Search Results (38)

In this work, we employ the Darmois–Israel thin-shell formalism to construct both static and dynamic thin-shell configurations surrounding traversable wormholes. Initially, using the cut-and-paste technique, we perform a linearized stability analysis in the presence of a general cosmological constant. Our results show that for sufficiently large positive values of the cosmological constant—corresponding to the Schwarzschild–de Sitter geometry—the stability regions of the wormhole solutions are significantly enhanced compared to the Schwarzschild case. Subsequently, we construct static thin-shell solutions by matching an interior wormhole geometry to an exterior vacuum spacetime across a junction surface. In the spirit of minimizing the presence of exotic matter, we identify parameter domains in which the null and weak energy conditions are satisfied at the shell. We examine the surface stress-energy components in detail, determining regions where the tangential surface pressure is either positive or negative, interpreted, respectively, as the pressure or surface tension. Additionally, an expression describing the behavior of the radial pressure across the junction is derived. Finally, we determine key geometrical characteristics of the wormhole, including the throat radius and the junction interface radius, by imposing traversability conditions. Estimates for the traversal time and required velocity are also provided, further elucidating the physical viability of these configurations. Full article

It has been shown that if one solves self-consistently the semiclassical Einstein equations in the presence of a quantum scalar field, with a cutoff on the number of modes, spacetime become flatter when the cutoff increases. Here, we extend the result to include the effect of fields with spin 0, 1/2, 1 and 2. With minor adjustments, the main result persists. Remarkably, one can have positive curvature even if the cosmological constant in the bare action is negative. Full article

We study the Stueckelberg field in de Sitter space, which is a massive vector field with the gauge fixing (GF) term ${\displaystyle \frac{1}{2\zeta }}{({A^{\mu }}_{;\mu })}^2$. We obtain the vacuum stress tensor, which consists of the transverse, longitudinal, temporal, and GF parts, and each contains various UV divergences. By the minimal subtraction rule, we regularize each part of the stress tensor to its pertinent adiabatic order. The transverse stress tensor is regularized to the 0th adiabatic order, while the longitudinal, temporal, and GF stress tensors are regularized to the 2nd adiabatic order. The resulting total regularized vacuum stress tensor is convergent and maximally symmetric, has a positive energy density, and respects the covariant conservation, and thus, it can be identified as the cosmological constant that drives the de Sitter inflation. Under the Lorenz condition ${A^{\mu }}_{;\mu }=0$, the regularized Stueckelberg stress tensor reduces to the regularized Proca stress tensor that contains only the transverse and longitudinal modes. In the massless limit, the regularized Stueckelberg stress tensor becomes zero, and is the same as that of the Maxwell field with the GF term, and no trace anomaly exists. If the order of adiabatic regularization were lower than our prescription, some divergences would remain. If the order were higher, say, under the conventional 4th-order regularization, more terms than necessary would be subtracted off, leading to an unphysical negative energy density and the trace anomaly simultaneously. Full article

In this article, we consider the 4 + n dimensional spacetimes among which one is the four dimensional physical Universe and the other is an n-dimensional sphere with constant radius in the framework of Lanczos-Lovelock gravity. We find that the curvature of extra dimensional sphere contributes a huge but negative energy density provided that its radius is sufficiently small, such as the scale of Planck length. Therefore, the huge positive vacuum energy, i.e., the large positive cosmological constant is exactly cancelled out by the curvature of extra sphere. In the mean time the higher order of Lanczos-Lovelock term contributes an observations-allowed small cosmological constant if the number of extra dimensions is sufficiently large, such as n ≈ 69. Full article

We analyze Hayward black holes (BHs) with a negative cosmological constant surrounded by a cloud of strings, which we designate Hayward–Letelier AdS BHs. These solutions can be obtained by coupling the Einstein equations with nonlinear electrodynamics and the energy–momentum tensor of clouds of strings. We show that these solutions are no longer regular and have a curvature singularity at the center. In turn, we analyze the thermodynamics associated with these BHs by establishing the form of the Smarr formula and the first law of thermodynamics. We derive the expressions for the thermodynamic quantities such as pressure, temperature, heat capacity, Gibbs free energy, and isothermal compressibility. We explore the phase structure of these solutions by analyzing the behavior of the heat capacity and Gibbs free energy. These solutions exhibit a first-order phase transition, similar to van der Waals fluids. We also check the behavior of the thermodynamic quantities near the critical points and calculate the values of the critical exponents. This illustrates a robust analogy between our solutions and van der Waals fluids. Full article

