Null Dust Research Articles

Einstein Equations Under Polarized $${\mathbb{U}}$$ U (1) Symmetry in an Elliptic Gauge

We prove local existence of solutions to the Einstein--null dust system under polarized $\mathbb U(1)$ symmetry in an elliptic gauge. Using in particular the previous work of the first author on the constraint equations, we show that one can identify freely prescribable data, solve the constraints equations, and construct a unique local in time solution in an elliptic gauge. Our main motivation for this work, in addition to merely constructing solutions in an elliptic gauge, is to provide a setup for our companion paper in which we study high frequency backreaction for the Einstein equations. In that work, the elliptic gauge we consider here plays a crucial role to handle high frequency terms in the equations. The main technical difficulty in the present paper, in view of the application in our companion paper, is that we need to build a framework consistent with the solution being high frequency, and therefore having large higher order norms. This difficulty is handled by exploiting a reductive structure in the system of equations.

Conformal Killing horizons and their thermodynamics

Certain dynamical black hole solutions can be mapped to static spacetimes by conformal metric transformations. This mapping provides a physical link between the conformal Killing horizon of the dynamical black hole and the Killing horizon of the static spacetime. Using the Vaidya spacetime as an example, we show how this conformal relation can be used to derive thermodynamic properties of such dynamical black holes. Although these horizons are defined quasi-locally and can be located by local experiments, they are distinct from other popular notions of quasi-local horizons such as apparent horizons. Thus in the dynamical Vaidya spacetime describing constant accretion of null dust, the conformal Killing horizon, which is null by construction, is the natural horizon to describe the black hole.

Dynamical black holes in low-energy string theory

We investigate time-dependent spherically symmetric solutions of the four-dimensional Einstein-Maxwell-axion-dilaton system, with the dilaton coupling that occurs in low-energy effective heterotic string theory. A class of dilaton-electrovacuum radiating solutions with a trivial axion, previously found by Güven and Yörük, is re-derived in a simpler manner and its causal structure is clarified. It is shown that such dynamical spacetimes featuring apparent horizons do not possess a regular light-like past null infinity or future null infinity, depending on whether they are radiating or accreting. These solutions are then extended in two ways. First we consider a Vaidya-like generalisation, which introduces a null dust source. Such spacetimes are used to test the status of cosmic censorship in the context of low-energy string theory. We prove that — within this family of solutions — regular black holes cannot evolve into naked singularities by accreting null dust, unless standard energy conditions are violated. Secondly, we employ S-duality to derive new time-dependent dyon solutions with a nontrivial axion turned on. Although they share the same causal structure as their Einstein-Maxwell-dilaton counterparts, these solutions possess both electric and magnetic charges.

Axially Symmetric Null Dust Space-Time, Naked Singularity, and Cosmic Time Machine

We present a gravitational collapse null dust solution of the Einstein field equations. The space-time is regular everywhere except on the symmetry axis where it possesses a naked curvature singularity and admits one parameter isometry group, a generator of axial symmetry along the cylinder which has closed orbits. The space-time admits closed timelike curves (CTCs) which develop at some particular moment in a causally well-behaved manner and may represent a Cosmic Time Machine. The radial geodesics near the singularity and the gravitational lensing (GL) will be discussed. The physical interpretation of this solution, based on the study of the equation of the geodesic deviation, will be presented. It was demonstrated that this solution depends on the local gravitational field consisting of two components with amplitudes Ψ2 and Ψ4.

A toy Penrose inequality and its proof

We formulate and prove a toy version of the Penrose inequality. The formulation mimics the original Penrose inequality in which the scenario is the following: A shell of null dust collapses in Minkowski space and a marginally trapped surface forms on it. Through a series of arguments relying on established assumptions, an inequality relating the area of this surface to the total energy of the shell is formulated. Then a further reformulation turns the inequality into a statement relating the area and the outer null expansion of a class of surfaces in Minkowski space itself. The inequality has been proven to hold true in many special cases, but there is no proof in general. In the toy version here presented, an analogous inequality in (2+1)-dimensional anti-de Sitter space turns out to hold true.

