Shell Of Matter Research Articles

Vacuum for a massless quantum scalar field outside a collapsing shell in anti-de Sitter space–time

We consider a massless quantum scalar field on a two-dimensional space-time describing a thin shell of matter collapsing to form a Schwarzschild-anti-de Sitter black hole. At early times, before the shell starts to collapse, the quantum field is in the vacuum state, corresponding to the Boulware vacuum on an eternal black hole space-time. The scalar field satisfies reflecting boundary conditions on the anti-de Sitter boundary. Using the Davies-Fulling-Unruh prescription for computing the renormalized expectation value of the stress-energy tensor, we find that at late times the black hole is in thermal equilibrium with a heat bath at the Hawking temperature, so the quantum field is in a state analogous to the Hartle-Hawking vacuum on an eternal black hole space-time.

Interacting shells in AdS spacetime and chaos

We study the simplest two-body problem in asymptotically anti-de Sitter spacetime: two, infinitely thin, concentric spherical shells of matter. We include only gravitational interaction between the two shells, but we show that the dynamics of this system is highly nontrivial. We observe prompt collapse to a black hole, delayed collapse and even perpetual oscillatory motion, depending on the initial location of the shells (or their energy content). The system exhibits critical behavior, and we show strong hints that it is also chaotic.

Black hole collapse in the 1/c expansion

We present a first-principles CFT calculation corresponding to the spherical collapse of a shell of matter in three dimensional quantum gravity. In field theory terms, we describe the equilibration process, from early times to thermalization, of a CFT following a sudden injection of energy at time t=0. By formulating a continuum version of Zamolodchikov's monodromy method to calculate conformal blocks at large central charge c, we give a framework to compute a general class of probe observables in the collapse state, incorporating the full backreaction of matter fields on the dual geometry. This is illustrated by calculating a scalar field two-point function at time-like separation and the time-dependent entanglement entropy of an interval, both showing thermalization at late times. The results are in perfect agreement with previous gravity calculations in the AdS$_3$-Vaidya geometry. Information loss appears in the CFT as an explicit violation of unitarity in the 1/c expansion, restored by nonperturbative corrections.

The outer profile of dark matter haloes: an analytical approach

A steepening feature in the outer density profiles of dark matter halos indicating the splashback radius has drawn much attention recently. Possible observational detections have even been made for galaxy clusters. Theoretically, Adhikari et al. have estimated the location of the splashback radius by computing the secondary infall trajectory of a dark matter shell through a growing dark matter halo with an NFW profile. However, since they imposed a shape of the halo profile rather than computing it consistently from the trajectories of the dark matter shells, they could not provide the full shape of the dark matter profile around the splashback radius. We improve on this by extending the self-similar spherical collapse model of Fillmore \& Goldreich to a $\Lambda$CDM universe. This allows us to compute the dark matter halo profile and the trajectories simultaneously from the mass accretion history. Our results on the splashback location agree qualitatively with Adhikari et al. but with small quantitative differences at large mass accretion rates. We present new fitting formulae for the splashback radius $R_{\rm sp}$ in various forms, including the ratios of $R_{\rm sp} / R_{\rm 200c}$ and $R_{\rm sp} / R_{\rm 200m}$. Numerical simulations have made the puzzling discovery that the splashback radius scales well with $R_{\rm 200m}$ but not with $R_{\rm 200c}$. We trace the origin of this to be the correlated increase of $\Omega_{\rm m}$ and the average halo mass accretion rate with an increasing redshift.

Collapsing shells, critical phenomena, and black hole formation

We study the gravitational collapse of two thin shells of matter, in asymptotically flat spacetime or constrained to move within a spherical box. We show that this simple two-body system has surprisingly rich dynamics, which includes prompt collapse to a black hole, perpetually oscillating solutions or black hole formation at arbitrarily large times. Collapse is induced by shell crossing and the black hole mass depends sensitively on the number of shell crossings. At certain critical points, the black hole mass exhibits critical behavior, determined by the change in parity (even or odd) of the number of crossings, with or without mass-gap during the transition. Some of the features we observe are reminiscent of confined scalars undergoing "turbulent" dynamics.

