Static spherically symmetric wormholes with isotropic pressure

In this paper, we study classical general relativistic static wormhole configurations with pseudospherical symmetry. We show that, in addition to the hyperbolic wormhole solutions discussed by Lobo and Mimoso in [Phys. Rev. D 82, 044034 (2010)], there exists another wormhole class, which is a truly pseudospherical counterpart of spherical Morris--Thorne wormhole (contrary to the Lobo--Mimoso wormhole class), since all constraints originally defined by Morris and Thorne for spherically symmetric wormholes are satisfied. We show that, for both classes of hyperbolic wormholes, the energy density, at the throat, is always negative, while the radial pressure is positive, contrary to the spherically symmetric Morris--Thorne wormhole. Specific hyperbolic wormholes are constructed and discussed by imposing different conditions for the radial and lateral pressures, or by considering restricted choices for the redshift and the shape functions. In particular, we show that a hyperbolic wormhole cannot be sustained at the throat by phantom energy and that there are pseudospherically symmetric wormholes supported by matter with isotropic pressure and characterized by space sections with an angle deficit (or excess).

Wormholes in [formula omitted] gravity satisfying the null energy condition with isotropic pressure

In this study, we search for a new class of wormhole solutions in the framework of Brans–Dicke (BD) theory in the presence of anisotropic matter distribution. Considering a linear equation of state (EoS) between radial pressure and energy density profile we find exact static spherically symmetric solutions to the BD field equations which represent wormhole configurations. The solutions we obtain include both cases with zero and nonzero redshift functions, for which, the conditions on wormhole geometry together with the weak (WEC) and null (NEC) energy conditions put constraints on model parameters such as, the BD coupling and EoS parameters. These constraints also depend on other model parameters such as, the value of BD scalar field and energy density at the wormhole throat. The regularity of the obtained solutions is verified by calculating the Kretschmann scalar in order to ensure that curvature singularities are absent in the wormhole spacetime. We then find that BD wormholes in the presence of anisotropic matter can exist without violating NEC and WEC, either at the throat or across the entire spacetime.

The present status on the existence, structure and stability of static and stationary solutions of the Einstein-Vlasov system is reviewed. Under the assumptions that a spherically symmetric static object has isotropic pressure and non-increasing energy density outwards, Buchdahl showed 1959 the bound M/R<4/9, where M is the ADM mass and R the outer radius. Most static solutions of the Einstein-Vlasov system do not satisfy these assumptions. The bound M/R<4/9 nevertheless holds and it is sharp. An analogous bound in the charged case is also given. The important question of stability of spherically symmetric static solutions is presently open but numerical results are available and these are reviewed. A natural question is to go beyond spherical symmetry and consider axially symmetric solutions, and a recent result on the existence of axially symmetric stationary solutions is also discussed.

A new quark star model for a charged anisotropic stellar object is generated using the Einstein–Maxwell field equations. We use a metric function, linear equation of state, and a new measure of anisotropy in form of logarithmic function to formulate the model. For particular choices of parameters in the anisotropic measure, some anisotropic and isotropic models are regained as a special case. Physical analysis indicates that matter variables and gravitational potentials in the model are well behaved. The generated model satisfies the energy, regularity, causality, and stability conditions. The speed of sound is consistent with quark stars.

The objective of this paper is to study static spherically symmetric noncommutative wormhole solutions in the framework of $f(T)$ gravity. We construct $f(T)$ field equations in covariant and effective energy-momentum tensor forms to make a correspondence with general relativity. It is observed that the violation of energy conditions to support the nonstandard wormhole is due to the effective energy-momentum tensor. We explore the noncommutative wormhole solutions for two cases: (i) assume a viable power-law $f(T)$ model to construct the shape function and (ii) a particular shape function is taken to construct the $f(T)$ model. In the first case, only exotic matter forms a wormhole structure in teleparallel gravity, whereas for $f(T)$ gravity, normal matter threads these structures except for a particular range of $r$. For the constructed $f(T)$ model, there does not exist a physically acceptable wormhole solution similar to the teleparallel case.

In this paper we present a general framework for generating exact solutions to the Einstein field equations for static, anisotropic fluid spheres in comoving, isotropic coordinates obeying a linear equation of state of the form $p_{r} =\alpha \rho - \beta$ . We show that all possible solutions can be obtained via a single generating function defined in terms of one of the gravitational potentials. The physical viability of our solution-generating method is illustrated by modeling a static fluid sphere describing a strange star.

