Narrow Results

Among all electromagnetic theories which (a) are derivable from a Lagrangian, (b) satisfy the dominant energy condition, and (c) in the weak field limit coincide with classical linear electromagnetics, we identify a certain subclass with the property that the corresponding spherically symmetric, asymptotically flat, electrostatic spacetime metric has the mildest possible singularity at its center, namely, a conical singularity on the time axis. The electric field moreover has a point defect on the time axis, its total energy is finite, and is equal to the ADM mass of the spacetime. By an appropriate scaling of the Lagrangian, one can arrange the total mass and total charge of these spacetimes to have any chosen values. For small enough mass-to-charge ratio, these spacetimes have no horizons and no trapped null geodesics. We also prove the uniqueness of these solutions in the spherically symmetric class, and we conclude by performing a qualitative study of the geodesics and test-charge trajectories of these spacetimes.

In this paper two consequences of the generalized uncertainty principle (GUP) are discussed in a heuristic manner. Both could be regarded as the evidences that prefer the cosmic censorship hypothesis (CCH). The first one is that the second law tends to decline the massless charged particles if the effects of the GUP on the thermodynamics of a de Sitter spacetime are considered. This weakens the threat to the horizon of an extreme charged black hole. The second one is that the uv/ir correspondence provides a constraint on the relation between the energy and the size of a system, which is incompatible to the naked singularities.

We study the final outcome of gravitational collapse resulting from the plane symmetric charged Vaidya spacetime. Using the field equations, we show that the weak energy condition is always satisfied by collapsing fluid. It is found that the singularity formed is naked. The strength of singularity is also investigated by using Nolan's method. This turns out to be a strong curvature singularity in Tipler's sense and hence provides a counter example to the cosmic censorship hypothesis.

In this paper, the gravitational collapse has been studied in the context of higher-dimensional charged-Vaidya spacetime. It is shown that naked singularity always exists in this case and strong form of cosmic censorship is violated. This work extends the earlier studies on naked singularity formation in higher dimensions.

In this paper, the shadow and the corresponding naked singularity cast by a Kerr–Sen black hole are studied. It is found that the shadow of a rotating black hole would be a dark zone surrounded by a deformed circle, and the shadow is distorted more away from a circle when the black hole approaches the extremal case. Besides, it is shown that the mean radius of the shadow decreases and distortion parameter increases with the increasing of charge, respectively. However, the mean radius and the distortion parameter vary complicatedly with the change of spin parameter. In the beginning, both observables decrease rapidly with the increasing of specific angular momentum, nevertheless, they increase slightly in the latter part. These results show that there would be a significant effect of the spin on the shadows, which would be of great importance for probing the nature of the black hole.

Gravitational collapse of radiation shells in a non-self-similar higher dimensional spherically symmetric space–time is studied. Strong curvature naked singularities form a highly inhomogeneous collapse, violating the cosmic censorship conjecture. As a special case, self similar models can be constructed.

We study the spherically symmetric collapse of a fluid with nonvanishing radial pressure in higher dimensional space–time. We obtain the general exact solution in the closed form for the equation of state (P_r = γρ), which leads to the explicit construction of the root equation governing the nature (black hole versus naked singularity) of the central singularity. A remarkable feature of the root equation is its invariance for the cases; (D, γ = 0) and (D+1, γ = -1) where D is the dimension of space–time. For the ultimate end result of the collapse, these two cases are absolutely equivalent, which is indeed a very interesting new result that brings out the interplay between dimension D of space–time and the equation of state parameter γ.

In this paper, we consider the gravitational collapse of generalized Vaidya space–time when the matter satisfies the equation of the state either $P=0$ or $P=-\alpha \rho$, where $0<\alpha <1$. We show that in the case when type I of matter field is dust, then the apparent horizon will never appear but there is no a family of null radial future-directed geodesics which terminate at the central singularity in the past. Also, we show that in the case of negative pressure, the result of the gravitational collapse might be the naked singularity and the apparent horizon appears and in very short time disappears again. In the case of the negative pressure, we show that the result of the gravitational collapse might be the eternal naked singularity.