Effect of a cylindrical thin-shell of matter on the electrostatic self-force on a charge

The electrostatic self-force on a point charge in cylindrical thin-shell space-times is interpreted as the sum of a $bulk$ field and a $shell$ field. The $bulk$ part corresponds to a field sourced by the test charge placed in a space-time without the shell. The $shell$ field accounts for the discontinuity of the extrinsic curvature ${\kappa^p}_q$. An equivalent electric problem is stated, in which the effect of the shell of matter on the field is reconstructed with the electric potential produced by a non-gravitating charge distribution of total image charge $Q$, to interpret the shell field in both the interior and exterior regions of the space-time. The self-force on a point charge $q$ in a locally flat geometry with a cylindrical thin-shell of matter is calculated. The charge is repelled from the shell if ${\kappa^{p}}_{p}=\kappa<0$ (ordinary matter) and attracted toward the shell if $\kappa>0$ (exotic matter). The total image charge is zero for exterior problems, while for interior problems $Q/q=-\kappa \, r_e$, with $r_e$ the external radius of the shell. The procedure is general and can be applied to interpret self-forces in other space-times with shells, e.g., for locally flat wormholes we found $Q_{\mp}^{wh}/q=-1/ (\kappa_{wh} r_{\pm})$.

Spherically symmetric solutions in higher-derivative gravity

Extensions of Einstein gravity with quadratic curvature terms in the action arise in most effective theories of quantized gravity, including string theory. This article explores the set of static, spherically symmetric and asymptotically flat solutions of this class of theories. An important element in the analysis is the careful treatment of a Lichnerowicz-type ``no-hair'' theorem. From a Frobenius analysis of the asymptotic small-radius behavior, the solution space is found to split into three asymptotic families, one of which contains the classic Schwarzschild solution. These three families are carefully analyzed to determine the corresponding numbers of free parameters in each. One solution family is capable of arising from coupling to a distributional shell of matter near the origin; this family can then match onto an asymptotically flat solution at spatial infinity without encountering a horizon. Another family, with horizons, contains the Schwarzschild solution but includes also non-Schwarzschild black holes. The third family of solutions obtained from the Frobenius analysis is nonsingular and corresponds to ``vacuum'' solutions. In addition to the three families identified from near-origin behavior, there are solutions that may be identified as ``wormholes,'' which can match symmetrically onto another sheet of spacetime at finite radius.

Entropy of an extremal electrically charged thin shell and the extremal black hole

There is a debate as to what is the value of the entropy S of extremal black holes. There are approaches that yield zero entropy S=0, while there are others that yield the Bekenstein–Hawking entropy S=A+/4, in Planck units. There are still other approaches that give that S is proportional to r+ or even that S is a generic well-behaved function of r+. Here r+ is the black hole horizon radius and A+=4πr+2 is its horizon area. Using a spherically symmetric thin matter shell with extremal electric charge, we find the entropy expression for the extremal thin shell spacetime. When the shell's radius approaches its own gravitational radius, and thus turns into an extremal black hole, we encounter that the entropy is S=S(r+), i.e., the entropy of an extremal black hole is a function of r+ alone. We speculate that the range of values for an extremal black hole is 0≤S(r+)≤A+/4.

Gravitational collapse with rotating thin shells and cosmic censorship

Gravitational collapse of matter in the presence of rotation is a mostly unexplored topic but it might have important implications for cosmic censorship. Recently a convenient setup was identified to address this problem, by considering thin matter shells at the interface between two equal angular momenta Myers–Perry spacetimes in five dimensions. This note provides more details about the matching of such cohomogeneity-1 spacetimes and extends the results obtained therein to arbitrary higher odd dimensions. It is also pointed out that oscillatory orbits for shells in asymptotically flat spacetimes can be naturally obtained if the matter has a negative pressure component.

Bootstrapping Time Dilation Decoherence

We present a general relativistic model of a spherical shell of matter with a perfect fluid on its surface coupled to an internal oscillator, which generalizes a model recently introduced by the authors to construct a self-gravitating interferometer [1]. The internal oscillator evolution is defined with respect to the local proper time of the shell, allowing the oscillator to serve as a local clock that ticks differently depending on the shell's position and momentum. A Hamiltonian reduction is performed on the system, and an approximate quantum description is given to the reduced phase space. If we focus only on the external dynamics, we must trace out the clock degree of freedom, and this results in a form of intrinsic decoherence that shares some features with a proposed "universal" decoherence mechanism attributed to gravitational time dilation [2]. We note that the proposed decoherence remains present in the (gravity-free) limit of flat spacetime, emphasizing that the effect can be attributed entirely to proper time differences, and thus is not necessarily related to gravity. Whereas the effect described in [2] vanishes in the absence of an external gravitational field, our approach bootstraps the gravitational contribution to the time dilation decoherence by including self-interaction, yielding a fundamentally gravitational intrinsic decoherence effect.

