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In this paper, we review the theoretical basis for generation of gravitational waves and the detection techniques used to detect a gravitational wave. To materialize this goal in a thorough way, we first start with a mathematical background for general relativity from which a clue for gravitational wave was conceived by Einstein. Thereafter, we give the classification scheme of gravitational waves such as (i) continuous gravitational waves, (ii) compact binary inspiral gravitational waves and (iii) stochastic gravitational wave. Necessary mathematical insight into gravitational waves from binaries is also dealt with which follows detection of gravitational waves based on the frequency classification. Ground-based observatories as well as space borne gravitational wave detectors are discussed in a length. We have provided an overview on the inflationary gravitational waves. In connection to data analysis by matched filtering there are a few highlights on the techniques, e.g. (i) random noise, (ii) power spectrum, (iii) shot noise and (iv) Gaussian noise. Optimal detection statistics for a gravitational wave detection is also in the pipeline of the discussion along with detailed necessity of the matched filter and deep learning. [ABSTRACT FROM AUTHOR]

In this work, we present an anisotropic generalization of the Buchdahl static stellar model by implementing the method of extended gravitational decoupling and further requirement of vanishing complexity (Herrera, Phys Rev D 97:044010,2018). Starting off with a general spherically symmetric static metric with two unknown gravitational potentials, we impose the condition of vanishing complexity which then reduces the problem to a single‐generating metric function [Contreras and Stuchlik, Eur. Phys. J. C (2022) 82:706]. The Buchdahl ansatz is then employed to obtain the complete gravitational behavior of the isotropic seed solution. The method of extended gravitational decoupling is thereafter utilized to obtain an anisotropic counterpart of the Buchdahl perfect gravitating sphere. We subject our solution to rigorous physical tests to ensure that it serves as a viable candidate for compact objects such as neutron stars as well as pulsars. We show that the decoupling parameter plays a crucial role in determining the stability and regularity of several key physical features of the entire stellar model. A novel finding of our investigation is the energy exchange between the seed solution and the secondary source which we show is sensitive to the decoupling parameter. In addition, it has also been shown that the direction of energy flow depends on the radial distance of the shell from the center of the stellar configuration. [ABSTRACT FROM AUTHOR]

In this article we study the wormhole geometry in the galactic halo region under modified f(Q)$f(\mathcal {Q})$ gravity, especially symmetric teleparallel gravity, where the nonmetricity scalar Q$\mathcal {Q}$ drives the gravitational interaction. The wormhole solutions for the assumed form f(Q)=αQ+β$f(\mathcal {Q})=\alpha \mathcal {Q}+ \beta$ have been presented, where α and β are the model parameters. The assumption of f(Q)$f(\mathcal {Q})$ is based on the fact that its behavior should change with assumed parametric values of α as well as β within specific physical bounds. Two such models are presented based on the physically motivated shape function and energy conditions. We have elaborately shown, via mathematical calculations and graphical plots, the following features in our model: (i) energy conditions, especially NEC, which is very instructive in connection to energy violation in modified gravity theory, (ii) the wormhole solutions in the regime of Navarro‐Frenk‐White (NFW) density profiles for the galactic halo regions, (iii) treatment with particles moving in closed orbits around the wormholes which exhibit epicyclic frequencies, and (iv) the red‐blue shifts of the light coming from the wormhole throat in the vicinity of the dark matter halos. All the results and behaviors are satisfactory as well as interesting. In this article we study the wormhole geometry in the galactic halo region under modified f (Q) gravity, especially symmetric teleparallel gravity, where the nonmetricity scalar Q drives the gravitational interaction. The wormhole solutions for the assumed form f(Q) = αQ + β have been presented, where α and β are the model parameters. The assumption of f(Q) is based on the fact that its behavior should change with assumed parametric values of α as well as β within specific physical bounds. Two such models are presented based on the physically motivated shape function and energy conditions. We have elaborately shown, via mathematical calculations and graphical plots, the following features in our model: (i) energy conditions, especially NEC, which is very instructive in connection to energy violation in modified gravity theory, (ii) the wormhole solutions in the regime of Navarro‐Frenk‐White (NFW) density profiles for the galactic halo regions, (iii) treatment with particles moving in closed orbits around the wormholes which exhibit epicyclic frequencies, and (iv) the red‐blue shifts of the light coming from the wormhole throat in the vicinity of the dark matter halos. All the results and behaviors are satisfactory as well as interesting. [ABSTRACT FROM AUTHOR]