Ordinary 3D Baryon Acoustic Oscillations (BAO) data are model-dependent, requiring the assumption of a cosmological model to calculate comoving distances during data reduction. Throughout the present-day literature, the assumed model is $\mathsf{\Lambda }$CDM. However, it has been pointed out in several recent works that this assumption can be inadequate when analyzing alternative cosmologies, potentially biasing the Hubble constant ($H_0$) low, thus contributing to the Hubble tension. To address this issue, 3D BAO data can be replaced with 2D BAO data, which are only weakly model-dependent. The impact of using 2D BAO data, in combination with alternative cosmological models beyond $\mathsf{\Lambda }$CDM, has been explored for several phenomenological models, showing a promising reduction in the Hubble tension. In this work, we accommodate these models in the theoretically robust framework of bimetric gravity. This is a modified theory of gravity that exhibits a transition from a (possibly) negative cosmological constant in the early universe to a positive one in the late universe. By combining 2D BAO data with cosmic microwave background and type Ia supernovae data, we find that the inverse distance ladder in this theory yields a Hubble constant of $H_0=(71.0\pm 0.9)\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$, consistent with the SH0ES local distance ladder measurement of $H_0=(73.0\pm 1.0)\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$. Replacing 2D BAO with 3D BAO results in $H_0=(68.6\pm 0.5)\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$ from the inverse distance ladder. We conclude that the choice of BAO data significantly impacts the Hubble tension, with ordinary 3D BAO data exacerbating the tension, while 2D BAO data provide results consistent with the local distance ladder. Full article

The thermodynamics of black holes (BHs) and their corrections have become a hot topic in the study of gravitational physics, with significant progress made in recent decades. In this paper, we study the thermodynamics and corrections of spherically symmetric BHs in models $f\left(R\right)=R+\alpha R^2$ and $f\left(R\right)=R+2\gamma \sqrt{R+8\Lambda }$ under the $f\left(R\right)$ theory, which includes the electrodynamic field and the cosmological constant. Considering thermal fluctuations around equilibrium states, we find that, for both f(R) models, the corrected entropy is meaningful in the case of a negative cosmological constant (anti-de Sitter–RN spacetime) with $\Lambda =-1$. It is shown that when the BHs’ horizon radius is small, thermal fluctuations have a more significant effect on the corrected entropy. Using the corrected entropy, we derive expressions for the relevant corrected thermodynamic quantities (such as Helmholtz free energy, internal energy, Gibbs free energy, and specific heat) and calculate the effects of the correction terms. The results indicate that the corrections to Helmholtz free energy and Gibbs free energy, caused by thermal fluctuations, are remarkable for small BHs. In addition, we explore the stability of BHs using specific heat. The study reveals that the corrected BH thermodynamics exhibit locally stable for both models, and corrected systems undergo a Hawking–Page phase transition. Considering the requirement on the non-negative volume of BHs, we also investigate the constraint on the EH radius of BHs. Full article

In this paper, we systematically study the evolution of the Universe within the framework of a modified loop quantum cosmological model (mLQC-I) using various inflationary potentials, including chaotic, Starobinsky, generalized Starobinsky, polynomials of the first and second kinds, generalized T-models and natural inflation. In all these models, the big bang singularity is replaced by a quantum bounce, and the evolution of the Universe, both before and after the bounce, is universal and weakly dependent on the inflationary potentials, as long as the evolution is dominated by the kinetic energy of the inflaton at the bounce. In particular, the pre-bounce evolution can be universally divided into three different phases: pre-bouncing, pre-transition, and pre-de Sitter. The pre-bouncing phase occurs immediately before the quantum bounce, during which the evolution of the Universe is dominated by the kinetic energy of the inflaton. Thus, the equation of state of the inflaton is about one, $w\left(\varphi \right)\simeq 1$. Soon, the inflation potential takes over, so $w\left(\varphi \right)$ rapidly falls from one to negative one. This pre-transition phase is very short and quickly turns into the pre-de Sitter phase, whereby the effective cosmological constant of Planck size takes over and dominates the rest of the contracting phase. Throughout the entire pre-bounce regime, the evolution of both the expansion factor and the inflaton can be approximated by universal analytical solutions, independent of the specific inflation potentials. Full article