Phase State and Deliquescence Hysteresis of Ammonium-Sulfate-Seeded Secondary Organic Aerosol

The phase state of secondary organic aerosol (SOA) has an impact on its lifetime, composition, and its interaction with water. To better understand the effect of phase state of SOA on climate interactions, we studied the SOA phase state and the effect of its history and report here the phase state and the humidity-induced phase hysteresis of multicomponent-seeded SOA particles produced in a large, continuously stirred tank reactor. We determined the phase state of the particles by their bounced fraction impacting on a smooth substrate in a low-pressure impactor. The particles were composed of ammonium sulfate ([NH4]2SO4) seed and a secondary organic matter (SOM) shell formed from oxidized α-pinene or isoprene. The ammonium sulfate (AS) seed dominated the deliquescence of the α-pinene SOM multicomponent particles, whereas their efflorescence was strongly attenuated by the SOM coating. Particles coated with isoprene SOM showed continuous phase transitions with a lesser effect by the AS seed. The results agr...

Gravitational collapse with rotating thin shells and cosmic censorship

The study of gravitational collapse is a subject of great importance, both from an astrophysical and a holographic point of view. In this respect, exact solutions can be very helpful but known solutions are very scarce, especially when considering dynamical processes with rotation. We describe a setup in which gravitational collapse of rotating matter shells can be addressed with analytic tools, at the expense of going to higher dimensions and considering equal angular momenta spacetimes. The framework for an exact treatment of the dynamics, relying on a thin shell approximation, is developed. Our analysis allows the inclusion of a non-vanishing cosmological constant. Finally, we discuss applications of this machinery to the construction of stationary solutions describing matter around rotating black holes and to the cosmic censorship conjecture.

Variations in the release of silicate and orthophosphate along a salinity gradient: Do sediment composition and physical forcing have roles?

It was hypothesized that sediment composition, i.e. organic matters and minerals, and physical forcing can influence retention and release of silicate (SiO4) and orthophosphate (o-PO4) along salinity gradients. An experiment was performed to measure nutrient release by using treatments with and without sediment organic matter from the Guadalupe and Nueces Estuaries at five different salinities. The sample mixtures were shaken at intervals over the course of 48 h to simulate wind and river forcing. The release of silicate from sediments increased with time from 2 min to 48 h in all five salinities. The added orthophosphate concentration was adsorbed in most of the sediment containing organic matter and calcium-rich shells from both estuaries. From the sediments without organic matter, the release of orthophosphate was as high as 52 μmol/L. The sediment minerals quartz and calcite were abundant in both estuaries. The average quartz to corundum peak intensities ratio were 14.04 and 13.36 and the average calcite to corundum peak intensities ratio were 3.06 and 1.32 in the Guadalupe and Nueces Estuaries respectively. The average organic matter in the Guadalupe and Nueces estuaries were 10.67% and 13.39% respectively. The retention and release of orthophosphate from the sediments may have been caused by the bonding with organic matter and calcite in the sediments. These findings indicate that sediment composition was a significant contributor in the low dissolved orthophosphate concentration in the estuaries. The release of silicate from the sediments containing quartz, and organic matter, when shaken, indicate that the combined forcing of river and wind may have been maintaining the estuaries silicate concentrations.

Mach׳s principle as action-at-a-distance in GR: The causality question

A part of the revival of interest in Mach׳s principle since the early 1960s has involved work by physicists aimed at calculating various sorts of frame-dragging effects by matter shells surrounding an interior region, and arguing that under certain conditions or in certain limits (ideally, ones that can be viewed as plausibly similar to conditions in our cosmos) the frame dragging becomes “complete” (e.g. Lynden-Bell, Katz, & Bičák, 1995) . Such results can bolster the argument for the satisfaction of Mach׳s principle by certain classes of models of GR. Interestingly, the frame-dragging “effect” of (say) a rotational movement of cosmic matter around a central point is argued by these physicists to be instantaneous—not an effect propagating at the speed of light. Not all physicists regard this as unproblematic. But rather than exploring whether there is something unphysical about such instantaneous “action at a distance”, or a violation of the precepts of Special Relativity, I am interested in exploring whether these physicists׳ calculations should be thought of as showing local inertia (resistance to acceleration) to be an effect, with distant matter distributions being the cause. I will try to apply some leading philosophical accounts of causation to the physical models of frame dragging, to see whether they imply that the frame dragging is superluminal causation. I will then offer reflections on the difficulties of applying causal talk in physical theories.