In the present study we exhibit gravastar models which are effectively stable in their configuration as well as we thoroughly investigate dynamics of the physical systems. For this we have adopted the de Rham-Gabadadze-Tolly massive gravity and analyze Einstein's general relativity (GR) in the context of the consistent nonlinear interaction terms interpreted as a graviton mass. The studies follow the structured routes of the interior geometry, exterior geometry and thin-shell gravastar model. A linearized stability of thin-shell gravastars has been established via three special models, viz. linear model, polytropic model and van der Waals model. We have also critically analyzed dynamics of thin-shell gravastars with special emphasis on massless scalar field and massive scalar field. Altogether the results are very interesting and physically viable as far as stability issue of gravastars are concerned. [ABSTRACT FROM AUTHOR]

In recent years, a class of compact objects called gravastars have drawn immense interest as regular solutions to end state stellar collapse. Since the energy density involved in collapse process is expected to be high, it is a natural choice to study such compact objects in context of modified gravity theories which reduce to General Relativity (GR) in the low energy regime. We have already framed a model of gravastar in such a modified gravity framework involving extra dimensional Randall–Sundrum (RS) single brane gravity [R. Sengupta, S. Ghosh, S. Ray, B. Mishra and S. K. Tripathy, Phys. Rev. D 102, 024037 (2020)]. As a sequel in this paper, we substantially improve our previous model by choosing the Kuchowicz function as one of the metric potentials, which leads to many new interesting results and physical features from our analysis as discussed in this paper. Also, we provide essential additional stability checks on our gravastar model to investigate the possibility of any instability creeping in due to the higher-dimensional framework. Our present improved gravastar model is found to clear all the stability checks successfully. Very interestingly, the static spherically symmetric matter distributions are found to accommodate both classes of solutions obeying and violating the modified energy conditions on the RS brane as we find in this work. We can conclude from our analysis that the Kuchowicz metric potential is very effective for describing regular solutions to compact objects at substantially high energies on the three-brane. [ABSTRACT FROM AUTHOR]

This paper explores a new embedding anisotropic charged version of a solution to Einstein–Maxwell field equations in four-dimensional spacetime through the Karmarkar conditions and the gravitational decoupling via minimal geometric decoupling (MGD) technique by choosing Pant's interior solution [Astrophys. Space Sci. 331, 633 (2011)] as a seed solution to coupled system. Later, we integrate the coupled system within the MGD and explore a family of solutions to represent the realistic structure of nonrotating compact objects. Through the matching of the interior solutions so obtained to the exterior Reissner–Nordström metric, we tune the arbitrary constants for feasible models. After that, we subject our model to a rigorous test for a chosen parameter space to verify the physical viability of the solution for the neutron stars in EXO 1785-248 for a range of values of the decoupling constant σ. Further, we prove that the constant σ is inherently connected to critical physical properties such as the gravitational and surface redshifts, compactification factor, mass/radius relation, etc., of the same compact star candidate EXO 1785-248. The solutions thus obtained exhibit physically viable features which are thoroughly demonstrated through graphical plots. [ABSTRACT FROM AUTHOR]

In this paper, we present some cosmological models with a hybrid scale factor (HSF) in the framework of general relativity (GR). The HSF fosters an early deceleration as well as a late-time acceleration and mimics the present Universe. The dynamical aspects of different cosmological models with HSF in the presence of different matter fields have been discussed. [ABSTRACT FROM AUTHOR]

In the present investigation, compact stellar models are dealt with in the framework of the modified gravity theory, specifically of f (,) type. We have considered that the compact objects are following a spherically symmetric static metric and obtained the Einstein field equations in the spacetime of f (,). To make the Einstein equations solvable, we employ the methodology of conformal Killing vectors. Thereafter by using the MIT bag equation of state to the compact stars, considering that the stars are formed by strange quark, we find the solutions set. The solutions are examined via several physical testings which exhibit viability of the model. [ABSTRACT FROM AUTHOR]

