Stability of Circular Orbits in General Relativity: A Phase Space Analysis

Phase space method provides a novel way for deducing qualitative features of nonlinear differential equations without actually solving them. The method is applied here for analyzing stability of circular orbits of test particles in various physically interesting environments. The approach is shown to work in a revealing way in Schwarzschild spacetime. All relevant conclusions about circular orbits in the Schwarzschild-de Sitter spacetime are shown to be remarkably encoded in a single parameter. The analysis in the rotating Kerr black hole readily exposes information as to how stability depends on the ratio of source rotation to particle angular momentum. As a wider application, it is exemplified how the analysis reveals useful information when applied to motion in a refractive medium, for instance, that of optical black holes.Comment: 20 pages. Accepted for publication in Int. J. theor. Phy

On Traversable Lorentzian Wormholes in the Vacuum Low Energy Effective String Theory in Einstein and Jordan Frames

Three new classes (II-IV) of solutions of the vacuum low energy effective string theory in four dimensions are derived. Wormhole solutions are investigated in those solutions including the class I case both in the Einstein and in the Jordan (string) frame. It turns out that, of the eight classes of solutions investigated (four in the Einstein frame and four in the corresponding string frame), massive Lorentzian traversable wormholes exist in five classes. Nontrivial massless limit exists only in class I Einstein frame solution while none at all exists in the string frame. An investigation of test scalar charge motion in the class I solution in the two frames is carried out by using the Plebanski-Sawicki theorem. A curious consequence is that the motion around the extremal zero (Keplerian) mass configuration leads, as a result of scalar-scalar interaction, to a new hypothetical "mass" that confines test scalar charges in bound orbits, but does not interact with neutral test particles.Comment: 18 page

Wormhole with varying cosmological constant

It has been suggested that the cosmological constant is a variable dynamical quantity. A class of solution has been presented for the spherically symmetric space time describing wormholes by assuming the erstwhile cosmological constant $\Lambda$ to be a space variable scalar, viz., $\Lambda$ = $\Lambda (r)$ . It is shown that the Averaged Null Energy Condition (ANEC) violating exotic matter can be made arbitrarily small.Comment: 8 pages, 2 figures, Accepted in Gen. Rel. Gra

On static spherically symmetric solutions of the vacuum Brans-Dicke theory

It is shown that among the four classes of the static spherically symmetric solution of the vacuum Brans-Dicke theory of gravity only two are really independent. Further by matching exterior and interior (due to physically reasonable spherically symmetric matter source) scalar fields it is found that only Brans class I solution with certain restriction on solution parameters may represent exterior metric for a nonsingular massive object. The physical viability of the black hole nature of the solution is investigated. It is concluded that no physical black hole solution different from the Schwarzschild black hole is available in the Brans-Dicke theory.Comment: 15 pages, To be published in Gen. Rel. and Grav, typos in references correcte

Modeling galactic halos with predominantly quintessential matter

This paper discusses a new model for galactic dark matter by combining an anisotropic pressure field corresponding to normal matter and a quintessence dark energy field having a characteristic parameter $\omega_q$ such that $-1<\omega_q< -\frac{1}{3}$. Stable stellar orbits together with an attractive gravity exist only if $\omega_q$ is extremely close to $-\frac{1}{3}$, a result consistent with the special case studied by Guzman et al. (2003). Less exceptional forms of quintessence dark energy do not yield the desired stable orbits and are therefore unsuitable for modeling dark matter.Comment: 12 pages, 1 figur

Galactic rotation curves inspired by a noncommutative-geometry background

This paper discusses the observed at rotation curves of galaxies in the context of noncommutative geometry. The energy density of such a geometry is diffused throughout a region due to the uncertainty encoded in the coordinate commutator. This intrinsic property appears to be sufficient for producing stable circular orbits, as well as attractive gravity, without the need for dark matter.Comment: 12 pages, 3 figures. Published in Gen.Rel.Grav. 44 (2012) 905-91

Can electro-magnetic field, anisotropic source and varying Λ\Lambda be sufficient to produce wormhole spacetime ?

It is well known that solutions of general relativity which allow for traversable wormholes require the existence of exotic matter (matter that violates weak or null energy conditions [WEC or NEC]). In this article, we provide a class of exact solution for Einstein-Maxwell field equations describing wormholes assuming the erstwhile cosmological term $\Lambda$ to be space variable, viz., $\Lambda = \Lambda (r)$. The source considered here not only a matter entirely but a sum of matters i.e. anisotropic matter distribution, electromagnetic field and cosmological constant whose effective parts obey all energy conditions out side the wormhole throat. Here violation of energy conditions can be compensated by varying cosmological constant. The important feature of this article is that one can get wormhole structure, at least theoretically, comprising with physically acceptable matters.Comment: Some changes have been mad

Vacuum polarization of a scalar field in wormhole spacetimes

An analitical approximation of $$ for a scalar field in a static spherically symmetric wormhole spacetime is obtained. The scalar field is assumed to be both massive and massless, with an arbitrary coupling $\xi$ to the scalar curvature, and in a zero temperature vacuum state.Comment: 10 pages, RevTeX, two eps figure

Dynamic wormholes, anti-trapped surfaces, and energy conditions

Adapting and extending a suggestion due to Page, we define a wormhole throat to be a marginally anti-trapped surface, that is, a closed two-dimensional spatial hypersurface such that one of the two future-directed null geodesic congruences orthogonal to it is just beginning to diverge. Typically a dynamic wormhole will possess two such throats, corresponding to the two orthogonal null geodesic congruences, and these two throats will not coincide, (though they do coalesce into a single throat in the static limit). The divergence property of the null geodesics at the marginally anti-trapped surface generalizes the ``flare-out'' condition for an arbitrary wormhole. We derive theorems regarding violations of the null energy condition (NEC) at and near these throats and find that, even for wormholes with arbitrary time-dependence, the violation of the NEC is a generic property of wormhole throats. We also discuss wormhole throats in the presence of fully antisymmetric torsion and find that the energy condition violations cannot be dumped into the torsion degrees of freedom. Finally by means of a concrete example we demonstrate that even temporary suspension of energy-condition violations is incompatible with the flare-out property of dynamic throats.Comment: 32 pages in plain LaTex, no figures. Additional text and references adde

A new proposal for Galactic dark matter: Effect of f(T) gravity

It is still a challenging problem to the theoretical physicists to know the exact nature of the galactic dark matter which causes the galactic rotational velocity to be more or less a constant. We have proposed that the dark matter as an effect of f(T) gravity. Assuming the flat rotation curves as input we have shown that f(T) gravity can explain galactic dynamics. Here, we don' have to introduce dark matter. Spacetime metric inspired by f(T) gravity describes the region up to which the tangential velocity of the test particle is constant. This inherent property appears to be enough to produce stable circular orbits as well as attractive gravity.Comment: 7 pages and 1 figure. Minor corrections are made. Accepted for publication in Int.J.Theor.Phy