Self-gravitating interferometry and intrinsic decoherence

To investigate the possibility that intrinsic gravitational decoherence can be theoretically demonstrated within canonical quantum gravity, we develop a model of a self-gravitating interferometer. We search for evidence in the resulting interference pattern that would indicate coherence is fundamentally limited due to general relativistic effects. To eliminate the occurence of gravitational waves, we work in spherical symmetry, and construct the "beam" of the interferometer out of WKB states for an infinitesimally thin shell of matter. For internal consistency, we encode information about the beam optics within the dynamics of the shell itself, by arranging an ideal fluid on the surface of the shell with an equation of state that enforces beam-splitting and reflections. We then determine sufficient conditions for (interferometric) coherence to be fully present even after general relativistic corrections are introduced, test whether or not they can be satisfied, and remark on the implications of the results.

Instability of nonminimally coupled scalar fields in the spacetime of slowly rotating compact objects

Nonminimally coupled free scalar fields may be unstable in the spacetime of compact objects. Such instability can be triggered by classical seeds or, more simply, by quantum fluctuations giving rise to the so-called ``vacuum awakening effect.'' Here, we investigate how the parameter space that characterizes the instability is affected when the object gains some rotation. For this purpose, we focus on the stability analysis of nonminimally coupled scalar fields in the spacetime of slowly spinning matter shells.

Black hole firewalls, smoke and mirrors

The radiation emitted by a black hole (BH) during its evaporation has to have some degree of quantum coherence to accommodate a unitary time evolution. We parametrize the degree of coherence by the number of coherently emitted particles ${N}_{\text{coh}}$ and show that it is severely constrained by the equivalence principle. We discuss, in this context, the fate of a shell of matter that falls into a Schwarzschild BH. Two points of view are considered: that of a stationary external observer and that of the shell itself. From the perspective of the shell, the near-horizon region has an energy density proportional to ${N}_{\text{coh}}^{2}$ in Schwarzschild units. So, if ${N}_{\text{coh}}$ is parametrically larger than the square root of the BH entropy ${S}_{\mathrm{BH}}^{1/2}$, a firewall or more generally a ``wall of smoke'' forms and the equivalence principle is violated while the BH is still semiclassical. To have a degree of coherence that is parametrically smaller than ${S}_{\mathrm{BH}}^{1/2}$, one has to introduce a new sub-Planckian gravitational length scale, which likely also violates the equivalence principle. And so our previously proposed model which has ${N}_{\text{coh}}={S}_{\mathrm{BH}}^{1/2}$ is singled out. From the external-observer perspective, we find that the time it takes for the information about the state of the shell to get re-emitted from the BH is inversely proportional to ${N}_{\text{coh}}$. When the rate of information release becomes of order unity, the semiclassical approximation starts to break down and the BH becomes a perfect reflecting information mirror.

Collapsing thin shells with rotation

We construct exact solutions describing the motion of rotating thin shells in a fully backreacted five-dimensional rotating black hole spacetime. The radial equation of motion follows from the Darmois-Israel junction conditions, where both interior and exterior geometries are taken to be equal angular momenta Myers-Perry solutions. We show that rotation generates anisotropic pressures and momentum along the shell. Gravitational collapse scenarios including rotation are analyzed and a new class of stationary solutions is introduced. Energy conditions for the matter shell are briefly discussed.

Nonlocal (but also nonsingular) physics at the last stages of gravitational collapse

We study the end stages of gravitational collapse of the thin shell of matter in ingoing Eddington-Finkelstein coordinates. We use the functional Schrodinger formalism to capture quantum effects in the near singularity limit. We find that that the equations of motion which govern the behavior of the collapsing shell near the classical singularity become strongly non-local. This reinforces previous arguments that quantum gravity in the strong field regime might be non-local. We managed to solve the non-local equation of motion for the dust shell case, and found an explicit form of the wavefunction describing the collapsing shell. This wavefunction and the corresponding probability density are non-singular at the origin, thus indicating that quantization should be able to rid gravity of singularities, just as it was the case with the singular Coulomb potential.

Entanglement Tsunami: Universal Scaling in Holographic Thermalization

We consider the time evolution of entanglement entropy after a global quench in a strongly coupled holographic system, whose subsequent equilibration is described in the gravity dual by the gravitational collapse of a thin shell of matter resulting in a black hole. In the limit of large regions of entanglement, the evolution of entanglement entropy is controlled by the geometry around and inside the event horizon of the black hole, resulting in regimes of pre-local-equilibration quadratic growth (in time), post-local-equilibration linear growth, a late-time regime in which the evolution does not carry memory of the size and shape of the entangled region, and a saturation regime with critical behavior resembling those in continuous phase transitions. Collectively, these regimes suggest a picture of entanglement growth in which an "entanglement tsunami" carries entanglement inward from the boundary. We also make a conjecture on the maximal rate of entanglement growth in relativistic systems.