Anisotropic Energy-momentum Tensor Research Articles

Some aspects of Morris–Thorne wormhole in Scalar–Tensor theory

In this work, we reach the equations of motion of Morris–Thorne wormhole geometry by means of the Einstein Field Equations and Klein–Gordon Equation of Scalar–Tensor Theory. We discuss the anisotropic matter energy distribution. We determine a relation between the radial and the transverse pressures. Hence, we express the anisotropic energy–momentum tensor in terms of one pressure class, by means of that relation. Besides that, we check the isotropic case and show that there is no traversable wormhole (WH), in the zero redshift function situation, if the energy–momentum distribution of the universe is isotropic. In addition, we represent the conditions in order that the Null Energy Condition (NEC) is satisfied in the zero redshift function case, for anisotropic distribution. We also propose a special class of traversable WH shape functions. We will be calling the WHs corresponding to that class of functions as the Yukawa Type WHs. We expressed the NEC for those WHs particularly. Furthermore, we determine the radial and the transverse pressures in zero redshift function situation.

Generalized Tolman-Oppenheimer-Volkoff model and neutron stars

This work is motivated by the existence of mapping the extended theory of gravity with a standard energy-momentum tensor to general relativity with a modified energy-momentum tensor. We construct a modified anisotropic energy-momentum tensor from a standard isotropic energy-momentum tensor by adding a ``geometrical correction'' to precisely reproduce the Tolman-Oppenheimer-Volkoff equations predicted by the generalized Tolman-Oppenheimer-Volkoff (GTOV) model. This construction aims to calculate the moment of inertia ($I$) and tidal deformability ($\mathrm{\ensuremath{\Lambda}}$) of neutron stars (NSs) within the GTOV model. Therefore, we can comprehensively investigate the role of each free parameter of the GTOV model in NS properties. Furthermore, through this construction we can also utilize physically acceptable stability conditions for anisotropic stars to constrain the physical range of each parameter value and investigate the existence of a correlation among the parameters of the GTOV model. Except for $\ensuremath{\alpha}$, we find that the values of the GTOV free parameters can be limited to acceptable ranges. We also find that the parameters $\ensuremath{\theta}$, $\ensuremath{\chi}$, and $\ensuremath{\beta}$ are correlated, and the parameter $\mathrm{\ensuremath{\Gamma}}\ensuremath{\rightarrow}0$. With these free parameter ranges in hand, we study the role of each parameter of the GTOV model in NS properties, including $I$ and $\mathrm{\ensuremath{\Lambda}}$. We also revisit the hyperon puzzle in NSs within the GTOV model. We find that the $\ensuremath{\theta}$ parameter plays a crucial role in controlling the NS maximum mass value. We also find that the threshold ${k}_{2}$ peak for NS is ${k}_{2}\ensuremath{\approx}0.167$. Furthermore, if we use parameter sets with $\ensuremath{\theta}=\ensuremath{-}1$, the mass-radius predictions are compatible with recent NICER data on PSR $\mathrm{J}0030+0451$ and PSR $\mathrm{J}0740+6620$.

The wormhole model with an exponential shape function in the Finslerian framework

This paper aims to study the wormhole model with an exponential shape function within the framework of Finsler geometry. By considering anisotropic energy-momentum tensor, we have analyzed the wormhole solution of the gravitational field equation in the Finslerian context. To investigate the viability of the Finslerian wormhole solution, we have discussed the energy conditions and the nature of the parameters like radial and transverse equation-of-state parameters and density. The force due to the contribution of gravity is examined along with the anisotropic force and hydrostatic force to verify whether the obtained exact Finslerian wormhole solution is in equilibrium or not. Further, we have observed that the solution is feasible and physically interesting for analyzing wormholes in the Finslerian structure of space-time.

Wormholes in Poincarè gauge theory of gravity

In this work, we study static spherically symmetric solutions representing wormhole configurations in Poincarè gauge theory ( PGT ). The gravitational sector of the Lagrangian is chosen as a subclass of PGT Lagrangians for which the spin-[Formula: see text] is the only propagating torsion mode. The spacetime torsion in PGT has a dynamical nature even in the absence of intrinsic angular momentum (spin) of matter, hence torsion can play a principal role in the case of usual spin-less gravitating systems. We therefore consider a spin-less matter distribution with an anisotropic energy–momentum tensor ( EMT ) as the supporting source for wormhole structure to obtain a class of zero tidal force wormhole solutions. It is seen that the matter distribution obeys the physical reasonability conditions, i.e. the weak ( WEC ) and null ( NEC ) energy conditions either at the throat and throughout the spacetime. We further consider varying equations of state in radial and tangential directions via definitions [Formula: see text] and [Formula: see text] and investigate the behavior of state parameters at the throat of wormhole. We observe that our solutions allow for wormhole configurations without the need of exotic matter. Observational features of the wormhole solutions are also discussed utilizing gravitational lensing effects. It is found that the light deflection angle diverges at the throat (which indeed, effectively acts as a photon sphere) and can get zero and negative values depending on the model parameters.