In this work, we have attempted to generalize the Raychaudhuri equation by using the concept of foliation of spacetime. Some studies are performed with a few special cases and their physical implication are discussed. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We provide a strange star model under the framework of general relativity by using a general linear equation of state (EOS). The solution set thus obtained is employed on altogether 20 compact star candidates to constraint values of MIT bag model. No specific value of the bag constant (B) a priori is assumed, rather possible range of values for bag constant is determined from observational data of the said set of compact stars. To do so, the Tolman–Oppenheimer–Volkoff (TOV) equation is solved by homotopy perturbation method (HPM) and hence we get a mass function for the stellar system. The solution to the Einstein field equations represents a nonsingular, causal and stable stellar structure which can be related to strange stars. Eventually, we get an interesting result on the range of the bag constant as 4 1. 5 8 MeV fm − 3 < B < 3 1 9. 3 1 MeV fm − 3 . We have found the maximum surface redshift Z s max = 0. 6 3 and shown that the central redshift ( Z c ) cannot have value larger than 2 k , where k = 2. 0 1 0 7 8 9 ± 0. 0 7 3 2 0 3. Also, we provide a possible value of bag constant for neutron star with quark core using hadronic as well as quark EOS. [ABSTRACT FROM AUTHOR]

This paper discusses a generalized model for compact stars, assumed to be anisotropic in nature due to the presence of highly dense and ultra-relativistic matter distribution. After embedding the 4D Riemannian space locally and isometrically into a 5D pseudo-Euclidean space, we solve the Einstein equations by employing a class of physically acceptable metric functions. The physical properties determined include the anisotropic factor showing that the anisotropy is zero at the center and maximum at the surface. Other boundary conditions yield the values of various parameters needed for rendering the numerous plots and also led to the EOS parameters. It is further determined that the usual energy conditions are satisfied and that the compact structures are stable, based on several criteria, viz., the equilibrium of forces, Herrera cracking concept, adiabatic index, etc. We note that the proposed stellar model satisfies the Buchdahl condition. Finally, the values of the numerous constants and physical parameters are determined, specifically for the compact stellar object LMC X − 4 , which we choose as a representative of the compact stars to present the analysis of the obtained results. Finally, we show that the present generalized model can justify most of the compact stars including white dwarfs and ultra-dense compact stars for a suitable tuning of the parametric values of n. [ABSTRACT FROM AUTHOR]

In this paper, the Einstein–Maxwell spacetime is considered for compact stellar system. To find out solutions of the field equations, we adopt a finite and positive well-behaved metric potential. Under this particular choice, we therefore develop the expressions of the physical features, such as mass, charge, density and pressure, for stellar system in embedding class 1 spacetime. It is observed that all these features are physically viable. In the model, some known compact stars, viz. 4 U 1820–30, 4 U 1608–52 and E X O 1745–248 (I) & (I I) are studied successfully through physical analysis. It is also interesting to note that the obtained set of regular solutions to the Einstein–Maxwell equations represents an electromagnetic mass model for isotropic fluid without invoking any negative pressure. [ABSTRACT FROM AUTHOR]

In this paper, the effect of anisotropy on the tidal deformability of a compact neutron star is investigated. In particular, it is possible to quantify the tidal Love number, which is defined by tidal deformability. Tidal Love number provides the estimation of the tidal deformability of the binary system in response to the external gravitational field. The effect of anisotropy and compactness factor on the tidal Love number has been examined for a specific class of solutions that describes an anisotropic compact object. • A class of solutions for an anisotropic compact star is investigated. • The effect of anisotropy on the tidal deformability has been studied. • We quantify the tidal Love number via tidal deformability. • The effect of compactness factor has been examined. [ABSTRACT FROM AUTHOR]

We present model for anisotropic compact star under the general theory of relativity of Einstein. In the study a 4-dimensional spacetime has been considered which is embedded into the 5-dimensional flat metric so that the spherically symmetric metric has class 1. A set of solutions for the field equations are found depending on the index n involved in the physical parameters. The interior solutions have been matched smoothly at the boundary of the spherical distribution to the exterior Schwarzschild solution which necessarily provides values of the unknown constants. We have chosen the values of n as n = 2 and n =10 to 20000 for which interesting and physically viable results can be found out. The investigations on the physical features of the model include several astrophysical issues, like (i) regularity behaviour of stars at the centre, (ii) well behaved condition for velocity of sound, (iii) energy conditions, (iv) stability of the system via the following three techniques — adiabatic index, Herrera cracking concept and TOV equation, (v) total mass, effective mass and compactification factor and (vi) surface redshift. Specific numerical values of the compact star candidates LMC X-4 and SMC X-1 are calculated for central and surface densities as well as central pressure to compare the model value with actual observational data. [ABSTRACT FROM AUTHOR]

