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Register a new userUltra-high energy collision with neither black hole nor naked singularity
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We explore the collision between two concentric spherical thin shells. The inner shell is charged, whereas the outer one is either neutral or charged. In the situation we consider, the charge of the inner shell is larger than its gravitational mass, and the inside of it is empty and regular. Hence the domain just outside it is described by the overcharged Reissner-Nordstrom geometry whereas the inside of it is Minkowski. First, the inner shell starts to shrink form infinity with finite kinetic energy, and then the outer shell starts to shrink from infinity with vanishing kinetic energy. The inner shell bounces on the potential wall and collides with the ingoing outer shell. The energy of collision between these shells at their center of mass frame does not exceed the total energy of the system. By contrast, by virtue of the very large gamma factor of the relative velocity of the shells, the energy of collision between two of the constituent particles of these shells at their center of mass frame can be much larger than the Planck scale. This result suggests that the black hole or naked singularity is not necessary for ultra-high energy collision of particles.
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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.
We derive here the orbit equations of particles in naked singularity spacetimes, namely the Bertrand (BST) and Janis-Newman-Winicour (JNW) geometries, and for the Schwarzschild black hole. We plot the orbit equations and find the Perihelion precession of the orbits of particles in the BST and JNW spacetimes and compare these with the Schwarzschild black hole spacetime. We find and discuss different distinguishing properties in the effective potentials and orbits of particle in BST, JNW and Schwarzschild spacetimes, and the particle trajectories are shown for the matching of BST with an external Schwarzschild spacetime. We show that the nature of perihelion precession of orbits in BST and Schwarzschild spacetimes are similar, while in the JNW case the nature of perihelion precession of orbits is opposite to that of the Schwarzschild and BST spacetimes. Other interesting and important features of these orbits are pointed out.
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.
We first advance a mathematical novelty that the three geometrically and topologically distinct objects mentioned in the title can be exactly obtained from the Jordan frame vacuum Brans I solution by a combination of coordinate transformations, trigonometric identities and complex Wick rotation. Next, we study their respective accretion properties using the Page-Thorne model which studies accretion properties exclusively for $rgeq r_{text{ms}}$ (the minimally stable radius of particle orbits), while the radii of singularity/ throat/ horizon $r<r_{text{ms}}$. Also, its Page-Thorne efficiency $epsilon$ is found to increase with decreasing $r_{text{ms}}$ and also yields $epsilon=0.0572$ for Schwarzschild black hole (SBH). But in the singular limit $rrightarrow r_{s}$ (radius of singularity), we have $epsilonrightarrow 1$ giving rise to $100 %$ efficiency in agreement with the efficiency of the naked singularity constructed in [10]. We show that the differential accretion luminosity $frac{dmathcal{L}_{infty}}{dln{r}}$ of Buchdahl naked singularity (BNS) is always substantially larger than that of SBH, while Eddington luminosity at infinity $L_{text{Edd}}^{infty}$ for BNS could be arbitrarily large at $rrightarrow r_{s}$ due to the scalar field $phi$ that is defined in $(r_{s}, infty)$. It is concluded that BNS accretion profiles can still be higher than those of regular objects in the universe.
Motivated by the lack of rotating solutions sourced by matter in General Relativity as well as in modified gravity theories, we extend a recently discovered exact rotating solution of the minimal Einstein-scalar theory to its counterpart in Eddington-inspired Born-Infeld gravity coupled to a Born-Infeld scalar field. This is accomplished with the implementation of a well-developed mapping between solutions of Ricci-Based Palatini theories of gravity and General Relativity. The new solution is parametrized by the scalar charge and the Born-Infeld coupling constant apart from the mass and spin of the compact object. Compared to the spacetime prior to the mapping, we find that the high-energy modifications at the Born-Infeld scale are able to suppress but not remove the curvature divergence of the original naked null singularity. Depending on the sign of the Born-Infeld coupling constant, these modifications may even give rise to an additional timelike singularity exterior to the null one. In spite of that, both of the naked singularities before and after the mapping are capable of casting shadows, and as a consequence of the mapping relation, their shadows turn out to be identical as seen by a distant observer on the equatorial plane. Even though the scalar field induces a certain oblateness to the appearance of the shadow with its left and right endpoints held fixed, the closedness condition for the shadow contour sets a small upper bound on the absolute value of the scalar charge, which leads to observational features of the shadow closely resembling those of a Kerr black hole.
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