Black holes with a cosmological constant in bumblebee gravity

In this work, we present black hole solutions with a cosmological constant in bumblebee gravity, which provides a mechanism for the Lorentz symmetry violation by assuming a nonzero vacuum expectation value for the bumblebee field. From the gravitational point of view, such solutions are spherically symmetric black holes with an effective cosmological constant and are supported by an anisotropic energy-momentum tensor, conceived of as the manifestation of the bumblebee field in the spacetime geometry. Then we calculate the shadow angular radius for the proposed black hole solution with a positive effective cosmological constant. In particular, our results are the very first relation between the bumblebee field and the shadow angular size.

The effect of anisotropic stress and non-adiabatic pressure perturbations on the evolution of the comoving curvature perturbation

We derive the equation for the evolution of the curvature perturbation on the comoving time slice, , in the presence of anisotropic and non-adiabatic terms in the energy–momentum tensor of matter fields. The equation is obtained by manipulating the perturbed Einstein’s equations in the comoving time slice. It could be used to study the evolution of the comoving curvature perturbations for systems with an anisotropic energy–momentum tensor, such as in the presence of vector fields, in the presence of entropy, such as in a multi-field system, or in modified gravity theories. As a simple application, after checking that the comoving time slice for a multi-field system does not coincide with the uniform field time slice in general, we use the equation in the case of two minimally coupled scalar fields and derive a closed set of equations for the curvature and entropy perturbations on the comoving time slice.

From the colour glass condensate to filamentation: systematics of classical Yang\u2013Mills theory

The non-equilibrium early time evolution of an ultra-relativistic heavy ion collision is often described by classical lattice Yang–Mills theory, starting from the colour glass condensate (CGC) effective theory with an anisotropic energy momentum tensor as initial condition. In this work we investigate the systematics associated with such studies and their dependence on various model parameters (IR, UV cutoffs and the amplitude of quantum fluctuations) which are not yet fixed by experiment. We perform calculations for SU(2) and SU(3), both in a static box and in an expanding geometry. Generally, the dependence on model parameters is found to be much larger than that on technical parameters like the number of colours, boundary conditions or the lattice spacing. In a static box, all setups lead to isotropisation through chromo-Weibel instabilities, which is illustrated by the accompanying filamentation of the energy density. However, the associated time scale depends strongly on the model parameters and in all cases is longer than the phenomenologically expected one. In the expanding system, no isotropisation is observed for any parameter choice. We show how investigations at fixed initial energy density can be used to better constrain some of the model parameters.

Charged wormhole solutions in Einstein-Cartan gravity

Static solutions representing wormhole configurations in Einstein-Cartan theory ({{\sf ECT}}) in the presence of electric charge are obtained. The solutions are described by a constant redshift function with matter content consisting of a Weyssenhoff fluid along with an anisotropic matter and energy momentum tensor ({\sf EMT}) of the electric field which together generalize the anisotropic energy momentum tensor in Einstein-Maxwell theory in order to include the effects of the intrinsic angular momentum (spin) of the particles. Assuming the equation of state ({{\sf EoS}}) $p_r={\sf w}_1\rho$ and $p_t={\sf w}_2\rho$, we derive exact wormhole solutions satisfying weak and null energy conditions. Depending on the value of the spin square density at the wormhole throat these solutions can be asymptotically flat, de-Sitter or anti de-Sitter. Observational aspects of the wormhole solutions are also studied, using gravitational lensing effects. It is found that the throat can act as a photon sphere near which the light deflection angle has arbitrarily large values. Moreover, for a particular class of solutions, when ${\sf w}_1\rightarrow-{\sf w}_2$ the lensing features of the present model mimic those of the Ellis wormhole in the weak field limit.

