Non-adiabatic radiative collapse of a relativistic star under different initial conditions

We examine the role of space-time geometry in the non-adiabatic collapse of a star dissipating energy in the form of radial heat flow, studying its evolution under different initial conditions. The collapse of a star with interior comprising of a homogeneous perfect fluid is compared with that of a star filled with inhomogeneous imperfect fluid with anisotropic pressure. Both the configurations are spherically symmetric, however, in the latter case, the physical space $t= constant$ of the configurations is assumed to be inhomogeneous endowed with spheroidal or pseudo-spheroidal geometry. It is observed that as long as the collapse is shear-free, its evolution depends only on the mass and size of the star at the onset of collapse.Comment: To appear in Pramana- j. of physic

Global monopole as dual-vacuum solution in Kaluza-Klein spacetime

By application of the duality transformation, which implies interchange of active and passive electric parts of the Riemann curvature (equivalent to interchange of Ricci and Einstein tensors) it is shown that the global monopole solution in the Kaluza-Klein spacetime is dual to the corresponding vacuum solution. Further we also obtain solution dual to flat space which would in general describe a massive global monopole in 4-dimensional Euclidean space and would have massless limit analogus to the 4-dimensional dual-flat solution.Comment: 8 pages, LaTEX versio

Why Should You Study Mathematics?

How can one then be motivated to study mathematics? This article attempts to break these myths and supply an answer to the question an aspiring college student would ask of us: why should I choose a degree in mathematics and a career as a mathematician? Let me first get this notion out of the way that mathematics is a difficult subject. I am, by profession, a computer scientist. I study algorithms, applications, systems software, and hardware. When I tell people about my profession, most confide in me that they do not understand computers. Many others confess that they have found programming to be difficult. I find biology and medicine, with all those complex and difficult to spell terms, like hydroxychloroquine, to be harrowing. So, difficult is a relative term: one person’s difficult is another person’s easy. Once a subject is understood, it no longer remains hard or mysterious. To me, all it takes is motivation and perseverance - this applies to any field, not just to mathematics. So, why should you study mathematics

Classes of exact Einstein-Maxwell solutions

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.Comment: 16 pages, To appear in Gen. Relativ. Gravi

Maximum mass of a cold compact star

We calculate the maximum mass of the class of compact stars described by Vaidya-Tikekar \cite{VT01} model. The model permits a simple method of systematically fixing bounds on the maximum possible mass of cold compact stars with a given value of radius or central density or surface density. The relevant equations of state are also determined. Although simple, the model is capable of describing the general features of the recently observed very compact stars. For the calculation, no prior knowledge of the equation of state (EOS) is required. This is in contrast to the earlier calculations for maximum mass which were done by choosing first the relevant EOSs and using those to solve the TOV equation with appropriate boundary conditions. The bounds obtained by us are comparable and, in some cases, more restrictive than the earlier results.Comment: 18 pages including 4 *.eps figures. Submitted for publicatio

Relativistic Solution for a Class of Static Compact Charged Star in Pseudo Spheroidal Space-Time

Considering Vaidya-Tikekar metric, we obtain a class of solutions of the Einstein-Maxwell equations for a charged static fluid sphere. The physical 3-space (t=constant) here is described by pseudo-spheroidal geometry. The relativistic solution for the theory is used to obtain models for charged compact objects, thereafter a qualitative analysis of the physical aspects of compact objects are studied. The dependence of some of the properties of a superdense star on the parameters of the three geometry is explored. We note that the spheroidicity parameter $a$, plays an important role for determining the properties of a compact object. A non-linear equation of state is required to describe a charged compact object with pseudo-spheroidal geometry which we have shown for known masses of compact objects. We also note that the size of a static compact charged star is more than that of a static compact star without charge.Comment: 24 pages, 18 figures, 8 table

A duality relation for fluid spacetime

We consider the electromagnetic resolution of gravitational field. We show that under the duality transformation, in which active and passive electric parts of the Riemann curvature are interchanged, a fluid spacetime in comoving coordinates remains invariant in its character with density and pressure transforming, while energy flux and anisotropic pressure remaining unaltered. Further if fluid admits a barotropic equation of state, $p = (\gamma - 1) \rho$ where $1 \leq \gamma \leq 2$, which will transform to $p = (\frac{2 \gamma}{3 \gamma - 2} - 1) \rho$. Clearly the stiff fluid and dust are dual to each-other while $\rho + 3 p =0$, will go to flat spacetime. However the n $(\rho - 3 p = 0)$ and the deSitter $(\rho + p = 0$) universes ar e self-dual.Comment: 5 pages, LaTeX version, Accepted in Classical Quantum Gravity as a Lette