research Articles

Radiative properties and QPOs around charged black hole in Kalb–Ramond gravity

Studies of accretion disc luminosities and quasiperiodic oscillations around black holes may help us understand the gravitational properties of black hole spacetime. This work is devoted to studying the radiation properties of the accretion disk around the black holes in Kalb–Ramond gravity. We investigate the event horizon of the black hole spacetime and calculate the effective gravitational mass of the spacetime. Also, we analyze the circular motion of test particles in the black hole spacetime. The effects of the black hole charge and KR parameters on the particles’ effective mass, energy, and angular momentum at circular orbits and innermost stable circular orbits are studied. The frequency of Keplerian orbits and the radial and vertical oscillations of the particles along stable orbits are calculated and applied to analyze the existence of QPO in relativistic precession, warped disc, and epicyclic resonance models. QPO orbits’ locations with ratios of upper and lower frequencies of twin-peaked QPOs 3:2, 4:3, and 5:4 are analyzed compared to ISCO. We also obtain constrain values for the black hole mass, charge, KR field parameter, and QPO orbits found using Markovian chain Monte Carlo (MCMC) simulations for stellar mass (XTE J1550, GRS 1915+105), intermediate mass (M82-X1), and supermassive black holes (Sgr A*). Finally, we explore the radiative properties of the accretion disk around the charged black hole in KR gravity, such as the total radiation flux, accretion disc temperature, and differential luminosity.

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.

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.

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.

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.

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.

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.

Viable wormhole solutions in energy–momentum squared gravity

This paper investigates static wormhole solutions through Noether symmetry approach in the context of energy–momentum squared gravity. This newly developed proposal resolves the singularity of big bang and yields feasible cosmological results in the early times. We consider the particular model of this theory to establish symmetry generators and corresponding conserved quantities. For constant and variable red-shift functions, we examine the presence of viable traversable wormhole solutions for both dust and non-dust matter distributions and analyze the stable state of these solutions. We investigate the graphical interpretation of null and weak energy bounds for normal and effective energy–momentum tensors to examine the presence of physically viable wormhole geometry. It is found that realistic traversable and stable wormhole solutions are obtained for a particular model of this gravity.

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.

Parity violation in Poincaré gauge gravity

We analyze the parity violation issue in the Poincaré gauge theory of gravity for the two classes of models which are built as natural extensions of the Einstein–Cartan theory. The conservation laws of the matter currents are revisited and we clarify the derivation of the effective Einstein field equation and the structure of the effective energy–momentum current for arbitrary matter sources.

Some properties and implications of the creation pressure and the generalized equilibrium: modification of the adiabatic index, cosmological perturbations

The creation pressure, due to constant specific entropy particle production, vanishes for a fluid where the sum of the energy density and the isotropic pressure is zero; for example in an empty space–time with the cosmological constant interpreted as vacuum energy density. Within the framework of relativistic thermodynamics theories, the energy–momentum tensor of a linear barotropic fluid with constant specific entropy particle production and in generalized equilibrium can be written as the effective energy–momentum tensor of a perfect linear barotropic fluid where the adiabatic index is a homographic function of the initial adiabatic index. This function shows that by adding constant specific entropy particle production to a phantom fluid, the effective perfect fluid will be without phantom property, whereas there are some fluids that with specific entropy particle production have phantom property. This transformation is useful for obtaining the behaviour of the scale factor of cosmological models. By solving the equation that comes from the entropy production equation, then the transport equation in the framework of the Muller-Israel-Stewart second-order causal relativistic thermodynamics, assuming constant specific entropy particle production and the generalized equilibrium, we obtain the bulk viscosity coefficient ζ and the relaxation time τ. The relation ζ ∝ $$ \rho^{{\frac{1}{2}}} $$ between ζ and the energy density ρ is predicted in spatially flat homogeneous and isotropic (FLRW) cosmological model for any value of the constant state parameter. The gauge–invariant energy density contrast and velocity perturbations of the previous cosmological model in the matter-dominated era with isentropic particle production are studied. The modes of these perturbations are decaying faster than the corresponding modes for the perfect fluid perturbations in the particle number conservation case. Then the isentropic, usually called adiabatic, gauge–invariant energy density contrast and velocity perturbations in case of a perfect linear barotropic fluid with particle number conservation are studied, in particular for negative values of the constant state parameter.

Gravastars in f(R,T,RμνTμν) gravity

This work is devoted to study the analytical and regular solutions of a particular self-gravitating object (i.e., gravastar) in a particular theory of gravity. We derive the corresponding field equations in the presence of effective energy momentum tensor associated with the perfect fluid configuration of a spherical system. We then describe the mathematical formulations of the three respective regions i.e., inner, shell and exterior of a gravastar separately. Additionally, the significance and physical characteristics along with the graphical representation of gravastars are discussed in detail. It is seen that under some specific constraints, $f(R,T,R_{\mu\nu}T^{\mu\nu})$ gravity is likely to host gravastars.

Exact solutions of Einstein-\xe6ther gravity in Bianchi type V cosmology

We present the solution space of the field equations in the Einstein-æther theory for the case of a vacuum Bianchi Type V space-time. We also find that there are portions of the initial parameters space for which no solution is admitted by the reduced equations. Whenever solutions do exist, their physical interpretation is examined through the behavior of Ricci and/or Kretsmann scalar, as well as with the identification of the effective energy momentum tensor in terms of a perfect fluid. There are cases in which no singularities appear and others where the effective fluid is isotropic.