Inverse problem: What can we tell about the matter and energy in our Universe from its dimensionality and evolution

The most popular theories of everything are various versions of the superstring theory. The theories require existence of additional space dimensions, vibrations of which create the material particles in [Formula: see text] space. The additional space dimensions are understood as being currently smaller than the Planck Length and due to this not directly observable. We search for multidimensional models of the Universe (one time dimension; three isotropic, flat external dimensions, and [Formula: see text]-internal dimensions), which satisfy the multidimensional Einstein equations and which started from the same radius of all of the internal and external dimensions, with an anisotropic energy–momentum tensor. Analytical solution of [Formula: see text]-dimensional Einstein equation in a reparameterized time is reminded and discussed. The energy–momentum tensor is solely responsible for expansion of the external dimensions and shrinking of the internal ones; and to obtain this behavior of the space the tensor needs to fulfill some conditions i.e. the energy–momentum tensor cannot include only radiation, vacuum and baryonic matter. For the behavior of the physical space consistent with the one observed in our Universe, the dark energy and/or dark matter have to exist.

Neutron stars in the braneworld within the Eddington-inspired Born-Infeld gravity

We propose the disappearance of “the hyperon puzzle” in neutron star (NS) by invoking two new-physics prescriptions: modified gravity theory and braneworld scenario. By assuming that NS lives on a 3-brane within a 5d empty AdS bulk, gravitationally governed by Eddington-inspired Born-Infeld (EiBI) theory, the field equations can be effectively cast into the usual Einstein's with “apparent” anisotropic energy-momentum tensor. Solving the corresponding brane-TOV equations numerically, we study its mass-radius relation. It is known that the appearance of finite brane tension λ reduces the compactness of the star. The compatibility of the braneworld results with observational constraints of NS mass and radius can be restored in our model by varying the EiBI's coupling constant, κ. We found that within the astrophysically-accepted range of parameters (0<κ<6×106m2 and λ≫1 MeV4) the NS can have mass ∼2.1 M⊙ and radius ∼10 km.

Dynamic wormhole solutions in Einstein-Cartan gravity

In the present work we investigate evolving wormhole configurations described by a constant redshift function in Einstein-Cartan theory ({{\sf ECT}}). The matter content consists of a Weyssenhoff fluid along with an anisotropic matter which together generalize the anisotropic energy momentum tensor in general relativity ({{\sf GR}}) in order to include the effects of intrinsic angular momentum (spin) of particles. Using a generalized Friedmann-Robertson-Walker ({\sf FRW}) spacetime, we derive analytical evolving wormhole geometries by assuming a particular equation of state ({{\sf EoS}}) for energy density and pressure profiles. We introduce exact asymptotically flat and anti-de Sitter spacetimes that admit traversable wormholes and respect energy conditions throughout the spacetime. The rate of expansion of these evolving wormholes is determined only by the Friedmann equation in the presence of spin effects.

Einstein-Cartan wormhole solutions

In the present work we investigate wormhole structures and the energy conditions supporting them, in Einstein-Cartan theory ({\sf ECT}). The matter content consists of a Weyssenhoff fluid along with an anisotropic matter which together generalize the anisotropic energy momentum tensor in general relativity ({\sf GR}) to include spin effects. Assuming that the radial pressure and energy density obey a linear equation of state, we introduce exact asymptotically flat and anti-de-Sitter spacetimes that admit traversable wormholes and respect energy conditions. Such wormhole solutions are studied in detail for two specific forms for the redshift function, namely a constant redshift function and the one with power law dependency.

Dynamical instability of cylindrical symmetric collapsing star in generalized teleparallel gravity

This paper is devoted to analyze the dynamical instability of a self-gravitating object undergoes to collapse process. We take the framework of generalized teleparallel gravity with cylindrically symmetric gravitating object. The matter distribution is represented by locally anisotropic energy-momentum tensor. We develop basic equations such as dynamical equations along with matching conditions and Harrison-Wheeler equation of state. By applying linear perturbation strategy, we construct collapse equation which is used to accomplish the instability ranges in Newtonian and post-Newtonian regimes. We find these ranges for isotropic pressure as well as reduce the results in general relativity. The unstable behavior depends on matter, metric, mass and torsion based terms.

Anisotropic stellar structure equations for magnetized strange stars

The fact that a fermion system in an external magnetic field breaks the spherical symmetry suggests that its intrinsic geometry is axisymmetric rather than spherical. In this work we analyze the impact of anisotropic pressures, due to the presence of a magnetic field, in the structure equations of a magnetized quark star. We assume a cylindrical metric and an anisotropic energy momentum tensor for the source. We found that there is a maximum magnetic field that a strange star can sustain, closely related to the violation of the virial relations.

