Narrow Results

A breakthrough has been achieved in solving the Einstein field equations for a specific class of charged compact objects existing in higher dimensions with inhomogeneous matter distribution. The geometry of space-time is believed to be spheroid, encapsulated in $(n+2)$ dimensions of Euclidean space where $n=D-2$, $D$ be the space-time dimension. The internal physical $(n+1)$ space is elucidated by the Vaidya–Tikekar metric ansatz, which is defined by spheroidal and curvature parameters. The form of the equation of state in MIT bag model, $p=\frac{1}{3}(\rho -4B)$, where the constant $B$ is termed as bag constant, is implemented to investigate the relevant physical features of anisotropic strange quark stars containing a net amount of charge. The inclusion of higher dimensions effectively decreases the mass retained within a given radius of a compact object but increases its compactness. For a particular dimension, if one increases the value of $B$, the mass increases for a given value of radius. Determination of maximum radius and consequently, maximum mass have been obtained by equating the value of radial sound velocity as the extreme limit of causality $(=1)$ at the center of the star. Both the maximum mass and radius of a given compact object are found to increase when both charge and pressure anisotropy increase and decrease for an increment of surface density or bag constant $B$. The maximum mass attained in the model is $3.498M_{\odot }$. Prediction of the radius of some recently observed compact objects has also been done for different $D$, $B$, charge and pressure anisotropy parameters. Different energy conditions and stability criteria stand up throughout the compact object containing anisotropy in pressure and net charge. The tidal deformability of some compact objects has also been investigated using the present model.

We investigate the end state of the gravitational collapse of an inhomogeneous dust cloud in higher dimensional spacetime. The naked singularities are shown to be developing as the final outcome of non-marginally bound collapse. The naked singularities are found to be gravitationally strong in the sense of Tipler.

We investigate the spacetime of a global monopole in a five-dimensional spacetime in the presence of the cosmological term. Also the gravitational properties of the monopole solution are discussed.

The cosmological behavior is investigated for ten-dimensional scalar–tensor theory with matter. The matter is taken as an anisotropic fluid. As a simple ansatz, the anisotropic fluid for each four and six dimensions satisfies the same type of the equation of state with different coefficients, p_x,y = γ_x,yρ. Following the ansatz of the anisotropic matter, the spacetime then has a product structure which means that the spacetime is decomposed as four-dimensional spacetime (M_x) and six-dimensional transverse space (M_y). We focus on the solution such that the scale factors in each four and six dimensions behave differently. The corresponding cosmological solutions are obtained for general γ_x,y. By giving specific numeric values for the coefficients of the equation of state γ_x,y, we find the solution which behaves in such a way that the spatial three dimensions are expanding while the extra six dimensions are contracting.

We investigate the scale factor duality of the scalar–tensor theory in four and ten dimensions with matter. It is shown that when the pressure of the matter vanishes (γ = 0 for the equation of state p = γρ), the action is invariant under the duality. In addition, the action is invariant again under the change of the sign of the pressure (p→-p or γ→-γ). In higher dimensions, we distinguish the matter, e.g., in four dimensions p_x = γ_xρ and for extra six dimensions p_y = γ_y ρ. The scale factor duality in this case is that when γ_x = 0 the duality transformation acts on the four-dimensional scale factor and the dilaton with the extra dimensions intact while when γ_y = 0 it acts on the extra six dimensions and the dilaton with four dimensions intact.

In this paper, the gravitational collapse has been studied in the context of higher-dimensional charged-Vaidya spacetime. It is shown that naked singularity always exists in this case and strong form of cosmic censorship is violated. This work extends the earlier studies on naked singularity formation in higher dimensions.

The scalar–tensor theories (STTs) of gravity in spacetime dimensions (D+1)>2 are studied. By performing Hamiltonian analysis, we obtain the geometrical dynamics of the theories from their Lagrangian. The Hamiltonian formalism indicates that the theories are naturally divided into two sectors by the coupling parameter ω. The Hamiltonian structures in both sectors are similar to the corresponding structures of four-dimensional cases. It turns out that, similar to the case of general relativity (GR), there is also a symplectic reduction from the canonical structure of so(D+1) Yang–Mills theories coupled to the scalar field to the canonical structure of the geometrical STTs. Therefore, the non-perturbative loop quantum (LQG) gravity techniques can also be applied to the STTs in D+1 dimensions based on their connection-dynamical formalism.

We provide a new model of higher-dimensional wormholes supported by phantom energy derived from a scalar field with negative kinetic term. We have shown that the Averaged Null Energy Condition (ANEC) violating phantom energy can be reduced as desired. We have also noticed that dimension of the space–time plays a crucial role for measuring the ANEC violating matter needed.

A possible way to destroy the Tangherlini Reissner–Nordström black hole is discussed in the spirit of Wald’s gedanken experiment. By neglecting radiation and self force effects, the absorbing condition and destruction condition of the test point particle which is capable of destroying the black hole are obtained. We find that it is impossible to challenge the weak cosmic censorship for an initially extremal black hole in all dimensions. Instead, it is shown that the near extremal black hole will turn into a naked singularity in this particular process, in which case the allowed range of the particle’s energy is very narrow. The result indicates that the self-force effects may well change the outcome of the calculation.