Effect of f(R)-Gravity Models on Compact Stars

We study the possibility of forming anisotropic compact stars in the framework of $f(R)$-modified gravity in a static spherically symmetric space–time. We find the unknown coefficients involved in the metric using masses and radii of the compact stars 4U 1820-30, Cen X-3, EXO 1785-248, and LMC X-4. We obtain the hydrostatic equilibrium equation for different forces and use the generalized Tolman–Oppenheimer–Volkoff equation to analyze the behavior of stars. Moreover, we verify the regularity conditions, anisotropic behavior, energy conditions, and stability of the compact stars. We use the effective energy–momentum tensor in $f(R)$ gravity for the analysis. We show that in the framework of $f(R)$ gravity theory, these compact stars have physically acceptable patterns. Our results here also agree with those in general relativity, which is a special case of $f(R)$ gravity.

Superhorizon effects on the gauge invariant effective energy density in f(R) gravity

In this article we study the gauge invariant effective energy momentum tensor for cosmological perturbations in f(R) gravity during the inflationary epoch. Considering the super-horizon regime, we derive the effective energy density up to the one-loop corrections. It describes the back-reaction effect of the fluctuations on the background space-time.

Gravitational perturbations of nonsingular black holes in conformal gravity

It is believed that in the near future, gravitational wave detections will become a promising tool not only to test gravity theories, but also to probe extremely curved spacetime regions in our universe, such as the surroundings of black holes. In this paper, we investigate the quasinormal modes (QNMs) of the axial gravitational perturbations of a class of non-singular black holes conformally related to the Schwarzschild black hole. These non-singular black holes can be regarded as the vacuum solution of a family of conformal gravity theories which are invariant under conformal transformations. After conformal symmetry is broken, these black holes produce observational signatures different from those of the Schwarzschild black hole, such as their QNM frequencies. We assume that the spacetime is described by the Einstein equation with the effective energy momentum tensor of an anisotropic fluid. The master equation describing the QNMs is derived, and the QNM frequencies are evaluated with the Wentzel-Kramers-Brillouin (WKB) method up to the 6th order. As expected, the QNM spectra of these non-singular black holes deviate from those of the Schwarzschild black hole, indicating the possibility of testing these black hole solutions with the help of future gravitational wave detections.

Galactic halo traversable wormhole solutions in f(𝒢,T) gravity

This paper explores static spherically symmetric wormhole solutions in the galatic halo region for [Formula: see text] gravity ([Formula: see text] and [Formula: see text] represent the Gauss–Bonnet invariant and trace of the energy–momentum tensor, respectively). We formulate the explicit expressions for matter variables and evaluate wormhole solutions either specifying [Formula: see text] model to construct shape function or taking specific form of the shape function to determine [Formula: see text] model. It is found that null energy condition for the effective energy–momentum tensor is violated throughout the evolution in both cases while physically acceptable wormhole solutions exist only for a considered [Formula: see text] model.

Rotational motion of a stationary axisymmetric relativistic heat conducting fluid configuration

The present work describes some dynamical features associated with the dissipation caused by the heat flow in the context of rotational motion of a heat conducting fluid based on Carter’s two-fluid model. A covariant solutions to a pair of Maxwell’s like equations governing the evolution of a heat conducting fluid are used to determine the heat flow vector and the matter part of fluid’s 4-velocity under the assumption that the space-time configuration representing the gravitational field of a heat conducting fluid is non-circular stationary and axisymmetric. These results are used to derive the rotational velocity in terms of gradients of the effective energy and effective angular momentum per particle. It is demonstrated that the meridional circulations of the matter part of fluid induce the rotational velocity in addition to the usual rotational velocity found in a circular space-time. It is shown that the differential rotation along the thermal –fluid vorticity causes the twist of matter part of fluid’s vortex lines in addition to the other effects .It is found that the gravitational isorotation is balanced by counter rotating thermal isorotation in the case of differentially rotating thermal-fluid surfaces in a frame of reference in which thermal –fluid helicity is conserved. The dynamic interaction between the matter part of fluid and the entropy fluid leads to the mutual exchange between the energy and angular momentum per baryon of the matter part of fluid and the flux of energy and angular momentum per entropon per unit of local temperature coupled to heat flow vector created by the entropy fluid.

Viable wormhole solutions and Noether symmetry in [formula omitted] gravity

This paper investigates wormhole solutions of spherically symmetric spacetime via Noether symmetry approach in f(R,T) gravity. For this purpose, we choose f(R,T) models appreciating indirect curvature–matter coupling and examine symmetry generators with associated conserved quantities. We determine possible existence of realistic traversable wormhole solutions for both dust as well as non-dust distributions and also study stable behavior of these solutions. For both models, we use constant as well as variable forms of red-shift function. To analyze physical existence of wormhole solutions, we study the behavior of null/weak energy conditions with respect to ordinary as well as effective energy–momentum tensors. It is concluded that there exist physically viable traversable as well as stable wormhole solutions in most of the cases.