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Register a new userAnisotropic generalization of Buchdahl bound for specific stellar models
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Anisotropy is one factor that appears to be significantly important in the studies of relativistic compact stars. In this paper, we make a generalization of the Buchdahl limit by incorporating an anisotropic effect for a selected class of exact solutions describing anisotropic stellar objects. In the isotropic case of a homogeneous distribution, we regain the Buchdahl limit $2M/R leq 8/9$. Our investigation shows a direct link between the maximum allowed compactness and pressure anisotropy vi-a-vis geometry of the associated $3$-space.
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In this work, we present a class of relativistic and well-behaved solution to Einsteins field equations describing anisotropic matter distribution. We perform our analysis by proposing a Buchdahl ansatz which represents almost all the known analytic solutions to the spherically symmetric, static Einstein equations with a perfect fluid source, including, in particular, the Vaidya-Tikekar. We have considered three different cases for generalized Buchdahl dimensionless parameter K. Our suggested solution is free from physical and geometric singularities, satisfies causality condition, and relativistic adiabatic index(gamma), and exhibits well-behaved nature, as well as, all energy conditions and equilibrium condition are well-defined, which implies that our model is physically acceptable.
Hamiltonian matrices appear in a variety or problems in physics and engineering, mostly related to the time evolution of linear dynamical systems as for instance in ion beam optics. The time evolution is given by symplectic transfer matrices which are the exponentials of the corresponding Hamiltonian matrices. We describe a method to compute analytic formulas for the matrix exponentials of Hamiltonian matrices of dimensions $4times 4$ and $6times 6$. The method is based on the Cayley-Hamilton theorem and the Faddeev-LeVerrier method to compute the coefficients of the characteristic polynomial. The presented method is extended to the solutions of $2,ntimes 2,n$-matrices when the roots of the characteristic polynomials are computed numerically. The main advantage of this method is a speedup for cases in which the exponential has to be computed for a number of different points in time or positions along the beamline.
We give the Buchdahl stability bound in Eddington-inspired Born-Infeld (EiBI) gravity. We show that this bound depends on an energy condition controlled by the model parameter $kappa$. From this bound, we can constrain $kappalesssim 10^{8}text{m}^2$ if a neutron star with a mass around $3M_{odot}$ is observed in the future. In addition, to avoid the potential pathologies in EiBI, a emph{Hagedorn-like} equation of state associated with $kappa$ at the center of a compact star is inevitable, which is similar to the Hagedorn temperature in string theory.
In the present study we have proposed a new model of an anisotropic compact star which admits the Chaplygin equation of state. For this purpose, we consider Buchdahl ansatz. We obtain the solution of proposed model in closed form which is non-singular, regular and well-behaved. In addition to this, we show that the model satisfies all the energy conditions and maintains the hydrostatic equilibrium equation. This model represents compact stars like PSR B0943+10, Her X-1 and SAX J1808.4-3658 to a very good approximate.
From arguments based on Heisenbergs uncertainty principle and Paulis exclusion principle, the molar specific heats of degenerate ideal gases at low temperatures are estimated, giving rise to values consistent with the Nerst-Planck Principle (third law of Thermodynamics). The Bose-Einstein condensation phenomenon based on the behavior of specific heat of massive and non-relativistic boson gases is also presented.
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