The paper investigates the vacuum expectation value of the surface energy–momentum tensor (SEMT) for a scalar field with general curvature coupling in the geometry of two branes orthogonal to the boundary of anti-de Sitter (AdS) spacetime. For Robin boundary conditions on the branes, the SEMT is decomposed into the contributions corresponding to the self-energies of the branes and the parts induced by the presence of the second brane. The renormalization is required for the first parts only, and for the corresponding regularization the generalized zeta function method is employed. The induced SEMT is finite and is free from renormalization ambiguities. For an observer living on the brane, the corresponding equation of state is of the cosmological constant type. Depending on the boundary conditions and on the separation between the branes, the surface energy densities can be either positive or negative. The energy density induced on the brane vanishes in special cases of Dirichlet and Neumann boundary conditions on that brane. The effect of gravity on the induced SEMT is essential at separations between the branes of the order or larger than the curvature radius for AdS spacetime. In the considerably large separation limit, the decay of the SEMT, as a function of the proper separation, follows a power law for both massless and massive fields. For parallel plates in Minkowski bulk and for massive fields the fall-off of the corresponding expectation value is exponential. Full article

We studied Einstein’s gravity with negative cosmological constant coupled to nonlinear electrodynamics proposed earlier. The metric and mass functions and corrections to the Reissner–Nordström solution are obtained. Black hole solutions can have one or two horizons. Thermodynamics and phase transitions of magnetically charged black holes in Anti-de Sitter spacetime are investigated. The first law of black hole thermodynamics is formulated and the generalized Smarr relation is proofed. By calculating the Gibbs free energy and heat capacity we study the black hole stability. Zero-order (reentrant), first-order, and second-order phase transitions are analyzed. The Joule–Thomson expansion is considered, showing the cooling and heating phase transitions. It was shown that the principles of causality and unitarity are satisfied in the model under consideration. Full article

We quantized the full Einstein equations in a globally hyperbolic spacetime $N=N^{n+1}$, $n\ge 3$, and found solutions of the resulting hyperbolic equation in a fiber bundle E which can be expressed as a product of spatial eigenfunctions (eigendistributions) and temporal eigenfunctions. The spatial eigenfunctions form a basis in an appropriate Hilbert space while the temporal eigenfunctions are solutions to a second-order ordinary differential equation in ${\mathbb{R}}_{+}^{}$. In case $n\ge 17$ and provided the cosmological constant $\Lambda$ is negative, the temporal eigenfunctions are eigenfunctions of a self-adjoint operator ${\widehat{H}}_0$ such that the eigenvalues are countable and the eigenfunctions form an orthonormal basis of a Hilbert space. Full article

The Reissner–Nordstrom spacetimes and some generalised Reissner–Nordstrom spacetimes are analysed. The blackhole solutions are considered. The generalised Reissner–Nordstrom spacetimes with a cosmological-constant term, endowed with a Schwarzschild solid-angle element, are analytically delineated: the radii of the blackholes are analytically calculated and newly parameterised; the coordinate-singularity-avoiding coordinate extension is newly found, i.e., such that the tortoise-coordinate transformation can therefore be applied; the new conditions for merging the solutions as the physical horizons are analytically outlined; the new parameter space of the model is set and constrained; the new role of the cosmological-constant term in designating the Schwarzschild radius is demonstrated; the Reissner–Nordstrom–deSitter case and in the Reissner–Nordstrom–anti-deSitter one are newly demonstrated to be characterised in a different analytical manner. Furthermore, a new family of solutions is found, qualified after the cosmological-constant term. The generalised Reissner–Nordstrom spacetimes with a linear term, endowed with a Schwarzschild solid-angle element, are analytically studied: the radii are enumerated and newly parameterised; the new conditions for the merging of the radii as the physical horizons are set; the new parameter space of the system is arranged and constrained; the role of the linear-term parameter in the delineation of the Schwarzschild radius is newly proven to be apt to imply a small modification only. The generalised Reissner–Nordstrom spacetimes, endowed with a Schwarzschild solid-angle element, with a linear term and a cosmological-constant term are newly inspected: the radii are analytically calculated and newly parameterised; the new conditions for the merging of the radii as the physical horizons are prescribed; the new parameter space of the scheme is appointed and constrained; the roles of the parameters are newly scrutinised in their application to modify the physical interpretation of the Reissner–Nordstrom parameters only in a small manner; the coordinate-singularity-avoiding coordinate extensions are newly found, i.e., such that the tortoise-coordinate transformation can therefore be applied; the definition of the physical radii is newly found; the results are newly demonstrated in both cases of a positive value of the cosmological constant and in the case of a negative value of the cosmological constant in a different manner; the role of the linear-term parameter is also newly enunciated. More over, a new family of solutions is found, which is delineated after particular values of the linear term and of the cosmological-constant one. The quantum implementation of the models is prospectively envisaged. Full article

