General Relativity and Gravitation最新文献

This paper explores the viability and stability of compact stellar objects characterized by anisotropic matter in the framework of (f(textrm{Q},textrm{T})) theory, where (textrm{Q}) denotes non-metricity and (textrm{T}) represents the trace of the energy-momentum tensor. We consider a specific model of this theory to obtain explicit expressions for the field equations governing the behavior of matter and geometry in this context. Furthermore, the Karmarkar condition is employed to assess the configuration of static spherically symmetric structures. The values of unknown constants in the metric potentials are determined through matching conditions of the interior and exterior spacetimes. Various physical quantities such as fluid parameters, energy constraints, equation of state parameters, mass, compactness and redshift are graphically analyzed to evaluate the viability of the considered compact stars. The Tolman–Oppenheimer–Volkoff equation is used to examine the equilibrium state of the stellar models. Moreover, the stability of the proposed compact stars is investigated through sound speed and adiabatic index methods. This study concludes that the proposed compact stars analyzed in this theoretical framework are viable and stable, as all the required conditions are satisfied.

The triumph of general relativity under the banner “gravity is geometry” began with confirming the crucial effects within the Solar system and proceeded recently to the strong-field shadow effect for the compact object in the center of the Milky Way. Here, we examine some of those phenomena for the Einstein-scalar equations in the antiscalar regime to reveal the difference from vacuum both in weak and strong fields. As a result, we find that for week-field perihelion shift the difference between vacuum and antiscalar cases proves to be observationally imperceptible in practice, even for S-cluster stars with high eccentricities, except for the S62 star with measurable difference per century. In strong-field case, we reconsider the shadow effect (this time without involving complex-valued scalar field) as the most perspective from an observational viewpoint. Even though the resulting difference is quite appreciable (about 5%), no conclusion can be made until the mass of the central object is known with the accuracy an order of magnitude higher than the currently available.

Abstract

Within the context of Rastall gravity, we investigate the hydrostatic equilibrium and dynamical stability against radial pulsations of compact stars, where a free parameter (beta ) measures the deviations from General Relativity (GR). We derive both the modified Tolman–Oppenheimer–Volkoff (TOV) equations and the Sturm–Liouville differential equation governing the adiabatic radial oscillations. Such equations are solved numerically in order to obtain the compact-star properties for two realistic equations of state (EoSs). For hadronic matter, the fundamental mode frequency (omega _0) becomes unstable almost at the critical central energy density corresponding to the maximum gravitational mass. However, for quark matter, where larger values of (vert beta vert ) are required to observe appreciable changes in the mass-radius diagram, there exist stable stars after the maximum-mass configuration for negative values of (beta ) . Using an independent analysis, our results reveal that the emergence of a cusp can be used as a criterion to indicate the onset of instability when the binding energy is plotted as a function of the proper mass. Specifically, we find that the central-density value where the binding energy is a minimum corresponds precisely to (omega _0^2 =0) .

Abstract

We obtain a novel model of oscillating non-singular cosmology on the spatially flat Randall–Sundrum (RS) II brane. At early times, the universe is dominated by a scalar field with an inflationary emergent potential (V(phi )=A(e^{Bphi }-1)^2) , A and B being constants. Interestingly, we find that such a scalar field can source a non-singular bounce, replacing the big bang on the brane. The turnaround again happens naturally on the brane dominated by a phantom dark energy [favoured by observations (Knop et al. in Astrophys J 598:102, 2003. Spergel et al. in Astrophys J Suppl 148:175, 2003. Tegmark et al. in Phys Rev D 69:103501, 2004) at late times], thus avoiding the big rip singularity and leading upto the following non-singular bounce via a contraction phase. There is a smooth non-singular transition of the brane universe through both the bounce and turnaround, leading to alternate expanding and contracting phases. This is the first model where a single braneworld of positive tension can be made to recycle as discussed in details in the concluding section.

This work proposes more solutions for the Wheeler–DeWitt equation in a flat FLRW minisuperspace. We study quantum cosmology in the framework of the de Broglie–Bohm interpretation and investigate the quantum cosmological effects throughout the evolution of the universe. In a particular solution, the tendency for a scalar field to roll down the potential is balanced by the quantum force, and a Minkowski spacetime is obtained.

We study the higher dimensional scenario of an anisotropic compact star using the Buchdahl–Vaidya–Tikekar metric ansatz. In our formalism, the anisotropy is assumed in such a way that, in the absence of it, the solution reduces to Schwarzschild’s interior solution in (D ge 4) dimensions. The model is so developed that it correlates anisotropy to the curvature parameter K which characterizes a departure from spherical geometry of the (t=) constant hypersurface of the associated spacetime when embedded in a 4 dimensional Euclidean space. Due to the particular choice of anisotropy, the pressure balancing equation for hydrostatic equilibrium continues to have the same form in higher dimensions. Consequently, our approach permits extending a four-dimensional solution to a higher dimensional spacetime without deforming the sphericity of the configuration. Making use of the model, we propose a higher dimensional anisotropic analogue of the Buchdahl bound on compactness. We show that additional dimension as well as anisotropy reduce the compactification limit. Our technique helps to regain the original Buchdahl limit in (D=4) dimensions and also, in the absence of anisotropy, the compactification limit in higher dimensions obtained earlier by Leon and Cruz (Gen Relativ Gravit 32:1207–1216, 2000. https://doi.org/10.1023/A:1001982402392). It turns out that the maximum achievable dimension remains model dependent through the causality condition and the compactification limit. We scrutinize the model under all the requisite physical conditions for a relativistic anisotropic fluid sphere which might serve as the internal structure of a compact star in higher dimensions. We analyze the consequences of the departure from homogeneous spherical distribution and dimensionality on the physical behaviour of the star. The EOS becomes stiffer in higher dimensions and comparatively lower anisotropic stress. Our calculation shows that the central density reduces as we move towards higher dimensions and inclusion of anisotropy increases the rate of fall of the density profile. We also note that the two pressures get reduced considerably in higher dimensions. We show that, for a given curvature parameter specifying the sphericity, an extra dimension is analogous to moving towards a homogeneous distribution of an anisotropic star.