Cosmic strings in $$f\left( R,L_m\right) $$ f R , L m gravity

We consider Kasner-type static, cylindrically symmetric interior string solutions in the $$f\left( R,L_m\right) $$ theory of modified gravity. The physical properties of the string are described by an anisotropic energy-momentum tensor satisfying the condition $$T_t^t=T_z^z$$ ; that is, the energy density of the string along the $$z$$ -axis is equal to minus the string tension. As a first step in our study we obtain the gravitational field equations in the $$f\left( R,L_m\right) $$ theory for a general static, cylindrically symmetric metric, and then for a Kasner-type metric, in which the metric tensor components have a power law dependence on the radial coordinate $$r$$ . String solutions in two particular modified gravity models are investigated in detail. The first is the so-called “exponential” modified gravity, in which the gravitational action is proportional to the exponential of the sum of the Ricci scalar and matter Lagrangian, and the second is the “self-consistent model”, obtained by explicitly determining the gravitational action from the field equations under the assumption of a power law dependent matter Lagrangian. In each case, the thermodynamic parameters of the string, as well as the precise form of the matter Lagrangian, are explicitly obtained.

Higher Dimensional Spherically Symmetric Expanding Wormholes in Einstein’s Gravity

We present (n+1)-dimensional expanding structures in a cosmological background. Due to the expansion of spacetime the throat of wormholes enlarge with time. These solutions are examined in the Einstein’s framework. A general linear relation between diagonal elements of an anisotropic energy-momentum tensor is assumed and the spherically symmetric structures are obtained. Solutions include naked singularity and expanding wormholes in an open universe. The traversibility of wormhole solutions is explored and we find that they are basically traversable. Finally, we consider the corresponding energy-momentum tensor properties and specially take into account the standard energy conditions.

The influence of strong magnetic fields on proto-quark stars

We analyze different stages of magnetized quark star evolution incorporating baryon number conservation and using an anisotropic energy–momentum tensor. The first stages of the evolution are simulated through the inclusion of trapped neutrinos and fixed entropy per particle, while in the last stage the star is taken to be deleptonized and cold. We find that, although strong magnetic fields modify quark star masses, the evolution of isolated stars needs to be constrained by fixed baryon number, which necessarily lowers the possible star masses. Moreover, magnetic field effects, measured by the difference between the parallel and perpendicular pressures, are more pronounced in the beginning of the star evolution, when there is a larger number of charged leptons and up quarks. We also show that having a spatially varying magnetic field allows for larger magnetic fields to be supported.

An anisotropic standing wave braneworld and associated Sturm–Liouville problem

We present a consistent derivation of the recently proposed 5D anisotropic standing wave braneworld generated by gravity coupled to a phantom-like scalar field. We explicitly solve the corresponding junction conditions, a fact that enables us to give a physical interpretation to the anisotropic energy–momentum tensor components of the brane. So matter on the brane represents an oscillating fluid which emits anisotropic waves into the bulk. We also analyze the Sturm–Liouville problem associated with the correct localization condition of the transverse to the brane metric and scalar fields. It is shown that this condition restricts the physically meaningful space of solutions for the localization of the fluctuations of the model.

BRANEWORLDS AND DARK MATTER

Two problems related to dark matter are considered in the context of a braneworld model in which the confinement of gauge fields on the brane is achieved by invoking a confining potential. First, we show that the virial mass discrepancy can be addressed if the conserved geometrical term appearing in this model is considered as an energy–momentum tensor of an unknown type of matter, the so-called X-matter whose equation of state (EoS) is also obtained. Second, the galaxy rotation curves are explained by assuming an anisotropic energy–momentum tensor for the X-matter.

On the existence of certain axisymmetric interior metrics

One of the effects of noncommutative coordinate operators is that the delta function connected to the quantum mechanical amplitude between states sharp to the position operator gets smeared by a Gaussian distribution. Although this is not the full account of the effects of noncommutativity, this effect is, in particular, important as it removes the point singularities of Schwarzschild and Reissner–Nordström solutions. In this context, it seems to be of some importance to probe also into ringlike singularities which appear in the Kerr case. In particular, starting with an anisotropic energy-momentum tensor and a general axisymmetric ansatz of the metric together with an arbitrary mass distribution (e.g., Gaussian), we derive the full set of Einstein equations that the noncommutative geometry inspired Kerr solution should satisfy. Using these equations we prove two theorems regarding the existence of certain Kerr metrics inspired by noncommutative geometry.