arXiv subjects

Rajibul Shaikh

Publications and source records attributed to Rajibul Shaikh.

32 records · Page 2Linked to original sources

arXiv2019

Black hole shadow in a general rotating spacetime obtained through Newman-Janis algorithm

The Newman-Janis (NJ) algorithm has been extensively used in the literature to generate rotating black hole solutions from nonrotating seed spacetimes. In this work, we show, using various constants of motion, that the null geodesic equations in an arbitrary stationary and axially symmetric rotating spacetime obtained through the NJ algorithm can be separated completely, provided that the algorithm is applied successfully without any inconsistency. Using the separated null geodesic equations, we then obtain an analytic general formula for obtaining the contour of a shadow cast by a compact object whose gravitational field is given by the arbitrary rotating spacetime under consideration. As special cases, we apply our general analytic formula to some known black holes and reproduce the corresponding results for black hole shadow. Finally, we consider a new example and study shadow using our analytic general formula.

gr-qc↗

arXiv2019

Analytical approach to strong gravitational lensing from ultracompact objects

Strong gravitational lensing from black holes results in the formation of relativistic images, in particular, relativistic Einstein rings. For objects with event horizons, the radius of the unstable light ring (photon sphere) is the lowest radius at which a relativistic image might be formed. For horizonless ultracompact objects, additional relativistic images and rings can form inside this radius. In this paper, we provide an analytical approach to deal with strong gravitational lensing from such ultracompact objects, which is substantially different from the black hole cases, first reported by Bozza. Here, our analysis indicates that the angular separations and magnifications of relativistic images inside the unstable light ring (photon sphere) might be several orders of magnitude higher compared to the ones outside it. This indicates fundamental differences in the nature of strong gravitational lensing from black holes and ultracompact objects.

gr-qc↗

arXiv2019

Tidal effects away from the equatorial plane in Kerr backgrounds

We study tidal effects on self-gravitating Newtonian stars rotating around a Kerr black hole in stable circular orbits away from the equatorial plane. Such cases are exemplified by a non-vanishing Carter's constant. Here, we calculate the tidal disruption limit (Roche limit) of the star numerically, in Fermi normal coordinates. The Roche limit is found to depend strongly on the choice of the orbit, and differs significantly from the equatorial plane result as one approaches nearly polar orbits. As expected, this difference is large when the star is close to the black hole (near to the innermost stable circular orbit) and becomes smaller when the star is far from it. We also discuss the dependence of the Roche limit on the equation of state of the star, taking two specific parameter values as examples.

gr-qc↗

arXiv2019

Overcharging black holes and cosmic censorship in Eddington-inspired Born-Infeld gravity

The Eddington-inspired Born-Infeld (EiBI) gravity is a modification of the theory of general relativity inspired by the nonlinear Born-Infeld electrodynamics. The theory is described by a series of higher curvature terms added to the Einstein-Hilbert action with the parameter $κ$. The EiBI gravity has several interesting exact neutral and charged black hole solutions. We study the problem of overcharging extremal black hole solutions of EiBI gravity using a charged test particle to create naked singularity. We show that unlike general relativity, the overcharging could be possible for a charged extremal black hole in EiBI gravity as long as the matter sector is described by usual Maxwell's electrodynamics. Once the matter sector is also modified in accordance to the Born-Infeld prescription with the parameter $b$, the overcharging is not possible as long as the parameters obey the condition $4 κb^2 \leq 1$.

gr-qc↗

arXiv2018

A novel gravitational lensing feature by wormholes

Horizonless compact objects with light rings (or photon spheres) are becoming increasingly popular in recent years for several reasons. In this paper, we show that a horizonless object such as a wormhole of Morris-Thorne type can have two photon spheres. In particular, we show that, in addition to the one present outside a wormhole throat, the throat can itself act as an effective photon sphere. Such wormholes exhibit two sets of relativistic Einstein ring systems formed due to strong gravitational lensing. We consider a previously obtained wormhole solution as a specific example. If such type of wormhole casts a shadow at all, then the inner set of the relativistic Einstein rings will form the outer bright edge of the shadow. Such a novel lensing feature might serve as a distinguishing feature between wormholes and other celestial objects as far as gravitational lensing is concerned.