We study the Schwinger pair creation of scalar charged particles by a homogeneous electric field in an expanding universe in the quantum kinetic approach. We introduce an adiabatic vacuum for the scalar field based on the Wentzel–Kramers–Brillouin solution to the mode equation in conformal time and apply the formalism of Bogolyubov coefficients to derive a system of quantum Vlasov equations for three real kinetic functions. Compared to the analogous system of equations previously reported in the literature, the new one has two advantages. First, its solutions exhibit a faster decrease at large momenta which makes it more suitable for numerical computations. Second, it predicts no particle creation in the case of conformally coupled massless scalar field in the vanishing electric field, i.e., it respects the conformal symmetry of the system. We identify the ultraviolet divergences in the electric current and energy–momentum tensor of produced particles and introduce the corresponding counterterms in order to cancel them.

We study the renormalized stress-energy tensor (RSET) for a massless, conformally coupled scalar field on global anti-de Sitter space-time in four dimensions. Robin (mixed) boundary conditions are applied to the scalar field. We compute both the vacuum and thermal expectation values of the RSET. The vacuum RSET is a multiple of the space-time metric when either Dirichlet or Neumann boundary conditions are applied. Imposing Robin boundary conditions breaks the maximal symmetry of the vacuum state and results in an RSET whose components with mixed indices have their maximum (or maximum magnitude) at the space-time origin. The value of this maximum depends on the boundary conditions. We find similar behaviour for thermal states. As the temperature decreases, thermal expectation values of the RSET approach those for vacuum states and their values depend strongly on the boundary conditions. As the temperature increases, the values of the RSET components tend to profiles which are the same for all boundary conditions. We also find, for both vacuum and thermal states, that the RSET on the space-time boundary is independent of the boundary conditions and determined entirely by the trace anomaly.

Wormholes are considered to be hypothetical tunnels connecting two distant regions of the universe or two different universes. In general relativity (GR), the formation of traversable WH requires the consideration of exotic matter that violates energy conditions (ECs). If the wormhole geometry can be described in modified gravitational theories without introducing exotic matter, it will be significant for studying these theories. In the paper, we analyze some physical properties of static traversable WH within the framework of f(R, T) modified gravitational theory. Firstly, we explore the validity of the null, weak, dominant and strong energy conditions for wormhole matter for the considered (f(R,T)=R+alpha R^2+lambda T) model. Research shows that it is possible to obtain traversable WH geometry without bring in exotic matter that violates the null energy condition (NEC) in the f(R, T) theory. The violation of the dominant energy condition (DEC) in this model may be related to quantum fluctuations or indicates the existence of special matter that violates this EC within the wormhole. Moreover, it is found that in the (f(R,T)=R+alpha R^2+lambda T) model, relative to the GR, the introduction of the geometric term (alpha R^2) has no remarkable impact on the wormhole matter components and their properties, while the appearance of the matter-geometry coupling term (lambda T) can resolve the question that WH matter violates the null, weak and strong energy condition in GR. Additionally, we investigate dependency of the valid NEC on model parameters and quantify the matter components within the wormhole using the “volume integral quantifier”. Lastly, based on the modified Tolman–Oppenheimer–Volkov equation, we find that the traversable WH in this theory is stable. On the other hand, we use the classical reconstruction technique to derive wormhole solution in f(R, T) theory and discuss the corresponding ECs of matter. It is found that all four ECs (NEC, WEC, SEC and DEC) of matter in the traversable wormholes are valid in this reconstructed f(R, T) model, i.e we provide a wormhole solution without introducing the exotic matter and special matter in f(R, T) theory.

In this paper, we discuss the interaction of non-Abelian SU(2) Yang–Mills progressive waves with gravitational waves. We solve and obtain some interesting solutions to pure Yang–Mills equations in different backgrounds, and perturbative solutions induced due to gravitational waves. These perturbations show ‘beat patterns’ and depending on boundary conditions, changes in frequency. In flat space-time, when the Yang–Mills fields and the gravitational waves are in the same direction there is no interaction, unless there is self interaction of the Yang–Mills fields. In the system with non-zero self interaction the amplitudes of the perturbation are inversely proportional to the Yang–Mills coupling constant. In a cosmological background, the Yang–Mills fields and the gravitational wave interact when they are in the same direction even without self interaction of the Yang–Mills progressive fields. We find that in the electroweak symmetry broken phase of the gauge fields, the interactions are perturbative only for an infinitesimal time.