Evolutions from extremality

We examine the evolution of extremal spherically symmetric black holes, developing both general theory as well as the specific cases of (charged) null dust and massless scalar field spacetimes. As matter accretes onto extremal marginally trapped tubes, they generically evolve to become non-extremal with the initial extremal horizon bifurcating into inner and outer non-extremal horizons. At the start of this process arbitrarily slow matter accretion can cause a geometrically invariant measure of horizon growth to jump from zero to infinity. We also consider dynamical horizons that are extremal throughout their evolution and see that such spacetimes contain two extremal black hole horizons: an inner isolated one and an outer dynamical one. We compare these extremal dynamical horizons with the dynamical extreme event horizon spacetimes of Murata, Reall and Tanahashi.

Comment on self-consistent model of black hole formation and evaporation

In an earlier work, Kawai et al proposed a model of black-hole formation and evaporation, in which the geometry of a collapsing shell of null dust is studied, including consistently the back reaction of its Hawking radiation. In this note, we illuminate the implications of their work, focusing on the resolution of the information loss paradox and the problem of the firewall.

On global well-posedness for the Einstein-Maxwell-Euler system in Bondi coordinates

Weanalyze the Einstein-Maxwell equations for an irrotational stiff fluid. Under the spherical symmetry assumption on the space-time, in Bondi coordinates, the considered model is reduced to a nonlinear evolution system of partial integrodifferential equations. Assuming regularity at the center of symmetry and that the matter content of the initial light cone is the so-called null dust, the characteristic initial value problem associated to the obtained system is solved globally by a contraction mapping argument. In future work we will address the issue of global well-posedness for the considered model in other physically interesting cases where the matter content of the initial light cone is not the null dust.

Cloud of strings for radiating black holes in Lovelock gravity

We present exact spherically symmetric null dust solutions in the third order Lovelock gravity with a string cloud background in arbitrary $N$ dimensions,. This represents radiating black holes and generalizes the well known Vaidya solution to Lovelock gravity with a string cloud in the background. We also discuss the energy conditions and horizon structures, and explicitly bring out the effect of the string clouds on the horizon structure of black hole solutions for the higher dimensional general relativity and Einstein-Gauss-Bonnet theories. It turns out that the presence of the coupling constant of the Gauss-Bonnet terms and/or background string clouds completely changes the structure of the horizon and this may lead to a naked singularity. We recover known spherically symmetric radiating models as well as static black holes in the appropriate limits.

Gravitating dyons in Vaidya geometry

Gravitating monopoles and dyons in Einstein–Yang–Mills (EYM) or Einstein–Yang–Mills–Higgs (EYMH) systems have been extensively studied for various curved space–times, including those of black holes. We construct dyonic solutions of the EYMH theory in Vaidya space–time using a set of generalized Julia–Zee ansatz for the fields. It is found that the dyonic charge is static in nature and it does not contribute to the energy of the null dust.

Spherical gravitational collapse in 5D Einstein-Gauss-Bonnet gravity

We have considered a spherical gravitational collapse of inhomogeneous dust (and null dust) in Einstein gravity with the Gauss-Bonnet (GB) combination of quadratic curvature terms. It turns out that the presence of the coupling constant of the GB terms completely changes the causal structure of the singularities from the analogous general relativistic case. The gravitational collapse of inhomogeneous dust in the five-dimensional GB extended Einstein equations leads to formation of a massive, but weak, timelike singularity, which is forbidden in general relativity. The apparent horizons of two different collapsing solutions have shown interesting mathematical similarity.

Gravitational collapse in pure Lovelock gravity in higher dimensions

We study collapse of inhomogeneous dust and null dust (Vaidya radiation) in pure Lovelock gravity in higher dimensions. Since pure Lovelock gravity is kinematic in odd d=2N+1 dimension, hence pertinent dimension for the study is even d=2N+2, where N is degree of Lovelock polynomial. It turns out that pure Lovelock collapse favors naked singularity as against black hole for the Einstein case in the same dimension while strength of singularity as measured by divergence of Kretshmann scalar is interestingly the same in the two cases; i.e. the corresponding scalars have the same fall off behavior.

Holographic thermalization from Kerr-AdS

We study thermalization of a strongly coupled theory holographically dual to a thin shell of null dust with non-zero angular momentum collapsing to Kerr-AdS. We calculate thermalization time for two point correlation functions. It happens that in the 3-dimensional case the thermalization time is just proportional to the distance between points where the correlator is evaluated. This is a very surprising and rather unexpected generalization of the same relation in the case of zero momentum.

