Spectral features of radiation from Nordström and Kerr-Newman white holes

Unlike the Schwarzschild white hole, Nordström and Kerr-Newman white holes cannot explode right down from the space time singularityR=0. For example a charged white hole has to commence explosion (i.e., comes into existence) with a radiusR ₀=R _c (2?R _c /R _b )^?1 whereR _c is the ‘classical radius’ andR _b is the final radius attained when the stationary state is reached. That means charged and rotating black holes also cannot hit the singularityR=0 and perish. Here the explosion is decelerated by the presence of charge and rotation and hence the radiation emitted would be not as energetic as in the Schwarzschild case where its energy is infinitely large for emission fromR=0.     

On the static Lovelock black holes

We consider static spherically symmetric Lovelock black holes and generalize the dimensionally continued black holes in such a way that they asymptotically for large $r$ go over to the d-dimensional Schwarzschild black hole in dS/AdS spacetime. This means that the master algebraic polynomial is not degenerate but instead its derivative is degenerate. This family of solutions contains an interesting class of pure Lovelock black holes which are the $N$ th order Lovelock $\Lambda $ -vacuum solutions having the remarkable property that their thermodynamical parameters have the universal character in terms of the event horizon radius. This is in fact a characterizing property of pure Lovelock theories. We also demonstrate the universality of the asymptotic Einstein limit for the Lovelock black holes in general.     

On the equivalence of the Einstein–Hilbert and the Einstein–Palatini formulations of general relativity for an arbitrary connection

In the framework of the Einstein–Palatini formalism, even though the projective transformation connecting the arbitrary connection with the Levi-Civita connection has been floating in the literature for a long time and perhaps the result was implicitly known in the affine gravity community, yet as far as we know Julia and Silva were the first to realise its gauge character. We rederive this result by using the Rosenfeld–Dirac–Bergmann approach to constrained Hamiltonian systems and do a comprehensive self contained analysis establishing the equivalence of the Einstein–Palatini and the metric formulations without having to impose the gauge choice that the connection is symmetric. We also make contact with the the Einstein–Cartan theory when the matter Lagrangian has fermions.     

Inheriting geodesic flows

We investigate the propagation equations for the expansion, vorticity and shear for perfect fluid space-times which are geodesic. It is assumed that space-time admits a conformal Killing vector which is inheriting so that fluid flow lines are mapped conformally. Simple constraints on the electric and magnetic parts of the Weyl tensor are found for conformal symmetry. For homothetic vectors the vorticity and shear are free; they vanish for nonhomothetic vectors. We prove a conjecture for conformal symmetries in the special case of inheriting geodesic flows: there exist no proper conformal Killing vectors (ψ _;ab ≠ 0) for perfect fluids except for Robertson-Walker space-times. For a nonhomothetic vector field the propagation of the quantity ln (R _ab u ^a u ^b ) along the integral curves of the symmetry vector is homogeneous.     

Isothermal fluid sphere: Uniqueness and conformal mapping

We prove the theorem: A necessary and sufficient condition for a spacetime to represent an isothermal fluid sphere (linear equation of state with density falling off as inverse square of the curvature radius) without boundary is that it is conformal to a spacetime of zero gravitational mass (‘minimally’ curved).     

A conformal mapping and isothermal perfect fluid model

Instead of the metric conformal to flat spacetime, we take the metric conformal to a spacetime which can be thought of as minimally curved in the sense that free particles experience no gravitational force yet it has non-zero curvature. The base spacetime can be written in the Kerr-Schild form in spherical polar coordinates. The conformal metric then admits the unique three-parameter family of perfect fluid solutions which are static and inhomogeneous. The density and pressure fall off in the curvature radial coordinates asR ^–2, for unbounded cosmological model with a barotropic equation of state. This is the characteristic of an isothermal fluid. We thus have an ansatz for an isothermal perfect fluid model. The solution can also represent bounded fluid spheres.     

Charged particle orbits in the field of two charges placed symmetrically near a schwarzschild black hole

From the Copson and Linet solution for the electrostatic field due to a point charge near a Schwarzschild black hole, we have deduced the field due to two equal charges placed symmetrically (diametrically opposite) about the hole. It turns out that the motion of a test-charged particle is completely solvable only in the equatorial plane, because theϑ-equation does not yield the first integral forϑ ≠π/2. We have however considered circular orbits about the axis forϑ=constant ≠π/2 by requiring bothϑ andr to remain fixed all through the motion. Forϑ ≠π/2 orbits, in contrast to the similar classical situation, there occur forbiddenϑ-ranges. This seems to be a relativistic effect.     

Generating Spacetimes of Zero Gravitational Mass

We propose a geometric restriction on Euclidean/Minkowski distance in the embedding space being proportional to distance in the embedded space, to generate spacetimes with vanishing gravitational mass (R_ikuⁱu^k = 0, u_iuⁱ = 1). They are in fact dual-flat. This is also the condition that characterizes global monopoles and textures.