In recent years it is generally believed that we should consider positive vacuum energy density or cosmological constant. Also as higher dimensional theory is important at the early stages of the Universe, so it will be interesting to study classical tests of cosmology in a higher dimensional generalized Kantowski–Sachs model. For matter field, we consider dust and a cosmological constant and examine which are physically permissible.

We have examined cosmic no-hair theorem for anisotropic Bianchi-models in Einstein–Cartan theory and it is possible to have inflationary solution with a scalar field. It has been noted that during the inflationary era, the evolution of the Universe does not depend on the form of the potential but the late time behaviour is dependent on the potential for the inflation field.

Spherically symmetric inhomogeneous dust collapse has been studied in higher dimensional space–time and the factors responsible for the appearance of a naked singularity are analyzed in the region close to the centre for the marginally bound case. It is clearly demonstrated that in the former case naked singularities do not appear in the space–time having more than five dimension, which appears to a strong result. The non-marginally bound collapse is also examined in five dimensions and the role of shear in developing naked singularities in this space–time is discussed in details. The five-dimensional space–time is chosen in the later case because we have exact solution in closed form only in five dimension and not in any other case.

The generalized Szekeres family of solution for quasi-spherical space–time of higher dimensions are obtained in the scalar tensor theory of gravitation. Brans–Dicke field equations expressed in Dicke's revised units are exhaustively solved for all the subfamilies of the said family. A particular group of solutions may also be interpreted as due to the presence of the so-called C-field of Hoyle and Narlikar and for a chosen sign of the coupling parameter. The models show either expansion from a big bang type of singularity or a collapse with the turning point at a lower bound. There is one particular case which starts from the big bang, reaches a maximum and collapses with the in course of time to a crunch.

In this paper we present a class of exact inhomogeneous solutions to Einstein's equations for higher dimensional Szekeres metric with perfect fluid and a cosmological constant. We also show particular solutions depending on the choices of various parameters involved and for dust case. Finally, we examine the asymptotic behaviour of some of these solutions.

In this article, we study higher-dimensional cosmological models with quark–gluon plasma in the context of general relativity. For this purpose, we consider quark–gluon plasma as a perfect fluid in the higher-dimensional universes. After solving Einstein's field equations, we have analyzed this matter for the different types of universes in the higher- and four-dimensional universes. Also, we have discussed the features of obtained solutions.

Einstein–Maxwell field equations corresponding to a higher-dimensional description of static spherically symmetric space–time are solved under two specific sets of conditions: (i) ρ ≠ 0, ν′ = 0 and (ii) ρ = 0, ν′ ≠ 0, where ρ and ν represent the mass density and metric potential. The solution sets thus obtained satisfy the criteria of being an electromagnetic mass model such that the gravitational mass vanishes for the vanishing charge density σ and also the space–time becomes flat. Physical features related to other parameters are also discussed.

We propose a mechanism for the origin of matter in the universe in the framework of Einstein–Gauss–Bonnet gravity in higher dimensions. The new static black hole solution recently discovered by the authors,¹ with the Kaluza–Klein split of space–time as a product of the usual with a space of negative constant curvature, is indeed a pure gravitational creation of a black hole which is also endowed with a Maxwell-like gravitational charge in four-dimensional vacuum space–time. This solution has been further generalized to include radially flowing radiation, which means that extra-dimensional curvature also produces matter distribution asymptotically, resembling charged null dust. The static black hole could thus be envisioned as being formed from anti–de Sitter space–time by the collapse of radially inflowing charged null dust. It thus establishes the remarkable reciprocity between matter and gravity — as matter produces gravity (curvature), gravity produces matter. After the Kaluza–Klein generation of the Maxwell field, this is the first instance of realization of matter without matter in the classical framework.

By considering the product of the usual four-dimensional space–time with two dimensional space of constant curvature, an interesting black hole solution has recently been found for Einstein–Gauss–Bonnet gravity. It turns out that this as well as all others could easily be made to radiate Vaidya null dust. However, there exists no Kerr analog in this setting. To get the physical feel of the four-dimensional black hole space–times, we study asymptotic behavior of stresses at the two ends, r → 0 and r → ∞.

In this work, we review thoroughly the origin, development and present status of gravastar which has been thought to be an alternative to black hole along with its future feasibility in the sense of astrophysical observation. The Mazur–Mottola model of the gravastar is introduced first followed by a review of its generalizations within the context of general relativity including physical applications like primordial and cylindrical gravastars. The study of gravastar in higher- and lower-dimensional general relativity (GR) including the higher-dimensional theories with physical insight like the Randall–Sundrum model is presented. The gravastar models in a number of modified gravity models starting from $f(R,T)$ to Rastall–Rainbow gravity have been reviewed.

In this work, we study some parameterizations of the deceleration parameter and investigate the accretion of the fluid in these parameterized models upon the higher-dimensional black hole (BH) and wormholes. For the undergoing analysis, $(n+2)$-dimensional wormhole (proposed by Morris and Thorne) and Schwarzschild BH were chosen in the backdrop of higher-dimensional Friedmann–Robertson–Walker (FRW) space-time. For these parameterized models, we analyze the change of masses of BH and wormhole in different dimensions.