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This study deals with the spherically symmetric radiating star (with dissipative perfect fluids) with a central vacuum cavity, evolving under the assumption of expansion-free motion. The analytical model of the such dynamics star is discussed in three regimes — diffusion approximation, geodesic motion and self-similarity — and the solutions of dynamical equations are obtained in its complete generality. The structure scalars, which are related to the fundamental properties of fluid distribution, are also discussed which played a very important role in the dynamics of cavity models. It has been shown that energy density is homogeneous but violates the energy condition under quasi-static diffusion approximation.

In this paper, first, we deduce various classes of Bianchi type-I perfect fluid solutions in the $f(T)$ gravity. In order to obtain the above-mentioned classes, we use some algebraic techniques that help to formulate 18 cases. As an application, we bifurcate the obtained classes according to their conformal vector fields (CVFs). Inspecting each class using the process of direct integration, we come to know that in one case, the space-time admits proper CVFs whereas in rest of the cases, obtained metrics either become conformally flat or admit underlying symmetries of the CVFs i.e. homothetic vector fields (HVFs) or Killing vector fields (KVFs). The overall dimension of CVFs for the Bianchi type-I perfect fluid space-times in $f(T)$ gravity turns out to be three, four, five, six and fifteen.

In this paper, we have investigated the physical behavior of cosmological models in modified Teleparallel gravity with a general function $f(T)=\alpha T+\beta {(-T)}^n$ where $\alpha ,\beta$ and $n$ are model parameters and $T$ is the torsion scalar. We have considered a homogeneous and isotropic Friedman universe filled with perfect fluid. We have derived the deceleration parameter $q(\omega ,H(z))$ in terms of equation of state (EoS) parameter $\omega$ and Hubble parameter $H(z)$. We have investigated the variation of $q$ over the observed values of Hubble constant in various observations within the range of redshift $0.07\le z\le 2.30$. Also, we have studied effective energy density ${\rho }^{\mathrm{\text{eff}}}$, effective pressure $p^{\mathrm{\text{eff}}}$ and effective EoS parameter ${\omega }^{\mathrm{\text{eff}}}$. We have observed that the second term of $f(T)$ function behaves just like variable cosmological term $\mathrm{\Lambda }$ (${\omega }^{\mathrm{\text{eff}}}\approx -1$) at late-time universe and causes the acceleration in expansion and works just like dark energy candidates. Also, we have evaluated the age of the present universe for various stages of matter $p=\omega \rho$ and various $f(T)$ functions.

The main purpose of this paper is to study and explore some characteristics of static perfect fluid space-time on paracontact metric manifolds. First, we show that if a $K$-paracontact manifold $M^{2n+1}$ is the spatial factor of a static perfect fluid space-time, then $M^{2n+1}$ is of constant scalar curvature $-2n(2n+1)$ and squared norm of the Ricci operator is given by $4n^2(2n+1)$. Next, we prove that if a $(\kappa ,\mu )$-paracontact metric manifold $M^{2n+1}$ with $\kappa >-1$ is a spatial factor of static perfect space-time, then for $n=1$, $M^{2n+1}$ is flat, and for $n>1$, $M^{2n+1}$ is locally isometric to the product of a flat $(n+1)$-dimensional manifold and an $n$-dimensional manifold of constant negative curvature $-4$. Further, we prove that if a paracontact metric 3-manifold $M^3$ with $Q\varphi =\varphi Q$ is a spatial factor of static perfect space-time, then $M^3$ is an Einstein manifold. Finally, a suitable example has been constructed to show the existence of static perfect fluid space-time on paracontact metric manifold.

The purpose of this paper is to investigate proper conformal vector fields (CVFs) of Bianchi type-I perfect fluid space-times in the $f(R$, $T)$ theory of gravity, where $R$ and $T$ are the Ricci scalar and the trace of energy–momentum tensor, respectively. To seek the proper CVFs, we perform a classification of the space-times by imposing different restrictions on the space-time components. The whole classification consists of 12 cases. By studying each case thoroughly, we conclude that in the $f(R$, $T)$ theory of gravity, the overall dimension of CVFs for the Bianchi type-I space-times turns out to be 3, 4, 5 and 15.

Here, I introduce a method to obtain the stress-energy tensor of the perfect fluid by adding a suitable term to the Einstein–Hilbert action. This term has the physical interpretation of pressure and variation should be understood with respect to the metric. In this derivation, velocity potentials are not needed.

