Inflationary f (R) Cosmologies by Heba Sami, Joseph Ntahompagaze, Amare Abebe

“…This paper discusses a simple procedure to reconstruct f ( R ) -gravity models from exact cosmological solutions of the Einstein field equations with a non-interacting classical scalar field-and-radiation background. …”
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Lie symmetry approach to the time-dependent Karmarkar condition by Andronikos Paliathanasis, Robert S. Bogadi, Megandhren Govender

“…Abstract We obtain solutions of the time-dependent Einstein Field Equations which satisfy the Karmarkar condition via the method of Lie symmetries. …”
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Anisotropic generalization of well-known solutions describing relativistic self-gravitating fluid systems: an algorithm by S. Thirukkanesh, F. C. Ragel, Ranjan Sharma, Shyam Das

“…Abstract We present an algorithm to generalize a plethora of well-known solutions to Einstein field equations describing spherically symmetric relativistic fluid spheres by relaxing the pressure isotropy condition on the system. …”
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Classical Variational Theory of the Cosmological Constant and Its Consistency with Quantum Prescription by Claudio Cremaschini, Massimo Tessarotto

“…The manifestly-covariant Hamiltonian structure of classical General Relativity is shown to be associated with a path-integral synchronous Hamilton variational principle for the Einstein field equations. A realization of the same variational principle in both unconstrained and constrained forms is provided. …”
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Impacts of complexity factor on the transition of fluid configurations from isotropic to anisotropic environment and vice versa by M. Zubair, Hafsa Jameel, Hina Azmat

“…We consider gravitational decoupling via MGD (Minimal Geometric Deformation) approach for spherically symmetric systems with static background and explore the scenarios where the isotropization of an anisotropic solution of Einstein field equations is possible. Moreover, we work on generating the new analogues of Durgapal–Fuloria model under different conditions associated with complexity factor. …”
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Isotropization and change of complexity by gravitational decoupling by R. Casadio, E. Contreras, J. Ovalle, A. Sotomayor, Z. Stuchlik

“…Abstract We employ the gravitational decoupling approach for static and spherically symmetric systems to develop a simple and powerful method in order to (a) continuously isotropize any anisotropic solution of the Einstein field equations, and (b) generate new solutions for self-gravitating distributions with the same or vanishing complexity factor. …”
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Dark matter and dark energy denote the gravitation of the expanding universe by Arto Annila, Mårten Wikström

“…In line with the Einstein field equations, the vacuum quanta embodying gravitation, geometrized as spacetime, equate in dynamic balance to the quanta embodying the substance of the stress–energy tensor. …”
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Twistor theory of higher-dimensional black holes by Metzner, N

“…This thesis will propose such a generalized Ernst potential, point out where the rod structure of the space-time can be found in the twistor picture and thereby provide a procedure for generating solutions to the Einstein field equations in higher dimensions from the rod structure, other asymptotic data, and the requirement of a regular axis. …”

Symmetries in Classical and Quantum Treatment of Einstein’s Cosmological Equations and Mini-Superspace Actions by Theodosios Christodoulakis, Alexandros Karagiorgos, Adamantia Zampeli

“…The use of automorphisms of the various Bianchi-type Lie algebras as Lie-point symmetries of the corresponding Einstein field equations entails a reduction of their order and ultimately leads to the entire solution space. …”
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Relativistic modeling of stellar objects in a Schwarzschild’s coordinates with embedded class one spacetime by Amit Kumar Prasad, Mahesh Kumar, Jitendra Kumar

“…Abstract In this study, we investigate a new relativistic anisotropic Einstein field equations solution for compact stars under embedding class 1 conditions. …”
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On the number of light rings in curved spacetimes of ultra-compact objects by Shahar Hod

“…In a very interesting paper, Cunha, Berti, and Herdeiro have recently claimed that ultra-compact objects, self-gravitating horizonless solutions of the Einstein field equations which have a light ring, must possess at least two (and, in general, an even number of) light rings, of which the inner one is stable. …”
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Pinching Theorems for Statistical Submanifolds in Sasaki-Like Statistical Space Forms by Ali H. Alkhaldi, Mohd. Aquib, Aliya Naaz Siddiqui, Mohammad Hasan Shahid

“…Finally, we provide the condition under which the metric of Sasaki-like statistical manifolds with constant curvature is a solution of vacuum Einstein field equations.…”
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The evolution of time-dependent Λ and G in multi-fluid Bianchi type-I cosmological models by Alfedeel Alnadhief H. A., Abebe Amare

“…The observationally known values of Ωm,Ωr{\Omega }_{{\rm{m}}},{\Omega }_{{\rm{r}}} and ΩΛ{\Omega }_{\Lambda } have been used to solve the Einstein field equations for the model and the resulting behaviours of the physical and dynamical quantities, with particular emphasis on late-time cosmology, are discussed. …”
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Hidden simplicity of the gravity action by Clifford Cheung, Grant N. Remmen

“…The corresponding equations of motion are the Einstein field equations rewritten as two coupled first-order differential equations. …”
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Studies an analytic model of a spherically symmetric compact object in Einsteinian gravity by Abdelghani Errehymy, Mohammed Daoud

“…We have imposed a collective function based on an adjustable coefficient to solve the Einstein field equations (EFEs). We investigate the general physical characteristics of high-density astrophysical objects based on the required solutions, with the inside structure of the stellar objects, such as the energy conditions, stability analysis, mass function, surface redshift function, velocity of sound and compactness of stellar objects through theoretical expression as well as graphic plots. …”
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A comparative study of the linear and colour-flavour-locked equation of states for compact objects by S. Thirukkanesh, Anand Kaisavelu, Megan Govender

“…Abstract In this work we present a general framework for obtaining exact solutions to the Einstein field equations describing strange stars obeying a colour-flavour-locked (CFL) equation of state. …”
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Anisotropic Universes Sourced by Modified Chaplygin Gas by Saibal Ray, Sunil Kumar Tripathy, Rikpratik Sengupta, Bibhudutta Bal, Sonali Monalisa Rout

“…We obtain the volume and scale factors as solutions to the Einstein Field Equations (EFEs) for the anisotropic universes, and check whether the initial anisotropy is washed out or not for different values of the MCG parameters present in the solution by obtaining the anisotropy parameters for each solution. …”
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ON THE POST-LINEAR QUADRUPOLE-QUADRUPOLE METRIC by FRANCISCO FRUTOS ALFARO, MICHAEL SOFFEL

“…Solving the Einstein field equations, we added terms of second order in the quadrupole moment to its post-linear version in order to compare it with solutions found by Blanchet in the multi-polar post-Minkowskian framework. …”
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Mechanical Entropy and Its Implications by Pharis E. Williams

“…An extension of the gauge principle into a five-dimensional manifold, then restricting the generality of the five-dimensional manifold by using the conservation principle, shows that the four-dimensional hypersurface that is embedded within the 5-D manifold is required to obey Einstein's field equations. The 5-D gravitational quantum equations of the solar system are presented.…”
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Barrow Holographic Dark Energy Model in Bianchi Type-III Universe with Quintessence by Chandra Rekha Mahanta, Dibyajyoti Das

“…We assume the cold dark matter and Barrow holographic dark energy to be non-interacting and obtain exact solutions of the Einstein field equations by considering a hybrid expansion law and assuming that the expansion scalar is proportional to the shear scalar. …”
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