Einstein Equations Research Articles

General relativistic moving-mesh hydrodynamic simulations with arepo and applications to neutron star mergers

ABSTRACT We implement general relativistic hydrodynamics in the moving-mesh code arepo. We also couple a solver for the Einstein field equations employing the conformal flatness approximation. The implementation is validated by evolving isolated static neutron stars using a fixed metric or a dynamical space–time. In both tests, the frequencies of the radial oscillation mode match those of independent calculations. We run the first moving-mesh simulation of a neutron star merger. The simulation includes a scheme to adaptively refine or derefine cells and thereby adjusting the local resolution dynamically. The general dynamics are in agreement with independent smoothed particle hydrodynamics and static-mesh simulations of neutron star mergers. Coarsely comparing, we find that dynamical features like the post-merger double-core structure or the quasi-radial oscillation mode persist on longer time scales, possibly reflecting a low numerical diffusivity of our method. Similarly, the post-merger gravitational wave emission shows the same features as observed in simulations with other codes. In particular, the main frequency of the post-merger phase is found to be in good agreement with independent results for the same binary system, while, in comparison, the amplitude of the post-merger gravitational wave signal falls off slower, i.e. the post-merger oscillations are less damped. The successful implementation of general relativistic hydrodynamics in the moving-mesh arepo code, including a dynamical space–time evolution, provides a fundamentally new tool to simulate general relativistic problems in astrophysics.

Compact stellar model with vanishing complexity under Vaidya–Tikekar background geometry

We make use of the condition of vanishing complexity, based on the current definition proposed by Herrera (Phys Rev D 97:044010, 2018), to find exact interior solutions to the Einstein equations for describing compact stellar objects. In the framework of general relativity, the complexity factor is an outcome of the orthogonal splitting of the Riemann tensor from which structure scalars are obtained. By using the Vaidya–Tikekar (V–T) metric ansatz (J Astrophys Astron 3:325, 1982) for the spacetime of a static spherically symmetric matter distribution, we model superdense, relativistic stars. The interior spacetime is matched to the exterior Schwarzschild solution across the boundary of the star where the radial pressure vanishes. The physical viability of the model has been tested following the current data corresponding to the pulsar 4U1820-30\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ 4U 1820-30 $$\\end{document}. The stability of the model fulfilled the given criteria, namely the Tolman–Oppenheimer–Volkoff equation, the adiabatic index and the causality conditions.

An Einstein-Maxwell interior solution obeying Karmarkar condition

For the Einstein-Maxwell equation system, with perfect fluid in a static and spherically symmetrical spacetime, we report an analytical internal solution which is obtained by imposing the Karmarkar condition, the behaviour of the solution is such that the density and pressures are monotonically decreasing functions while the electric field function is a monotonically increasing function that is adequate to represent compact objects. In particular we have these characteristics for the observational values of mass (1.29 ± 0.05) M⊙ and radius (8.831 ± 0.09) km of the star SMC X-4. We will analyze the two extremes the one of minimum compactness umin = 0.20523 (M = 1.24 M⊙, R = 8.921 km) and the one of maximum compactness umax = 0.22635 (M = 1.34 M⊙, R = 8.741 km), resulting that the electric charge Qumin ∈ [1.5279, 1.8498]1020C and Qumax ∈ [1.6899, 1.9986]1020C respectively, implying that the case with higher compactness has a higher electric charge. Also in a graphic manner, it is shown that the causality condition is satisfied and that the solution is stable against infinitesimal radial adiabatic perturbation and also in regards to the Harrison-Novikov-Zeldovich criteria

Spherically-symmetric non-static solutions of Einstein’s equations

In this paper, we considered non-static vacuum spherically symmetric solutions of the Einstein equations and harmonicity conditions in the coordinate system with a non-zero space-time component in the metric. For the case of the weak field, a particular solution of the approximate equations was obtained, which corresponds to a nonstatic source whose boundary moves with a constant speed. For the exact Einstein’s equations we obtained a wave-type solution, determined by two implicitly specified functions, depending on the retarded argument and on the radial coordinate, respectively. The connection between these solutions and the Birkhoff theorem is discussed.

Masses at null infinity for Einstein's equations in harmonic coordinates

Masses at null infinity for Einstein's equations in harmonic coordinates

Osnovna saznanja o crnim rupama

Introduction/purpose: Starting from general relativity, black hole generation and effects are investigated. Method: Einstein's equation and its Schwarzschild solution are employed to study black holes. Quantum mechanics is used to obtain Hawking's radiation. Results: Black holes are actually not completely black - they radiate energy during their lifetime. Conclusions: Black holes could evaporate and this effect is observable if their mass is sufficiently small. Their entropy scales differently with respect to their mass from that of other objects in thermodynamics.

