Null Dust Fluid Research Articles

Extremal rotating BTZ black holes cannot be dressed in (anti-)self-dual Maxwell field

Abstract Under the (anti-)self-dual condition for orthonormal components of the Faraday tensor, the three-dimensional Einstein-Maxwell system with a negative cosmological constant Λ admits a solution obtained by Kamata and Koikawa and later by Cataldo and Salgado in the most general form. Actually, Clément first obtained this solution and interpreted it as a regular particle-like solution without horizon. Nevertheless, it has been erroneously stated in some literature that this Clément-Cataldo-Salgado (CCS) solution, locally characterized by a single parameter, describes a black hole even in the charged case as it reduces to the extremal rotating Bañados-Teitelboim-Zanelli (BTZ) solution in the vacuum limit and its curvature invariants are constant. In this paper, we supplement Clément’s interpretation by showing that there appears a parallelly propagated curvature singularity corresponding to an infinite affine parameter along spacelike geodesics at the location of the Killing horizon in the extremal rotating BTZ solution when the (anti-)self-dual Maxwell field is added. If the spatial coordinate θ is periodic, closed timelike curves exist near the singularity. It is also shown that the CCS solution is of the Cotton type N (in contrast to charged rotating BTZ black holes which are of type I away from the horizon), and the energy-momentum tensor of the Maxwell field is of the Hawking-Ellis type II. The metric solves the Einstein-Λ equations also with a massless scalar field or a null dust fluid. We explicitly demonstrate that it belongs to the Kundt shear-free, non-twisting, and non-expanding class of geometries, whereas extremal rotating BTZ black holes have expanding principal null directions. It means that the CCS metric represents the specific null (that is “radiative”) Maxwell field generated by a singular source, rather than an extremal rotating BTZ black hole dressed in an (anti-)self-dual Maxwell field.

Hawking-Ellis type of matter on Killing horizons in symmetric spacetimes

Spherically, plane, or hyperbolically symmetric spacetimes with an additional hypersurface orthogonal Killing vector are often called ``static'' spacetimes even if they contain regions where the Killing vector is nontimelike. It seems to be widely believed that an energy-momentum tenor for a matter field compatible with these spacetimes in general relativity is of the Hawking-Ellis type I everywhere. We show in arbitrary $n(\ensuremath{\ge}3)$ dimensions that, contrary to popular belief, a matter field on a Killing horizon is not necessarily of type I but can be of type II. Such a type-II matter field on a Killing horizon is realized in the Gibbons-Maeda-Garfinkle-Horowitz-Strominger black hole in the Einstein-Maxwell-dilaton system and may be interpreted as a mixture of a particular anisotropic fluid and a null dust fluid.

Scalar field as a null dust

We show that a canonical, minimally coupled scalar field which is non-self interacting and massless is equivalent to a null dust fluid (whether it is a test or a gravitating field), in a spacetime region in which its gradient is null. Under similar conditions, the gravitating and nonminimally coupled Brans-Dicke-like scalar of scalar-tensor gravity, instead, cannot be represented as a null dust unless its gradient is also a Killing vector field.

Naked singularity explosion in higher dimensions

Motivated by the recent argument that in the TeV-scale gravity trans-Planckian domains of spacetime as effective naked singularities would be generated by high-energy particle (and black-hole) collisions, we investigate the quantum particle creation by naked-singularity formation in general dimensions. Background spacetime is simply modeled by the self-similar Vaidya solution, describing the spherical collapse of a null dust fluid. In a generic case the emission power is found to be proportional to the quadratic inverse of the remaining time to a Cauchy horizon, as known in four dimensions. On the other hand, the power is proportional to the quartic inverse for a critical case in which the Cauchy horizon is `degenerate'. According to these results, we argue that the backreaction of the particle creation to gravity will be important in particle collisions, in contrast to the gravitational collapse of massive stellar objects, since the bulk of energy is carried away by the quantum radiation even if a quantum gravitational effect cutoff the radiation just before the appearance of naked singularity.

Asymptotically flat radiating solutions in third order Lovelock gravity

In this paper, we present an exact spherically symmetric solution of third order Lovelock gravity in n dimensions which describes the gravitational collapse of a null dust fluid. This solution is asymptotically (anti-)de Sitter or flat depending on the choice of the cosmological constant. Using the asymptotically flat solution for n{>=}7 with a power-law form of the mass as a function of the null coordinate, we present a model for a gravitational collapse in which a null dust fluid radially injects into an initially flat and empty region. It is found that a naked singularity is inevitably formed whose strength is different for the n=7 and n{>=}8 cases. In the n=7 case, the limiting focusing condition for the strength of curvature singularity is satisfied. But for n{>=}8, the strength of curvature singularity depends on the rate of increase of mass of the spacetime. These considerations show that the third order Lovelock term weakens the strength of the curvature singularity.

Naked Singularity Formation in Higher Curvature Gravity

We find an exact solution in dimensionally continued gravity in arbitrary dimensions which describes the gravitational collapse of a null dust fluid [1]. Considering the situation that a null dust fluid injects into the initially anti-de Sitter spacetime, we show that a naked singularity can be formed. In even dimensions, a massless ingoing null naked singularity emerges. In odd dimensions, meanwhile, a massive timelike naked singularity forms. These naked singularities can be globally naked if the ingoing null dust fluid is switched off at a finite time; the resulting spacetime is static and asymptotically anti-de Sitter spacetime. The curvature strength of the massive timelike naked singularity in odd dimensions is independent of the spacetime dimensions or the power of the mass function. This is a characteristic feature in Lovelock gravity.