gr-qc↗

arXiv2018

Shadows of spherically symmetric black holes and naked singularities

We compare shadows cast by Schwarzschild black holes with those produced by two classes of naked singularities that result from gravitational collapse of spherically symmetric matter. The latter models consist of an interior naked singularity spacetime restricted to radii $r\leq R_b$, matched to Schwarzschild spacetime outside the boundary radius $R_b$. While a black hole always has a photon sphere and always casts a shadow, we find that the naked singularity models have photon spheres only if a certain parameter $M_0$ that characterizes these models satisfies $M_0\geq 2/3$, or equivalently, if $R_b\leq 3M$, where $M$ is the total mass of the object. Such models do produce shadows. However, models with $M_0<2/3$ (or $R_b>3M$) have no photon sphere and do not produce a shadow. Instead, they produce an interesting `full-moon' image. These results imply that the presence of a shadow does not by itself prove that a compact object is necessarily a black hole. The object could be a naked singularity with $M_0\geq 2/3$, and we will need other observational clues to distinguish the two possibilities. On the other hand, the presence of a full-moon image would certainly rule out a black hole and might suggest a naked singularity with $M_0<2/3$. It would be worthwhile to generalize the present study, which is restricted to spherically symmetric models, to rotating black holes and naked singularities.

astro-ph.HE↗

arXiv2018

Wormholes with nonexotic matter in Born-Infeld gravity

We show that, in contrast to general relativity, in Eddington-inspired Born-Infeld gravity (EiBI), a violation of the null convergence condition does not necessarily lead to a violation of the null energy condition, by establishing a relationship between them. This serves as a motivation for finding wormhole solutions which can be supported by nonexotic matter in this gravity theory. We then obtain exact solutions of the field equations in EiBI gravity coupled to arbitrary nonlinear electrodynamics and anisotropic fluids. Depending on the signs and values of different parameters, the general solutions can represent both black holes and wormholes. In this work, we analyze the wormhole solutions. These wormholes are supported by nonexotic matter, i.e., matter satisfying all the energy conditions. As special cases of our general solutions, we work out several specific examples by considering Maxwell, power-law, Born-Infeld electrodynamics models and a particular form of an anisotropic fluid.

gr-qc↗

arXiv2018

Gravitational collapse in $(2+1)$-dimensional Eddington-inspired Born-Infeld gravity

We study here the gravitational collapse of dust in $(2+1)$-dimensional spacetimes for the formation of black holes (BH) and naked singularities (NS) as final states in a modified theory of gravity, with vanishing cosmological constant. From the perspective of cosmic censorship, we investigate the collapse of a dust cloud in Eddington-inspired Born-Infeld gravity (EiBI) and compare the results with those of general relativity (GR). It turns out that, as opposed to the general relativistic situation, where the outcome of dust collapse in $(2+1)$ dimensions is always a naked singularity, the EiBI theory has a certain range of parameter values that avoid the naked singularity. This indicates that a $(3+1)$-dimensional generalization of these results could be useful and worth examining. Finally, using the results here, we show that the singularity avoidance through homogeneous bounce in cosmology in this modified gravity is not stable.

gr-qc↗

arXiv2018

Shadows of rotating wormholes

We study shadows cast by a certain class of rotating wormholes and point out the crucial role of a rotating wormhole throat in the formation of a shadow. Overlooking this crucial role of a wormhole throat has resulted incomplete results in the previous studies on shadows of the same class of rotating wormholes. We explore the dependence of the shadows on the spin of the wormholes. We compare our results with that of the Kerr black hole. With increasing values of the spin, the shapes of the wormhole shadows start deviating considerably from that of the black hole. Such considerable deviation, if detected in future observations, may possibly indicate the presence of a wormhole. In other words, the results obtained here indicate that, through the observations of their shadows, the wormholes which are considered in this work and have reasonable spin, can be distinguished from a black hole.