In this paper, we have explored the behavior of dynamics of neutral test particles near the brane-world black hole (BH). We have discussed the stability/instability near the circular orbits with the help of extremal and nonextremal BH. In this consideration, we investigate the last stable circular orbit $(r_{\mathrm{\text{LSCO}}})$ that decreases with the increase of black hole parameters and concluded that the circular orbits are stable at $r>r_{\mathrm{\text{LSCO}}}$. The effective potential vanishes at horizon in extremal BH. In case of nonextremal BH, the angular momentum decreases, whereas energy increases with the increase in dark parameter $\beta$. Moreover, we find the conditions for the naked singularity and also express the effective potential that increases with the increase of angular momentum. Finally, the center-of-mass energy (CME) is constructed by the collision of particles in the vicinity of brane-world black hole and observed that the CME decreases with the increase of black hole parameters.

In this paper we give necessary transformation to diagonalize generalized Vaidya spacetime in the simplest cases.

We show that a Reissner–Nordström (RN) black hole can be formed by dropping a charged thin dust shell onto a RN naked singularity. This is in contrast to the fact that a RN naked singularity is prohibited from forming by dropping a charged thin dust shell onto a RN black hole. This implies the strong tendency of the RN singularity to be covered by a horizon in favor of cosmic censorship. We show that an extreme RN black hole can also be formed from a RN naked singularity by the same process in a finite advanced time. We also discuss the evolution of the charged thin dust shells and the causal structure of the resultant space–times.^a

The statements expressed in this paper are those of the authors and do not represent the views of Sumitomo Mitsui Banking Corporation or its staff.

In this paper, we will investigate the consequences of loop quantum gravitational modifications on the formation of naked singularities. The loop quantum gravitational effects will be incorporated in the collapsing system using gravity’s rainbow. This will be done by using rainbow functions, which are constructed from loop quantum gravitational modifications to the energy momentum dispersion. It will be observed that this modification will prevent the formation of naked singularity. Thus, such a modification can ensure that the weak cosmic censorship hypothesis will hold for any collapsing system

In this paper, the structure of the generalized Vaidya space–time when the type-II of the matter field satisfies the equation of the state $P=\rho$ is investigated. Satisfying all energy conditions, we show that this space–time contains the “eternal” naked singularity. It means that once the singularity is formed it will never be covered with the apparent horizon. However. in the case of the apparent horizon formation the resulting object is a white hole. We also prove that this space–time contains only null naked singularity.

We study the occurrence of naked singularities in the spherically symmetric collapse of a charged null fluid in an expanding de Sitter background — a piece of charged Vaidya–de Sitter spacetime. The naked singularities are found to be gravitationally strong in Tipler's sense and thus violate the cosmic censorship hypothesis.

We investigate the occurrence and nature of a naked singularity in the gravitational collapse of an inhomogeneous dust cloud described by a self-similar higher dimensional Tolman–Bondi space–time. Bound, marginally bound and unbound space–times are analyzed. The degree of inhomogeneity of the collapsing matter necessary to form a naked singularity is given.

A class of solutions to Einstein field equations is studied, which represents gravitational collapse of thick spherical shells made of self-similar and shear-free fluid with heat flow. It is shown that such shells satisfy all the energy conditions, and the corresponding collapse always forms naked singularities.

We investigate the occurrence and nature of naked singularities in the gravitational collapse of an adiabatic perfect fluid in self-similar higher dimensional space–times. It is shown that strong curvature naked singularities could occur if the weak energy condition holds. Its implication for cosmic censorship conjecture is discussed. Known results of analogous studies in four dimensions can be recovered.

Spherically symmetric inhomogeneous dust collapse has been studied in higher dimensional space–time and the factors responsible for the appearance of a naked singularity are analyzed in the region close to the centre for the marginally bound case. It is clearly demonstrated that in the former case naked singularities do not appear in the space–time having more than five dimension, which appears to a strong result. The non-marginally bound collapse is also examined in five dimensions and the role of shear in developing naked singularities in this space–time is discussed in details. The five-dimensional space–time is chosen in the later case because we have exact solution in closed form only in five dimension and not in any other case.

We investigate the nature of singularities arising in Husain solution. We analyze both spherical and non-spherical gravitational collapse in Husain spacetime. An interesting feature that emerges is that gravitational collapse of spherical cosmological Husain solution leads to the formation of naked singularities, while non-spherical cosmological collapse proceeds to form a black hole. Further strength of naked singularities arising in these spacetimes has been analyzed. It is found that these naked singularities are strong in Tipler's sense.

We analyze the dynamics of an apparent horizon in higher dimensional (HD) dust collapse. We have taken into consideration two different types of dust models. We propose the concept of a "trapped range" of initial data in different higher dimensional space–times. We show that "trapped range" of initial data increases with the increase in dimensions of the space–times.