Light propagation in the vicinity of the ModMax black hole

ModMax is a nonlinear electrodynamics theory with the same symmetries as Maxwell electrodynamics. Static spherically symmetric solutions have been derived by coupling ModMax electrodynamics with the Einstein equations, which can represent a black hole. In this paper, we analyze light propagation in the vicinity of the ModMax black hole. We determine birefringence, light trajectories, deflection, redshifts, as well as the shadow of the black hole using the effective or optical metric to determine the optical paths of light; comparison is done with the corresponding effects in the neighborhood of the Reissner-Nordstrom black hole, that is the solution to the Einstein-Maxwell equations.

The Einstein equation solution inside a ball with uniform density

A great number of solutions of the Einstein field equation are known. They describe the gravitational field in the empty space-time, in the space-time with electromagnetic field and for a ball filled with a liquid under pressure. The present work is devoted to gravitational field generated by some mass distribution. One of the simplest cases is considered, when mass is uniformly distributed inside a ball and is not moving. The boundary problem for the Einstein equation is formulated. Solution outside the ball is the Schwartzschild solution in vacuum. The coordinates at which the Schwartzschild solution is written are different from the coordinates used in equations for components of the metric tensor inside the ball. Relations between internal and external coordinates are found on the ball surface. They allow to use the Schwartzschild solution for formulation of boundary conditions for internal solution. The solution of the boundary problem is found for the case of weak field. This solution can be used as an example in the analysis of laws of conservation for the gravitational field, in which interaction of mass with field generated by the mass gives a contribution to momentum and energy of the gravitational field.

Modelling of Charged Dark Energy Stars in a Tolman IV Spacetime

In this paper, we obtained a new class of solutions for the Einstein-Maxwell field equations with a charged anisotropic matter distribution considering the dark energy equation of state r p = ωρ , where ω is the dark energy parameter, is the radial pressure and is the energy density. We have chosen a form for the metric potential proposed for Tolman (1939) known as Tolman IV type potential. We found that the physical properties as the radial pressure, the anisotropy, energy density, mass function are regular and well behaved in the stellar interior but the strong energy condition is violated. The models are consistent with the upper limit on the mass of compact stars for Her X-1, 4U1538-52 and SAXJ1808.4-3658.

Study of Dark Energy Stars in a Buchdahl Spacetime

In this paper we obtained some spherically stellar configurations that represent new models of dark energy stars specifying particular forms for gravitational potential and the electric field intensity which allows solve the Einstein-Maxwell field equations. We have chosen the metric potential proposed by Buchdahl (1959) with the equation of state pr = wp where pr is the radial pressure, p is the dark energy density and w is the dark energy parameter. We found that the radial pressure, the anisotropy factor, energy density, metric coefficients, mass function, charge density are regular and well behaved in the stellar interior but the causality conditions and of strong energy are not satisfied. These models have great application in physics and cosmology due to the fact that several independent observations indicate that the universe is in a phase of accelerated expansion which can be explained by the presence of dark energy that has not been detected.

Non-Equilibrium Thermodynamics in the Non-Canonical Scalar Field Perturbed Space-Time: Stability Analysis

The space-time of the Universe has been perturbed under a scalar field ϕ considering the minimum coupling between and the background metric. The solutions of Einstein field equations have been obtained under perturbed geometry and the corresponding conservation equation shows the non-equilibrium thermodynamic prescription of the cosmic fluid. Following the stability criteria of the cosmic fluid along with the laws of thermodynamics, some constraints have been imposed on the choice of ϕ.

Quantum Extensions to the Einstein Field Equations

Quantum Extensions to the Einstein Field Equations

Математическая теория ускоренного расширения Вселенной на основе принципа наименьшего действия и модели Фридмана и Милна-Маккри

In classical works, equations for the fields of gravity and electromagnetism are proposed without deriving the right-hand sides. Here we give the derivation of the right-hand sides and analysis of the stress–energy tensor within the framework of the Vlasov–Maxwell–Einstein equations and models of the Milne–McCrea and Friedman type. New models of the accelerated expansion of the Universe without Einstein's lambda are proposed.

