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Register a new userDressing a Naked Singularity: an Example
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Considering the evolution of a perfect fluid with self-similarity of the second kind, we have found that an initial naked singularity can be trapped by an event horizon due to collapsing matter. The fluid moves along time-like geodesics with a self-similar parameter $alpha = -3$. Since the metric obtained is not asymptotically flat, we match the spacetime of the fluid with a Schwarzschild spacetime. All the energy conditions are fulfilled until the naked singularity.
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We consider a gravastar model made of anisotropic dark energy with an infinitely thin spherical shell of a perfect fluid with the equation of state $p = (1-gamma)sigma$ with an external de Sitter-Schwarzschild region. It is found that in some cases the models represent the bounded excursion stable gravastars, where the thin shell is oscillating between two finite radii, while in other cases they collapse until the formation of black holes or naked singularities. An interesting result is that we can have black hole and stable gravastar formation even with an interior and a shell cons tituted of dark and repulsive dark energy, as also shown in previous work. Besides, in one case we have a dynamical evolution to a black hole (for $Lambda =0$) or to a naked singularity (for $Lambda > 0$). This is the first time in the literature that a naked singularity emerges from a gravastar model.
It is generally believed that the shadows of either a black hole or naked singularity arise due to photon spheres developing in these spacetimes. Here we propose a new spherically symmetric naked singularity spacetime solution of Einstein equations which has no photon sphere, and we show that the singularity casts a shadow in the absence of the photon sphere. We discuss some novel features of this shadow and the lightlike geodesics in this spacetime. We compare the shadow of the naked singularity here with shadows cast by Schwarzschild black hole and the first type of Joshi-Malafarina-Narayan (JMN1) naked singularity, where for the last two spacetimes the shadow is formed due to the presence of a photon sphere. It is seen, in particular, that the size of shadow of the singularity is considerably smaller than that of a black hole. Our analysis shows that the shadow of this naked singularity is distinguishable from the shadow of a Schwarzschild black hole and the JMN1 naked singularity. These results are useful and important in the context of recent observations of shadow of the M87 galactic center.
It is now theoretically well established that not only a black hole can cast shadow, but other compact objects such as naked singularities, gravastar or boson stars can also cast shadows. An intriguing fact that has emerged is that the event horizon and the photon sphere are not necessary for a shadow to form. Now, when two different types of equally massive compact objects cast shadows of same size, then it would be very difficult to distinguish them from each other. However, the nature of the nulllike and timelike geodesics around the two compact objects would be different, since their spacetime geometries are different. Therefore, the intensity distribution of light emitted by the accreting matter around the compact objects would also be different. In this paper, we emphasize this phenomenon in detail. Here, we show that a naked singularity spacetime, namely, the first type of Joshi-Malafarina-Narayan (JMN1) spacetime can be distinguishable from the Schwarzschild blackhole spacetime by the intensity distribution of light, though they have same mass and shadow size. We also use the image processing techniques here to show this difference, where we use the theoretical intensity data. The differences that we get by using the image processing technique may be treated as a theoretical template of intensity differences, which may be useful to analyse the observational data of the image of a compact object.
We consider a gravastar model made of anisotropic dark energy with an infinitely thin spherical shell of a perfect fluid with the equation of state $p = (1-gamma)sigma$ with an external de Sitter-Schwarzschild region. It is found that in some cases the models represent the bounded excursion stable gravastars, where the thin shell is oscillating between two finite radii, while in other cases they collapse until the formation of black holes or naked singularities. An interesting result is that we can have black hole and stable gravastar formation even with an interior and a shell constituted of dark and repulsive dark energy, as also shown in previous work. Besides, in three cases we have a dynamical evolution to a black hole (for $Lambda=0$) or to a naked singularity (for $Lambda > 0$). This is the first time in the literature that a naked singularity emerges from a gravastar model.
In this paper, we derive the solutions of orbit equations for a class of naked singularity spacetimes, and compare these with timelike orbits, that is, particle trajectories in the Schwarzschild black hole spacetime. The Schwarzschild and naked singularity spacetimes considered here can be formed as end state of a spherically symmetric gravitational collapse of a matter cloud. We find and compare the perihelion precession of the particle orbits in the naked singularity spacetime with that of the Schwarzschild black hole. We then discuss different distinguishable physical properties of timelike orbits in the black hole and naked singularity spacetimes and implications are discussed. Several interesting differences follow from our results, including the conclusion that in naked singularity spacetimes, particle bound orbits can precess in the opposite direction of particle motion, which is not possible in Schwarzschild spacetime.
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