We present a new model of gravastar in the higher dimensional Einsteinian spacetime including Einstein’s cosmological constant Λ . Following Mazur and Mottola (2001, 2004) we design the star with three specific regions, as follows: (I) Interior region, (II) Intermediate thin spherical shell and (III) Exterior region. The pressure within the interior region is equal to the negative matter density which provides a repulsive force over the shell. This thin shell is formed by ultra relativistic plasma, where the pressure is directly proportional to the matter-energy density which does counter balance the repulsive force from the interior whereas the exterior region is completely vacuum assumed to be de Sitter spacetime which can be described by the generalized Schwarzschild solution. With this specification we find out a set of exact non-singular and stable solutions of the gravastar which seems physically very interesting and reasonable. [ABSTRACT FROM AUTHOR]

In this paper, we present a strange stellar model using Tolman V-type metric potential employing simplest form of the MIT bag equation of state (EOS) for the quark matter. We consider that the stellar system is spherically symmetric, compact and made of an anisotropic fluid. Choosing different values of n we obtain exact solutions of the Einstein field equations and finally conclude that for a specific value of the parameter n=1/2, we find physically acceptable features of the stellar object. Further, we conduct different physical tests, viz., the energy condition, generalized Tolman–Oppeheimer–Volkoff (TOV) equation, Herrera’s cracking concept, etc., to confirm the physical validity of the presented model. Matching conditions provide expressions for different constants whereas maximization of the anisotropy parameter provides bag constant. By using the observed data of several compact stars, we derive exact values of some of the physical parameters and exhibit their features in tabular form. It is to note that our predicted value of the bag constant satisfies the report of CERN-SPS and RHIC. [ABSTRACT FROM AUTHOR]

We study different dimensional fluids inspired by noncommutative geometry which admit conformal Killing vector (CKV). The solutions of the Einstein field equations were examined specifically for five different set of spacetime. We calculate the active gravitational mass and impose stability conditions of the fluid sphere. The analysis thus carried out immediately indicates that at four dimension only one can get a stable configuration for any spherically symmetric stellar system and any other dimension, lower or higher, becomes untenable as far as the stability of a system is concerned. [ABSTRACT FROM AUTHOR]

New solutions for (2 + 1)-dimensional Einstein-Maxwell spacetime are found for a static spherically symmetric charged fluid distribution with the additional condition of allowing conformal Killing vectors (CKV). We discuss physical properties of the fluid parameters. Moreover, it is shown that the model actually represents two structures, namely (i) Gravastar as an alternative of black hole and (ii) Electromagnetic Mass model depending on the nature of the equation of state of the fluid. Here the gravitational mass originates from electromagnetic field alone. The solutions are matched with the exterior region of the Bañados-Teitelboim-Zanelli (BTZ) type isotropic static charged black hole as a consequence of junction conditions. We have shown that the central charge density is dependent on the value of M0, the conserved mass of the BTZ black hole. This, in turn, depends on the black hole event horizon which again is related to the Hawking radiation temperature of a BTZ black hole. Thus, one may have a clue that the central charge density is related with Hawking radiation temperature of the BTZ black hole on the exterior region of the static charged fluid sphere. [ABSTRACT FROM AUTHOR]

Recently, the small value of the cosmological constant and its ability to accelerate the expansion of the universe is of great interest. We discuss the possibility of forming of anisotropic compact stars from this cosmological constant as one of the competent candidates of dark energy. For this purpose, we consider the analytical solution of Krori and Barua metric. We take the radial dependence of cosmological constant and check all the regularity conditions, TOV equations, stability and surface redshift of the compact stars. It has been shown as conclusion that this model is valid for any compact star and we have cited 4U 1820-30 as a specific example of that kind of star. [ABSTRACT FROM AUTHOR]

We present a model for the present accelerating Universe and focus on the different important physical variables involved in the model under the phenomenological assumption Λ∝ H with a prescription for equation of state parameter in the form $\omega(t)=\omega_{0}+\frac{\omega_{1}\tau}{t^{2}}$, where ω and ω are two constants and τ is a parameter having dimension of time t. General expressions for the density parameter Ω and deceleration parameter q are obtained which under specific bound reproduce some of the previous results. We explore physical features of these parameters which (i) provide the scenario of complete evolution of the cosmos with ω( t) and (ii) agree mostly with the observational status of the present phase of the accelerating Universe. [ABSTRACT FROM AUTHOR]

