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1.
Einstein field equations for static anisotropic spheres are solved and exact interior solutions obtained. This paper extends
earlier treatments to include anisotropic models which accommodate a wider variety of physically viable energy densities.
Two classes of solutions are possible. The first class contains the limiting caseμ,∝ r-2 for the energy density which arises in many astrophysical applications. In the second class the singularity at the centre
of the star is not present in the energy density. 相似文献
2.
Zheng J. Maharaj C. Liu J. Chai H. Liu H. Dear J. P. 《Mechanics of Composite Materials》2022,58(1):125-140
Mechanics of Composite Materials - In this research, the maximum stress, Hashin, Puck, LaRC03, and Northwestern University (NU) criteria are analyzed based literature data, analytical results... 相似文献
3.
Endgame studies have long served as a tool for testing human creativity and intelligence. We find that they can serve as a tool for testing machine ability as well. Two of the leading chess engines, Stockfish and Leela Chess Zero (LCZero), employ significantly different methods during play. We use Plaskett’s Puzzle, a famous endgame study from the late 1970s, to compare the two engines. Our experiments show that Stockfish outperforms LCZero on the puzzle. We examine the algorithmic differences between the engines and use our observations as a basis for carefully interpreting the test results. Drawing inspiration from how humans solve chess problems, we ask whether machines can possess a form of imagination. On the theoretical side, we describe how Bellman’s equation may be applied to optimize the probability of winning. To conclude, we discuss the implications of our work on artificial intelligence (AI) and artificial general intelligence (AGI), suggesting possible avenues for future research. 相似文献
4.
5.
The junction conditions for a magnetohydrodynamic fluid sphere undergoing dissipative gravitational collapse in the form of
a radial heat flux with shear are obtained. These conditions extend particular results of earlier treatments. We demonstrate
that the pressure is proportional to the magnitude of the heat flux as is the case in shear-free models. However in our case
the gravitational potentials must be solutions of the Einstein-Maxwell system of equations. The mass function m(v) is increased by a factor related to the charge Q of the radiating star. Physical quantities relating to the local conservation of momentum and surface redshift are obtained. 相似文献
6.
Byron P. Brassel Sunil D. Maharaj Rituparno Goswami 《General Relativity and Gravitation》2017,49(8):101
We establish the result that the standard Boulware–Deser spacetime can radiate. This allows us to model the dynamics of a spherically symmetric radiating dynamical star in five-dimensional Einstein–Gauss–Bonnet gravity with three spacetime regions. The local internal region is a two-component system consisting of standard pressure-free, null radiation and an additional string fluid with energy density and nonzero pressure obeying all physically realistic energy conditions. The middle region is purely radiative which matches to a third region which is the vacuum Boulware–Deser exterior. Our approach allows for all three spacetime regions to be modeled by the same class of metric functions. A large family of solutions to the field equations are presented for various realistic equations of state. A comparison of our solutions with earlier well known results is undertaken and we show that Einstein–Gauss–Bonnet analogues of these solutions, including those of Husain, are contained in our family. We also generalise our results to higher dimensions. 相似文献
7.
We obtain the general solution of Liouville's equation in Robertson-Walker space-times, based on Killing vector constants of the motion and a new time-dependent first integral. For photons the solution is generated by conformai Killing vectors. 相似文献
8.
We investigate the conformal geometry of spherically symmetric spacetimes in general without specifying the form of the matter
distribution. The general conformal Killing symmetry is obtained subject to a number of integrability conditions. Previous
results relating to static spacetimes are shown to be a special case of our solution. The general inheriting conformal symmetry
vector, which maps fluid flow lines conformally onto fluid flow lines, is generated and the integrability conditions are shown
to be satisfied. We show that there exists a hypersurface orthogonal conformal Killing vector in an exact solution of Einstein’s
equations for a relativistic fluid which is expanding, accelerating and shearing. 相似文献
9.
The Einstein–Maxwell equations with anisotropic pressures and electromagnetic field are studied with a polytropic equation of state. New exact solutions to the field equations are generated in terms of elementary functions. Special cases of the uncharged solutions of Feroze and Siddiqui (Gen Relativ Gravit 43:1025, 2011) and Maharaj and Mafa Takisa (Gen Relativ Gravit 44:1419, 2012) are recovered. We also obtain exact solutions for a neutral anisotropic gravitating body for a polytrope from our general treatment. Graphical plots indicate that the energy density, tangential pressure and anisotropy profiles are consistent with earlier treatments which suggest relevance in describing relativistic compact stars. 相似文献
10.