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71.
G. Z. Abebe K. S. Govinder S. D. Maharaj 《International Journal of Theoretical Physics》2013,52(9):3244-3254
We consider a relativistic radiating spherical star in conformally flat spacetimes. In particular we study the junction condition relating the radial pressure to the heat flux at the boundary of the star which is a nonlinear partial differential equation. The Lie symmetry generators that leave the equation invariant are identified and we generate an optimal system. Each element of the optimal system is used to reduce the partial differential equation to an ordinary differential equation which is further analysed. We identify new categories of exact solutions to the boundary conditions. Two classes of solutions are of interest. The first class depends on a self similar variable. The second class is separable in the spacetime variables. 相似文献
72.
We establish a new algorithm that generates a new solution to the Einstein field equations, with an anisotropic matter distribution,
from a seed isotropic solution. The new solution is expressed in terms of integrals of an isotropic gravitational potential;
and the integration can be completed exactly for particular isotropic seed metrics. A good feature of our approach is that
the anisotropic solutions necessarily have an isotropic limit. We find two examples of anisotropic solutions which generalise
the isothermal sphere and the Schwarzschild interior sphere. Both examples are expressed in closed form involving elementary
functions only. 相似文献
73.
We present a new class of exact interior solutions for anisotropic spheres to the Einstein field equations with a prescribed
energy density. This category of solutions has similar energy density profiles to the models of Chaisi and Maharaj (Gen. Rel.
Grav. 37, 1177–1189, 2005) whose approach we follow in the integration process. A distinguishing feature of the solutions
presented is that they satisfy a barotropic equation of state linearly relating the radial pressure to the energy density. 相似文献
74.
If G and H are vertex-transitive graphs, then the framing number fr(G,H) of G and H is defined as the minimum order of a graph every vertex of which belongs to an induced G and an induced H. This paper investigates fr(C
m,C
n) for m<n. We show first that fr(C
m,C
n)≥n+2 and determine when equality occurs. Thereafter we establish general lower and upper bounds which show that fr(C
m,C
n) is approximately the minimum of and n+n/m.
Received: June 12, 1996 / Revised: June 2, 1997 相似文献
75.
We find a simple inflationary solution in aninhomogeneous spacetime with heat flux. The heat fluxobeys a causal transport equation, and counteracts theinflationary decrease of energy density. At late times, the heat flux tends to zero and thefluid approaches the equation of state p =–. 相似文献
76.
P. Mafa Takisa S. D. Maharaj A. M. Manjonjo S. Moopanar 《The European Physical Journal C - Particles and Fields》2017,77(10):713
We consider spherical exact models for compact stars with anisotropic pressures and a conformal symmetry. The conformal symmetry condition generates an integral relationship between the gravitational potentials. We solve this condition to find a new anisotropic solution to the Einstein field equations. We demonstrate that the exact solution produces a relativistic model of a compact star. The model generates stellar radii and masses consistent with PSR J1614-2230, Vela X1, PSR J1903+327 and Cen X-3. A detailed physical examination shows that the model is regular, well behaved and stable. The mass–radius limit and the surface red shift are consistent with observational constraints. 相似文献
77.
Dyer, McVittie and Oattes (1987) presented the field equations for shearfree perfect fluid spacetimes which are spherically symmetric and admit a conformal symmetry. Two special solutions of these equations are found. Furthermore, in the general case, one field equation is solved in terms of a Painlevé transcendent, while the remaining equation is reduced to an Emden-Fowler equation. 相似文献
78.
We find new classes of exact solutions to the Einstein–Maxwell system of equations for a charged sphere with a particular
choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced
to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to
the Einstein–Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric
functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely
polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric
field intensity; in particular we generate the Einstein universe for particular parameter values. 相似文献
79.
S. Hansraj S. D. Maharaj T. Mthethwa 《International Journal of Theoretical Physics》2014,53(3):759-772
We study the Einstein-Maxwell equations for isotropic pressure distributions. We postulate a relationship between the electric field intensity and one of the gravitational potentials. An algorithm is developed that allows us to systematically generate new classes of exact solutions for charged relativistic stars. The solutions are expressed in terms of simple elementary functions; it is possible to parametrize the solutions so that different values of a constant allows us to tabulate the models. For a particular class it is possible to generate models without any integration. We study the qualitative features of a particular solution, and show that it is physically reasonable in the region of a spherical shell surrounding the centre. 相似文献
80.
M.C. KweyamaS.D. Maharaj K.S. Govinder 《Nonlinear Analysis: Real World Applications》2012,13(4):1721-1729
We study the evolution of shear-free spherically symmetric charged fluids in general relativity. We find a new parametric class of solutions to the Einstein-Maxwell system of field equations. Our charged results are a generalisation of earlier treatments for neutral relativistic fluids. We regain the first integrals found previously for uncharged matter as a special case. In addition an explicit first integral is found which is necessarily charged. 相似文献