Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics

Local anisotropy in self-gravitating systems

The universe is so much bigger than the bit we can see in our observable bubble   and we know nothing about what lies out there in the cosmos. The challenge is so  much bigger than is shown on this chart and it is evident that we really only  understand a tiny fraction of the whole cosmos.  Theories ​for Dark Energy have been around for a long time but we still have no  satisfactory explanation. None of the theories are adequate, some are clearly wrong    – an error of 10^120 is a really big miss!  Scott Dodelson of Carnegie Mellon University, one of the lead scientists behind the  Dark Energy Survey’s new map of cosmic structure says:

Dark Energy

Interior perfect fluid solutions for the Reissner-Nordstr\"om metric are studied on the basis of a new classification scheme. It specifies which two of the characteristics of the fluid are given functions and accordingly picks up one of the three main field equations, the other two being universal. General formulas are found for charged de Sitter solutions, the case of a constant energy component of the energy-momentum tensor, the case of known pressure (including charged dust), and the case of a linear equation of state. Explicit new global solutions, mainly in elementary functions, are given as illustrations. The known solutions are briefly reviewed and corrected.

Static charged perfect fluid spheres in general relativity

The full set of equations governing the evolution of self-gravitating spherically symmetric dissipative fluids with anisotropic stresses is deployed and used to carry out a general study on the behavior of such systems, in the context of general relativity. Emphasis is given to the link between the Weyl tensor, the shear tensor, the anisotropy of the pressure, and the density inhomogeneity. In particular we provide the general, necessary, and sufficient condition for the vanishing of the spatial gradients of energy density, which in turn suggests a possible definition of a gravitational arrow of time. Some solutions are also exhibited to illustrate the discussion.

Spherically symmetric dissipative anisotropic fluids: A General study

Bianchi type I, III, V, VI0, and Kantowski-Sachs type models have been investigated in a scalar tensor theory developed by Saez and Ballester (1985) and Saez (1985). The dynamical behaviour of the models has also been analyzed.

Some Bianchi-type cosmological models in a new scalar-tensor theory

We have studied the evolution of a homogeneous, anisotropic universe given by a Bianchi Type-V cosmological model filled with viscous fluid, in the presence of cos- mological constant Λ. The role of viscous fluid and Λ-term in the Bianchi Type-V universe has been studied.

Bianchi Type-V universe with a viscous fluid and Λ-term

Berman (1983) presented a law of variation of Hubble’s parameter that yields constant deceleration parameter models of the Universe. In this paper, Robertson-Walker models have been studied in Einstein’s theory with cosmological term and in cosmological theory based on Lyra’s geometry. Some simple models have been obtained. The necessary relations in each model have been derived, considering a perfect fluid.

Some cosmological models with constant deceleration parameter

The Bianchi Type-I Universe filled with dark energy from a wet dark fluid has been considered. A new equation of state for the dark energy component of the Universe has been used. It is modeled on the equation of state p = γ(ρ − ρ*) which can describe a liquid, for example water. The exact solutions to the corresponding field equations are obtained in quadrature form. The solution for constant deceleration parameter have been studied in detail for both power-law and exponential forms. The cases γ = 1 and γ = 0 have also been analysed.

Bianchi Type-I Universe with wet dark fluid

The solutions of Einstein’s equations in the presence of a creation field have been obtained for Bianchi type-I, III, V, VIo and Kantowski-Sachs (KS) universes in the quadrature form. Some physically interesting cases have been studied in detail.

T. P. Singh

Papers

Some Bianchi-type cosmological models in a new scalar-tensor theory

Bianchi Type-V universe with a viscous fluid and Λ-term

Some cosmological models with constant deceleration parameter

Bianchi Type-I Universe with wet dark fluid

Bianchi type-I, III, V, VIo and Kantowski-Sachs universes in creation-field cosmology