Thermalization of causal holographic information

We study causal wedges associated with a given sub-region in the boundary of asymptotically AdS spacetimes. Part of our motivation is to better understand the recently proposed holographic observable, causal holographic information (CHI), which is given by the area of a bulk co-dimension two surface lying on the boundary of the causal wedge. It has been suggested that CHI captures the basic amount of information contained in the reduced density matrix about the bulk geometry. To explore its properties further we examine its behaviour in time-dependent situations. As a simple model we focus on null dust collapse in an asymptotically AdS spacetime, modeled by the Vaidya-AdS geometry. We argue that while CHI is generically quasi-telelogical in time-dependent backgrounds, for suitable choice of sub-regions in conformal field theories, the temporal evolution of CHI is entirely causal. We comment on the implications of this observation and more generally on features of causal constructions and contrast our results with the behaviour of holographic entanglement entropy. Along the way we also derive the rate of early time growth and late time saturation (to the thermal value) of both CHI and entanglement entropy in these backgrounds.

On the response of particle detectors in Vaidya spacetimes

Using the formalism of the interaction picture we calculate an expression for the Wightman function for only the spherically symmetric modes of a quantum Klein–Gordon scalar field in a general Vaidya spacetime with ingoing null dust. It is demonstrated that particle detectors following time-like trajectories that are in the ground state at some instant of time outside of the collapsing shell will have a subsequent evolution that is independent of the configuration of the ingoing null dust. For detectors that are taken to be in the ground state at a time interior to the shell it is shown that their response will depend on the configuration of the ingoing null dust. Relevance to the information loss paradox is discussed.

Gravitational collapse of null dust inf(R)gravity

We find exact nonstatic null-dust solutions in metric $f(R)$ gravity, imposed by the constant scalar curvature, which describes the gravitational collapse of null dust in (anti-)de Sitter [(A)dS] higher-dimensional (HD) background. The situation where a null dust injects into the initially HD-(A)dS spacetime leads to a naked singularity from gravitational collapse in HD-$f(R)$ gravity, violating cosmic censorship conjecture. Further, we find exact null-dust solutions to constant curvature imposed non-Abelian $f(R)$ Yang-Mills gauge theory by employing the Wu-Yang ansatz in four dimensions. This generates an identical geometry as one would expect for charge null dust in the Abelian $f(R)$ Maxwell theory, i.e., precisely the charged-Vaidya-(A)dS corresponding to Yang-Mills gauge charge. The four-dimensional charged null-dust solutions in the $f(R)$ Maxwell theory are also, separately, derived.

Holographic evolution of the mutual information

We compute the time evolution of the mutual information in out of equilibrium quantum systems whose gravity duals are Vaidya spacetimes in three and four dimensions, which describe the formation of a black hole through the collapse of null dust. We find the holographic mutual information to be non monotonic in time and always monogamous in the ranges explored. We also find that there is a region in the configuration space where it vanishes at all times. We show that the null energy condition is a necessary condition for both the strong subadditivity of the holographic entanglement entropy and the monogamy of the holographic mutual information.

Evolution of two-point functions from holography

We consider a thermalization process in a 2-dimensional CFT that has a holographic description in terms of the gravitational collapse of a thin shell of null dust. This model represents a sudden perturbation of the CFT vacuum that communicates a uniform energy density to the system. We study the evolution of two-point functions at spacelike separated points (t 1, l) and (t 2 , 0), and reproduce the generic pattern first derived from the analysis of quantum quenches to critical systems. A crucial characteristic of these setups is that the excitations generated by the initial perturbation presents non-trivial quantum correlations. As a consequence, for any t i < ∞ equilibration is only effective on finite regions whose size grows as a lightfront. The behavior on larger regions is greatly determined by the initial state, which for the quenches we consider and the holographic model has relevant differences. However in both cases for late times the dependence on the scale l of the two-point functions enters through the effective distance l − t 1 − t 2. We interpret the onset of this behavior as an equilibration time for occupation numbers in these 2-dimensional models.

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.

Depletion of energy from naked singular regions during gravitational collapse

A distinguishable and observable physical property of Naked Singular Regions of the spacetime formed during a gravitational collapse has important implications for both experimental and theoretical relativity. We examine here whether energy can escape physically from naked singular regions to reach either a local or a distant observer within the framework of general relativity. We find that in case of imploding null dust collapse scenarios field outgoing singular null geodesics including the cauchy horizon can be immersed between two Vaidya spacetimes as null boundary layers with non vanishing positive energy density. Thus energy can transported from the naked singularity to either a local or a distant observer. And example illustrating that similar considerations can be applied to dust models is given.