gr-qc↗

arXiv2017

Gravitational lensing by scalar-tensor wormholes and the energy conditions

We study gravitational lensing by a class of zero Ricci scalar wormholes which arise as solutions in a scalar-tensor theory of gravity. An attempt is made to find a possible link between lensing features, stable/unstable photon orbits and the energy conditions on the matter required to support these spacetimes. Our analysis shows (for this class of wormholes) that light rays always exhibit a positive deflection if the energy conditions are satisfied (nonexotic matter content). In contrast, if the energy conditions are violated (exotic matter), the net deflection of a light ray may be positive, negative or even zero, depending on values of the metric and impact parameters. This prompts us to introduce a surface defined by a turning point value at which the net deflection of a light ray is equal to zero, even though we have a curved spacetime geometry. We argue that the existence of such a surface may be linked to exotic/energy condition violating matter. Wormholes in modified gravity with matter satisfying the energy conditions do not seem to have such a zero deflection surface. Finally, we study strong gravitational lensing briefly and also look into the formation of Einstein and relativistic Einstein rings. We conclude with some estimates on the wormhole mass, throat-radius and the detectability of the Einstein rings.

gr-qc↗

arXiv2016

Wormholes, the weak energy condition, and scalar-tensor gravity

We obtain a large class of Lorentzian wormhole spacetimes in scalar-tensor gravity, for which the matter stress energy does satisfy the weak energy condition. Our constructions have zero Ricci scalar and an everywhere finite, non-zero scalar field profile. Interpreting the scalar-tensor gravity as an effective on-brane theory resulting from a two-brane Randall--Sundrum model of warped extra dimensions, it is possible to link wormhole existence with that of extra dimensions. We study the geometry, matter content, gravitational red-shift and circular orbits in such wormholes and argue that our examples are perhaps among those which may have some observational relevance in astrophysics in future. We also study traversability and find that our wormholes are indeed traversable for values of the metric parameters satisfying the weak energy condition.

gr-qc↗

arXiv2015

Lorentzian wormholes in Eddington-inspired Born-Infeld gravity

We show that it is possible to construct a wide class of Lorentzian wormholes in Eddington-inspired Born-Infeld gravity with a stress energy which does not violate the weak or null energy condition. The wormholes exist in a certain region of the parameter space. In fact, it is shown that there is a critical value of a parameter defined in our work, below which we have wormholes. Above the critical value, we have a regular black hole spacetime. We put a restriction on the equation of state parameter $α$ ($p_θ=αρ$) to have wormholes. We also put a lower limit on both the theory parameter $|κ|$ and the throat radius, to restrict the tidal acceleration (at the throat) below one Earth gravity. As a special case of our general solution, we retrieve the wormhole supported by an electric field for a charge-to-mass ratio greater than the critical value $\left(\frac{Q}{M}\right)_c\approx 1.144$.

gr-qc↗

arXiv2015

Evolution of geodesic congruences in a gravitationally collapsing scalar field background

The evolution of timelike geodesic congruences in a spherically symmetric, nonstatic, inhomogeneous spacetime representing gravitational collapse of a massless scalar field is studied. We delineate how initial values of the expansion, rotation and shear of a congruence, as well as the spacetime curvature, influence the global behavior and focusing properties of a family of trajectories. Under specific conditions, the expansion scalar is shown to exhibit a finite jump (from negative to positive value) before focusing eventually occurs. This nonmonotonic behavior of the expansion, observed in our numerical work, is successfully explained through an analysis of the equation for the expansion. Finally, we bring out the role of the metric parameters (related to nonstaticity and spatial inhomogeneity), in shaping the overall behavior of geodesic congruences.

gr-qc↗

arXiv2014

Kinematics of trajectories in classical mechanics

In this paper, we show how the study of kinematics of a family of trajectories of a classical mechanical system may be unified within the framework of analysis of geodesic flows in Riemannian geometry and Relativity. After setting up the general formalism, we explore it through studies on various one and two dimensional systems. Quantities like expansion, shear and rotation (ESR), which are more familiar to the relativist, now re-appear while studying such families of trajectories in configuration space, in very simple mechanical systems. The convergence/divergence of a family of trajectories during the course of time evolution, the shear and twist of the area enclosing the family, and the focusing/defocusing of the trajectories within a finite time are investigated analytically for these systems. The understanding of the configuration space developed through such investigations is elaborated upon, and possible future avenues are pointed out.

gr-qc↗