In a recent article we showed that the vacuum energy density in two spacetime dimensions for a wide variety of integrable quantum field theories has the form ${\rho }_{\mathrm{vac}}=-m^2/2\mathfrak{g}$ where m is a physical mass and $\mathfrak{g}$ is a generalized coupling, where in the free field limit $\mathfrak{g}\to 0$, ${\rho }_{\mathrm{vac}}$ diverges. This vacuum energy density has the form $⟨T_{\mu \nu }⟩=-{\rho }_{\mathrm{vac}}{g}_{\mu \nu }$, and has previously been considered as a contribution to the stress energy tensor in Einstein’s gravity as a “cosmological constant”. We speculated that in four spacetime dimensions ${\rho }_{\mathrm{vac}}$ takes a similar form ${\rho }_{\mathrm{vac}}=-m^4/2\mathfrak{g}$, but did not support this idea in any specific model. In this article, we study this problem for $\lambda {\varphi }^4$ theory in d spacetime dimensions. We show how to obtain the exact${\rho }_{\mathrm{vac}}$ for the sinh–Gordon theory in the weak coupling limit by using a saddle point approximation. This calculation indicates that the vacuum energy can be well-defined, positive or negative, without spontaneous symmetry breaking. We also show that ${\rho }_{\mathrm{vac}}$ satisfies a Callan–Symanzik type of renormalization group equation. For the most interesting case physically, ${\rho }_{\mathrm{vac}}$ is positive and can arise from a marginally relevant negative coupling $\mathfrak{g}$ and the vacuum energy flows to zero at low energies. Full article

In this note, I derive the Chandrasekhar instability of a fluid sphere in (N + 1)-dimensional Schwarzschild–Tangherlini spacetime and take the homogeneous (uniform energy density) solution for illustration. Qualitatively, the effect of a positive (negative) cosmological constant tends to destabilize (stabilize) the sphere. In the absence of a cosmological constant, the privileged position of (3 + 1)-dimensional spacetime is manifest in its own right. As it is, the marginal dimensionality in which a monatomic ideal fluid sphere is stable but not too stable to trigger the onset of gravitational collapse. Furthermore, it is the unique dimensionality that can accommodate stable hydrostatic equilibrium with a positive cosmological constant. However, given the current cosmological constant observed, no stable configuration can be larger than ${10}^{21}{\mathrm{M}}_{\odot }$. On the other hand, in (2 + 1) dimensions, it is too stable either in the context of Newtonian Gravity (NG) or Einstein’s General Relativity (GR). In GR, the role of negative cosmological constant is crucial not only to guarantee fluid equilibrium (decreasing monotonicity of pressure) but also to have the Bañados–Teitelboim–Zanelli (BTZ) black hole solution. Owing to the negativeness of the cosmological constant, there is no unstable configuration for a homogeneous fluid disk with mass $0<\mathcal{M}\le 0.5$ to collapse into a naked singularity, which supports the Cosmic Censorship Conjecture. However, the relativistic instability can be triggered for a homogeneous disk with mass $0.5<\mathcal{M}\lesssim 0.518$ under causal limit, which implies that BTZ holes of mass ${\mathcal{M}}_{\mathrm{BTZ}}>0$ could emerge from collapsing fluid disks under proper conditions. The implicit assumptions and implications are also discussed. Full article

It is well known that the universe is undergoing accelerated expansion during recent times and that it underwent a decelerated expansion in early times. The deceleration parameter, essentially the second derivative of the scale factor, can be used to describe these eras, with a negative parameter for acceleration and a positive parameter for deceleration. Apart from the standard $\Lambda$CDM model in general relativity, there are many cosmological models in various other theories of gravity. In order to describe these models, especially the deviation from general relativity, the jerk parameter was introduced, which is basically the third derivative of the scale factor. In the $\Lambda$CDM model in general relativity, the jerk parameter j is constant, and $j=1$. The constant jerk parameter, $j=1$, leads to two different scale factor solutions, one power law and the other exponential. The power-law solution corresponds to a model in which our universe expands with deceleration, while the exponential solution corresponds to a model in which it expands by accelerating. In this study, the cosmological consequences of such a selection of the jerk parameter on the non-minimally coupled $f(R,T)$ theory of gravity (where R is the Ricci scalar, and T is the trace of the energy–momentum tensor) and the dynamic properties of these models are investigated on a flat Friedmann–Lemaitre–Robertson–Walker backgfround. Full article