Effects of Gauss-Bonnet term on final fate of gravitational collapse

We obtain a general spherically symmetric solution of a null dust fluid in n(⩾ 5)- dimensions in Gauss-Bonnet gravity. Using the solution for n ⩾ 5 with a specific form of the mass function, we present a model for a gravitational collapse in which a null dust fluid radially injects into an initially flat and empty region. It is found that a naked singularity is inevitably formed and its properties are quite different between n = 5 and n ⩾ 6. In the n ⩾ 6 case, a massless ingoing null naked singularity is formed, while in the n = 5 case, a massive timelike naked singularity is formed, which does not appear in the general relativistic case. The strength of the naked singularities is weaker than that in the general relativistic case. These naked singularities can be globally naked when the null dust fluid is turned off after a finite time and the field settles into the empty asymptotically flat spacetime.

Effects of Gauss–Bonnet term on the final fate of gravitational collapse

We obtain a general spherically symmetric solution of a null dust fluid in n(⩾4) dimensions in Gauss–Bonnet gravity. This solution is a generalization of the n-dimensional Vaidya–(anti)de Sitter solution in general relativity. For n = 4, the Gauss–Bonnet term in the action does not contribute to the field equations, so that the solution coincides with the Vaidya–(anti)de Sitter solution. Using the solution for n ⩾ 5 with a specific form of the mass function, we present a model for a gravitational collapse in which a null dust fluid radially injects into an initially flat and empty region. It is found that a naked singularity is inevitably formed and its properties are quite different between n = 5 and n ⩾ 6. In the n ⩾ 6 case, a massless ingoing null naked singularity is formed, while in the n = 5 case, a massive timelike naked singularity is formed, which does not appear in the general relativistic case. The strength of the naked singularities is weaker than that in the general relativistic case. These naked singularities can be globally naked when the null dust fluid is turned off after a finite time and the field settles into the empty asymptotically flat spacetime.

Effects of Lovelock terms on the final fate of gravitational collapse: analysis in dimensionally continued gravity

We find an exact solution in dimensionally continued gravity in arbitrary dimensions which describes the gravitational collapse of a null dust fluid. Considering the situation where a null dust fluid injects into the initially anti-de Sitter spacetime, we show that a naked singularity can be formed. In even dimensions, a massless ingoing null naked singularity emerges. In odd dimensions, meanwhile, a massive timelike naked singularity forms. These naked singularities can be globally naked if the ingoing null dust fluid is switched off at a finite time; the resulting spacetime is static and asymptotically anti-de Sitter spacetime. The curvature strength of the massive timelike naked singularity in odd dimensions is independent of the spacetime dimensions or the power of the mass function. This is a characteristic feature in Lovelock gravity.

COLLAPSING AND EXPANDING CYLINDRICALLY SYMMETRIC FIELDS WITH LIGHTLIKE WAVE-FRONTS IN GENERAL RELATIVITY

The dynamics of collapsing and expanding cylindrically symmetric gravitational and matter fields with lightlike wave-fronts is studied in General Relativity, using the Barrabés–Israel method. As an application of the general formulae developed, the collapse of a matter field that satisfies the condition RABgAB =0, (A,B = z, φ), in an otherwise flat spacetime background is studied. In particular, it is found that the gravitational collapse of a purely gravitational wave or a null dust fluid cannot be realized in a flat spacetime background. The studies are further specified to the collapse of purely gravitational waves and the general conditions for such collapse are found. It is shown that after the waves arrive at the axis, in general, part of them is reflected to spacelike infinity along the future light cone, and part of it is focused to form spacetime singularities on the symmetry axis. The cases where the collapse does not result in the formation of spacetime singularities are also identified.

BRANE COSMOLOGY WITH NON-STATIC BULK

We study the brane world motion in non-static bulk by generalizing the second Randall-Sundrum scenario Explicitly, we take the bulk to be a Vaidya-AdS metric, which describes the gravitational collapse of a spherically symmetric null dust fluid in Anti-de Sitter spacetime. We point out that during an inflationary phase on the brane, black holes will tend to be thermally nucleated in the bulk We analyze the thermodynamical properties of this brane-world. We point out that during an inflationary phase on the brane, black holes will tend to be thermally nucleated in the bulk. Thermal equilibrium of the system is discussed. We calculate the late time behavior of this system, including 1-loop effects. We argue that at late times a sufficiently large black hole will relax to a point of thermal equilibrium with the brane-world environment. This result has interesting implications for early-universe cosmology.

Thermal equilibration of brane-worlds

We analyze the thermodynamical properties of brane-worlds, with a focus on the second model of Randall and Sundrum. We point out that during an inflationary phase on the brane, black holes will tend to be thermally nucleated in the bulk. This leads us to ask the question: Can the black hole - brane-world system evolve towards a configuration of thermal equilibrium? To answer this, we generalize the second Randall-Sundrum scenario to allow for non-static bulk regions on each side of the brane-world. Explicitly, we take the bulk to be a {\it Vaidya-AdS} metric, which describes the gravitational collapse of a spherically symmetric null dust fluid in Anti-de Sitter spacetime. Using the background subtraction technique to calculate the Euclidean action, we argue that at late times a sufficiently large black hole will relax to a point of thermal equilibrium with the brane-world environment. These results have interesting implications for early-universe cosmology.