By restricting ${\omega }^{\mathrm{\text{eff}}}=-1$ in this study, we rebuild a $f(T)$ gravity function from a $\mathrm{\Lambda }$CDM model. The equation for obtaining the $f(T)$ function is $f(T)=\frac{1}{2}T-2\alpha {(-T)}^{\frac{1}{2}}-\beta$, where $\alpha$ and $\beta$ are positive constants. A flat FLRW space-time metric has been taken into account, and modified field equations for the Hubble function and scaling factor have been solved. With two observational datasets, $H(z)$ and SNe Ia data, we placed observational constraints on the Hubble function and apparent magnitude $m(z)$ and we were able to determine the model parameters with the best match. These numbers have been used to analyze a number of cosmic phenomena occurring in the expanding cosmos. We have discovered a $\mathrm{\Lambda }$ model-closed transit phase decelerating to accelerating universe model.

We established an anisotropic Bianchi type-I dark energy model in this investigation’s $f(R,L_m)$ gravity, where $f(R,L_m)$ is an arbitrary function of the Ricci-scalar curvature $R$ and the matter Lagrangian $L_m$. For the sake of our analysis, we have taken a particular form of this function, which is represented by the equation $f(R,L_m)=\frac{R}{2}+\alpha L_m^n-\mathrm{\Lambda }$, where $\alpha ,n$ are model free parameters, and $\mathrm{\Lambda }$ is the “cosmological constant”. In order to derive the Hubble function $H(z)$ in terms of redshift $z$, we analytically solved the field equations and established a connection between the energy parameters ${\mathrm{\Omega }}_m,{\mathrm{\Omega }}_k,{\mathrm{\Omega }}_{\mathrm{\Lambda }}$ and $\omega$. By using the ${\chi }^2$-test, we compared this Hubble function to $H(z)$ datasets to find the model and energy parameters that fit the data the best. Also, we have analyzed our result with statefinder and Om diagnostic analysis that suggests the model to be a quintessence dark energy model and tends to $\mathrm{\Lambda }$CDM model in late time.

In this work, generalized weakly ${\mathscr{H}}$-symmetric space-times ${\text{(GWHS)}}_n$ are investigated, where ${\mathscr{H}}$ is any symmetric $(0,2)$ tensor. It is proved that, in a nontrivial ${\text{(GWHS)}}_n$ space-time, the tensor ${\mathscr{H}}$ has a perfect fluid form. Accordingly, sufficient conditions for a nontrivial generalized weakly Ricci symmetric space-time ${\text{(GWRS)}}_n$ to be either an Einstein space-time or a perfect fluid space-time are obtained. Also, conditions for space-times admitting either a generalized weakly symmetric energy-momentum tensor or a generalized weakly symmetric ${𝒵}$ tensor to be Einstein or perfect fluid space-times are provided.

We present a static axisymmetric solution of Einstein’s field equations. Assuming that the deviation from spherically symmetry is small, we linearize the corresponding field equations with the perfect fluid source and up to the first order in quadrupole.

Alcubierre proposed in 1994 that the well known special relativistic limitation that particles cannot travel with velocities bigger than the light speed can be bypassed when such trips are considered globally within specific general relativistic frameworks. Although initial results indicated this scenario as being unphysical, since it would seem to require negative mass-energy density, recent theoretical analyses suggest that such an unphysical situation may not always be necessarily true. In this paper, we present solutions of the Einstein equations using the original Alcubierre warp drive metric endowed with various matter-energy sources, namely dust, perfect fluid, anisotropic fluid, and perfect fluid within a cosmological constant spacetime. A connection of some of these solutions featuring shock waves described by the Burgers equation is also shown.

Formulating a perfect fluid filled spherically symmetric metric utilizing the 3+1 formalism for general relativity, we show that the metric coefficients are completely determined by the mass-energy distribution, and its time rate of change on an initial spacelike hypersurface. Rather than specifying Schwarzschild coordinates for the exterior of the collapsing region, we let the interior dictate the form of the solution in the exterior, and thus both regions are found to be written in one coordinate patch. This not only alleviates the need for complicated matching schemes at the interface, but also finds a new coordinate system for the Schwarzschild spacetime expressed in generalized Painleve-Gullstrand coordinates.

We use surface adapted ellipsoidal coordinates to obtain a first order post-Newtonian (PN) approximation to Dedekind ellipsoids with the intention of proceeding to higher orders.

Marginally stable perfect fluid tori with uniform distribution of specific angular momentum are determined in the Reissner–Nordström–(anti-)de Sitter black-hole and nakedsingularity spacetimes. Toroidal configurations are allowed only in the spacetimes admitting existence of stable circular geodesics. The configurations with equipotential surfaces crossing itself in a cusp allow accretion (inner cusp) and/or excretion (outer cusp) of matter from the toroidal configuration.

We present approximate exterior and interior solutions of Einstein's equations which describe the gravitational field of a static deformed mass distribution. The deformation of the source is taken into account up to the first order in the quadrupole.