In this paper we study the isotropic cases of static charged fluid spheres in general relativity. For this purpose we consider two different specializations and under these we solve the Einstein-Maxwell field equations in isotropic coordinates. The analytical solutions thus obtained are matched to the exterior Reissner-Nordström solutions which concern the values for the metric coefficients eν and eμ. We derive the pressure, density and pressure-to-density ratio at the center of the charged fluid sphere and boundary R of the star. Our conclusion is that static charged fluid spheres provide a good connection to compact stars. [ABSTRACT FROM AUTHOR]

Exact solutions to the Einstein field equations with cosmic string and a space-varying cosmological constant, viz. Λ = Λ(r), in the energy–momentum tensors are presented. Three cases have been studied: the variable cosmological constant (1) has power law dependence, (2) is proportional to the string fluid density, and (3) is purely a constant. Some cases of interesting physical consequences have been found where (i) the variable cosmological constant can be represented by a power law of the type Λ = 3r-2, (ii) the variable cosmological constant and the cosmic string density are interdependent according to the relation Λ = -8πρs, and (iii) the cosmic string density can be scaled by a power law of the type ρs = r-2. It is also shown that several known solutions can be recovered from the general form of the solutions obtained here. [ABSTRACT FROM AUTHOR]

Equation-of-state parameter plays a significant role for guessing the real nature of dark energy. Here polytropic equation-of-state p = ωρn is chosen for some of the kinematical Λ-models viz., $\Lambda \sim (\dot a/a)^2$, $\Lambda \sim \ddot a/a$ and Λ ~ ρ. Although in dust cases (ω = 0) closed form solutions show no dependency on the polytropic index n, but in non-dust situations some new possibilities are opened up including phantom energy with supernegative (ω < -1) equation-of-state parameter. [ABSTRACT FROM AUTHOR]

In this article, Einstein–Maxwell space–time is considered in connection with some of the astrophysical solutions previously obtained by Tolman (1939) and Bayin (1978). The effect of inclusion of charge in these solutions is investigated thoroughly and the nature of fluid pressure and mass density throughout the sphere is discussed. Mass–radius and mass–charge relations are derived for various cases of the charged matter distribution. Two cases are obtained where perfect fluid with positive pressures gives rise to electromagnetic mass models such that gravitational mass is of purely electromagnetic origin. [ABSTRACT FROM AUTHOR]

In this paper, we develop a new class of models for a compact star with anisotropic stresses inside the matter distribution. By assuming a linear equation of state for the anisotropic matter composition of the star we solve the Einstein field equations. In our approach, for the interior solutions we use a particular form of the an satz for the metric function g r r. The exterior solution is assumed as the Schwarzschild metric and is joined with the interior metric obtained across the boundary of the star. These matching of the metrices along with the condition of the vanishing radial pressure at the boundary lead us to determine the model parameters. The physical acceptability of the solutions has verified by making use of the current estimated data available from the pulsar 4 U 1608 − 52. Thereafter, assuming anisotropy due to tidal effects we calculate the Love numbers from our model and compare the results with the observed compact stars, viz. K S 1731 − 260 , 4 U 1608 − 52 , 4 U 1724 − 207 , 4 U 1820 − 30 , S A X J 1748. 9 − 2021 and E X O 1745 − 268. The overall situation confirms physical viability of the proposed approach, which can shed new light on the interior of the compact relativistic objects. • Investigation of a compact star with anisotropic stresses. • We assume a linear equation of state to solve the Einstein field equations. • Love numbers are calculated from the presented model. • We have compared the results with the observed compact stars. • Solutions provide a physical viability of the proposed approach. [ABSTRACT FROM AUTHOR]

We present a simple and effective new methodology to build up self-gravitating structures driven by an imperfect fluid distributions. This approach is developed within the framework of f (R , T) gravity theory by combining two geometrical schemes, the gravitational decoupling by means of minimal geometric deformation and the embedding technique, specifically the class I grasp. The former, allows to introduce extra matter fields into the system, modifying the energy–momentum tensor, as well as new degrees of freedom altering the mass function and its associated metric potential, i.e, the g r r component. On the other hand the class I focusing, provides precious and useful mathematical information to determine the full geometrical description of the internal spacetime. Furthermore, to obtain the final form of the modified material content the so-called mimic constraint procedure is employed. To check the mathematical, physical and astrophysical viability of the present proposal, we have framed a detailed discussion on the matching condition process and studied the effects introduced by the mimic constraint approach on the mass function. Finally, to support the feasibility of the results a thorough graphical analysis is performed. [ABSTRACT FROM AUTHOR]