Static spherically symmetric Einstein-æther models II: Integrability and the modified Tolman–Oppenheimer–Volkoff approach

Minimally deformed regular Bardeen black hole solutions in Rastall theory

Wormhole solutions in General Relativity (GR) require exotic matter sources that violate the null energy condition (NEC), and it is well-known that higher-order modifications of GR and some alternative matter sources can support wormholes. In this study, we explore the possibility of formulating traversable wormholes in f (R) modified gravity, which is perhaps the most widely discussed modification of GR, with two approaches. First, to investigate the effects of geometrical constraints on the global characteristics, we gauge the rr–component of the metric tensor and employ Padè approximation to check whether a well–constrained shape function can be formulated in this manner. We then derive the field equations with a background of string cloud and numerically analyse the energy conditions, stability, and amount of exotic matter in this space-time. Next, as an alternative source in a simple f (R) gravity model, we use the background cloud of strings to estimate the wormhole shape function and analyse the relevant properties of the space-time. These results are then compared with those of wormholes threaded by normal matter in the simple f (R) gravity model considered. The results demonstrate that string cloud is a viable source for wormholes with NEC violations; however, the wormhole space-times in the simple f (R) gravity model considered in this study are unstable.

We analyze the isothermal property in static fluid spheres within the framework of the modified f(R, T) theory of gravitation. The equation of pressure isotropy of the standard Einstein theory is preserved however, the energy density and pressure are expressed in terms of both gravitational potentials. Invoking the isothermal prescription requires that the isotropy condition assumes the role of a consistency condition and an exact model generalizing that of general relativity is found. Moreover it is found that the Einstein model is unstable and acausal while the f(R, T) counterpart is well behaved on account of the freedom available through an additional coupling constant. The case of a constant spatial gravitational potential is considered and the complete model is determined. This model is markedly different from its Einstein counterpart which is known to be isothermal. Dropping the restriction on the density and imposing a linear barotropic equation of state generates an exact solution and consequently a stellar distribution as the vanishing of the pressure is possible and a boundary hypersurface exists. Finally we comment on the case of relaxing the equation of state but demanding an inverse square fall-off of the density – this case proves intractable.

The impact of curvature divergences on physical observers in a black hole space–time, which, nonetheless, is geodesically complete is investigated. This space–time is an exact solution of certain extensions of general relativity coupled to Maxwell’s electrodynamics and, roughly speaking, consists of two Reissner–Nordström (or Schwarzschild or Minkowski) geometries connected by a spherical wormhole near the center. We find that, despite the existence of infinite tidal forces, causal contact is never lost among the elements making up the observer. This suggests that curvature divergences may not be as pathological as traditionally thought.

Estimation of concentration-dependent diffusion coefficient in pressure-decay experiment of heavy oils and bitumen

The objective of this paper is to provide a piece of theoretical evidence for the existence of cylindrically symmetric, time-independent wormhole models surrounded by the halos of fuzzy dark matter. To do so, we model our system by assuming a cylindrical spacetime coupled with locally anisotropic matter content. We calculate the shape function involved in the construction of fuzzy dark matter wormholes, by solving simultaneous equations of motion and density powered by Einasto energy profile. The investigation of the validity of null energy conditions is performed with the aim of seeing stable wormhole structures. The role of the equation of state parameter in the theoretical structure of the shape function and the redshift function is studied which would lead to understanding the signals’ gravitational redshift and the spatial distribution of the fuzzy wormholes. A few characteristics of the wormholes like hydrostatic equilibrium, and active C-energy are also noticed in the less complex wormholes. It is inferred that the stability as well as the size of the fuzzy dark matter wormholes can be fine-tuned by modulating the index parameter involved in the energy source.

Based on thermodynamics, we study the galactic clustering of an expanding Universe by considering the logarithmic and volume (quantum) corrections to Newton's law along with the repulsive effect of a harmonic force induced by the cosmological constant ($\mathrm{\ensuremath{\Lambda}}$) in the formation of the large scale structure of the Universe. We derive the $N$-body partition function for extended-mass galaxies (galaxies with halos) analytically. For this partition function, we compute the exact equations of states, which exhibit the logarithmic, volume, and cosmological constant corrections. In this setting, a modified correlation (clustering) parameter (due to these corrections) emerges naturally from the exact equations of state. We compute a corrected grand canonical distribution function for this system. Furthermore, we obtain a deviation in differential forms of the two-point correlation functions for both the point-mass and extended-mass cases. The consequences of these deviations on the correlation function's power law are also discussed.