Characteristic gluing with $\Lambda$: 1. Linearised Einstein equations on four-dimensional spacetimes

Characteristic gluing with $\Lambda$: 1. Linearised Einstein equations on four-dimensional spacetimes

Possibility of stable thin-shell around wormholes within string cloud and quintessential field via the van der Waals and polytropic EOS

In this work, we present the Einstein field equations (EFE) in the framework of a modified matter source and thus find out the solutions for the Wormhole. To obtain characteristic solutions set, we employ two kinds of equations of states (EOS), i.e., the van der Waals and polytropic EOS to the EFE. We adopt embedding class as a general technique for the system and discuss several physical attributes of the stellar system under embedded wormhole solutions. Detailed discussion about the matter contents of the thin-shell developed around the obtained wormhole solutions in the background of Schwarzschild BH surrounded by cloud and quintessence-type fluid distribution by using a well-known cut and paste approach. We have also performed stability analysis using the linearized radial perturbation method for the van der Waals EOS and polytropic EOS. Several interesting points have evolved from the entire investigation along with the features of the thin shell around the wormhole. It is interesting to mention that the van der Walls equation of state plays a remarkable role to maintain the stability of the thin-shell around the wormhole structure as compared to polytropic model for both choices of shape functions.

MATHEMATICAL ANALYSIS OF COSMOLOGICAL MODELS WITH LINEARLY VARYING DECELERATION PARAMETER

Bianchi type-V is investigated using a decaying cosmological constant with perfect fluid. The study solves Einstein field equations by assuming that the deceleration parameter q is functionally connected to the Hubble parameter H, which yields the scale factor a. As cosmic time t increases, the cosmological model experiences exponential inflation. The physical characteristics and behavior of the cosmological model are also covered.

Statefinder Diagnostic of Interacting Dark Fluid in Bianchi Type-IX Universe

In this paper, we deal with spatially homogeneous and anisotropic Bianchi types-IX and Universe filled with Holographic dark energy and cold dark matter. Assuming the condition that the shear scalar is proportional to expansion scalar, we have obtained solutions of Einstein field equations. The Statefinder diagnostic pair i.e. {r‚s} is adopted to distinguish our dark energy models from other dark energy models. Some important physical features of the models have been discussed.

Charged stellar structure in f(R,ϕ) gravity admitting Chaplygin equation of state

The aim of this paper is to examine the singularity-free solutions for anisotropic stellar structures in [Formula: see text] theory of gravity, where [Formula: see text] denotes the Ricci scalar and [Formula: see text] represents the scalar field. For this purpose, we consider the spherically symmetric spacetime to discuss the stellar structures with anisotropic fluid. Moreover, the Einstein field equations are solved by using Chaplygin equation of state, and the Karori–Barua metric. To analyze the charged stellar structure, we use the matching conditions of spherically symmetric spacetime with the Reissner–Nordstrom exterior metric and develop some expressions for finding the unknown parameters. We further investigate the graphical behavior of energy density, pressure components, anisotropic component, equation of state parameters, equilibrium condition, stability analysis, adiabatic index and energy conditions. Conclusively, our considered stellar structures under observations are realistic, stable, and are free from any singularities.

A study of compact stars within Rastall gravity

In this paper, we construct the exact interior solutions for compact stellar objects for perfect fluid distribution in phantom region in the framework of a non-conserved theory, i.e. Rastall gravity (RG). Under these circumstances, we develop the Einstein field equations (EFEs) for spherically symmetric metric using general forms of metric potentials, [Formula: see text] and [Formula: see text], here [Formula: see text] and [Formula: see text]. By matching of interior and exterior regions of the metric, we obtain the values of unknown constants of our considering model which helps to sketch the nature of important physical quantities like density, pressure, energy conditions, and stability. Finally, our obtained results lead us to conclude that our solutions are well behaved and physically viable for the specific choices of model parameters for two different stars (Vela X-1 and 4U1820-30).

The geometry of the Rindler black hole

Using Einstein's equations for gravity for a spherically symmetric field in a static state and the mass function method, a general form of the metric for Schwarzschild-type black holes is proposed. A qualitative analysis of Schwarzschild, Reissner–Nordström and Rindler geometries is performed. In the paper, it is found that Rindler black hole geometry is structurally inverse to Reissner–Nordström geometry, i.e. it has two T-regions and one R-region. In this regard Rindler geometry is like geometry of the Kottler black hole, which does not have flat asymptotics. Potential curves in the gravitational field of the Rindler black hole are constructed, which makes it possible to calculate the limits of finite motion for a test particle in this field. In addition, a qualitative comparison with the known Schwarzschild field metric is performed. Their similarity in behavior at small distances and absolutely different behavior at large scales are shown. Using the known accelerations of the Pioneer spacecraft, limits are numerically found for the T- and R-regions of their motion in the gravitational field of the Solar System.