Causal Boundary Research Articles

Stationary scattering for the nonlinear Schrödinger equation with point-like obstacles: exact solutions

AbstractWe solve the Nonlinear Schrödinger Equation (NLSE) in 1D in presence of one, two and several Dirac delta potentials. With the help of an equivalent central force problem we obtain the analytical solutions in terms of a biparametric family containing the Jacobi functions. Elliptic Jacobi functions are already reported in the literature but they have not been used in the context of a scattering problem under causal boundary conditions. In the simplest examples of one or two Dirac deltas we analyze how the nonlinear term of the equation affects the modulus and phase profiles of the wave function. We also study the transmission curves under the nonlinear modification of the tunneling behavior for the first time. For a Fabri-Perot configuration made of two deltas, we obtain the effect of nonlinear coupling in the positions of the local maxima (resonances). We lay the foundations for nonlinear Anderson localization of 1D BECs in a speckle field. Upon redefinition of parameters these novel results describe the dynamics of a stationary Higgs field in 1D. Finally, we discuss the conditions for soliton formation under the influence of a Dirac comb potential, giving rise to fully correlated locations and intensities of the defects.

Heisenberg soft hair on Robinson-Trautman spacetimes

We study 4 dimensional (4d) gravitational waves (GWs) with compact wavefronts, generalizing Robinson-Trautman (RT) solutions in Einstein gravity with an arbitrary cosmological constant. We construct the most general solution of the GWs in the presence of a causal, timelike, or null boundary when the usual tensor modes are turned off. Our solution space besides the shape and topology of the wavefront which is a generic compact, smooth, and orientable 2d surface Σ, is specified by a vector over Σ satisfying the conformal Killing equation and two scalars that are arbitrary functions over the causal boundary, the boundary modes (soft hair). We work out the symplectic form over the solution space using covariant phase space formalism and analyze the boundary symmetries and charges. The algebra of surface charges is a Heisenberg algebra. Only the overall size of the compact wavefront and not the details of its shape appears in the boundary symplectic form and is canonical conjugate to the overall mass of the GW. Hence, the information about the shape of the wavefront can’t be probed by the boundary observer. We construct a boundary energy-momentum tensor and a boundary current, whose conservation yields the RT equation for both asymptotically AdS and flat spacetimes. The latter provides a hydrodynamic description for our RT solutions.

Interplay between black holes and ultralight dark matter: analytic solutions

Dark matter (DM) can consist of a scalar field so light that DM particles in the galactic halo are best described by classical waves. We investigate how these classical solutions are influenced by the presence of a non-rotating supermassive black hole at the center of the galaxy, using an analytical, albeit approximate, approach.Relying on this analytic control, we examine the consequences of imposing causal boundary conditions at the horizon, which are typically overlooked. First, we examine the scenario where the backreaction of dark matter can be neglected. The scalar field decays like a power law at large distances, thus endowing the black hole with “hair”. We derive solutions for the field profile over a wide range of parameters, including cases with rotating dark matter. As a by-product, we extract the dynamical Love numbers for scalar perturbations. Next, we determine the spectrum of bound states and their behaviour.Finally, we incorporate the self-gravity of the scalar field, with a focus on the situation where dark matter forms a soliton (boson star) at the center of the galaxy. We derive an analytical expression for the soliton at every distance from the center. With a solution that remains applicable even at horizon scales, we can reliably compute the accretion rate of the black hole.

Universal horizons and black hole spectroscopy in gravitational theories with broken Lorentz symmetry

The violation of Lorentz invariance (LI) in gravitational theories, which allows superluminal propagations, dramatically alters the causal structure of the spacetime and modifies the notion of black holes (BHs). Instead of metric horizons, now universal horizons (UHs) define the boundaries of BHs, within which a particle cannot escape to spatial infinities even with an infinitely large speed. Then, a natural question is how the quasi-normal modes (QNMs) of a BH are modified, if one considers the UH as its causal boundary. In this paper, we study in detail this problem in Einstein–Aether theory, a vector-tensor theory that violates LI but yet is self-consistent and satisfies all observations to date. Technically, this poses several challenges, including singularities of the perturbation equations across metric horizons and proper identifications of ingoing modes at UHs. After overcoming these difficulties, we show that the QNMs of the Schwarzschild BH, also a solution of Einstein–Aether theory, consist of two parts, the metric and aether parts. The QNMs of the metric perturbations are quite similar to those obtained in general relativity and are consistent with current observations of gravitational waves. But the ones from aether perturbations are different, and our numerical studies indicate that they are even not stable. The latter is consistent with our previous studies, which showed that the stealth Schwarzschild BH suffers a Laplacian instability along the angular direction. The method and techniques developed in this paper can be applied to the studies of QNMs in other theories of gravity with broken LI.

Entrepreneurial orientation as a theory of new value creation

Explaining how and why entrepreneurial orientation (EO) enhances firm outcomes is critical as it explicates specific causal mechanisms and boundary conditions. However, despite over 40 years of inquiry, a theory gap is evident in much of the research that links EO to firm performance outcomes. In this study, we inductively derive EO as a theory of new value creation based upon an increase in consumer benefits (or reduction in costs) made possible through a commitment to continuous novelty within an organization’s product-market offerings. In addition to offering a theory explaining how and why EO creates new value through product-market variance as a new causal mechanism within the EO literature, our research affords practitioners greater insight into what to expect from EO and when it may be most gainfully employed in pursuing firm growth. To this end, our study considers relevant boundary conditions to applying our theory and what our theory implies for future research exploring organizational entrepreneurship.

Hydro & thermo dynamics at causal boundaries, examples in 3d gravity

We study 3-dimensional gravity on a spacetime bounded by a generic 2-dimensional causal surface. We review the solution phase space specified by 4 generic functions over the causal boundary, construct the symplectic form over the solution space and the 4 boundary charges and their algebra. The boundary charges label boundary degrees of freedom. Three of these charges extend and generalize the Brown-York charges to the generic causal boundary, are canonical conjugates of boundary metric components and naturally give rise to a fluid description at the causal boundary. Moreover, we show that the boundary charges besides the causal boundary hydrodynamic description, also admit a thermodynamic description with a natural (geometric) causal boundary temperature and angular velocity. When the causal boundary is the asymptotic boundary of the 3d AdS or flat space, the hydrodynamic description respectively recovers an extension of the known conformal or conformal-Carrollian asymptotic hydrodynamics. When the causal boundary is a generic null surface, we recover the null surface thermodynamics of [1] which is an extension of the usual black hole thermodynamics description.

The crowding out effect of financial incentives on conformity to pro-environmental social norms: a quasi-experiment on household recycling

Research has shown that financially incentivizing sustainable behaviors may undermine individuals’ conformity to pro-environmental social norms, but it remains unclear why and when such a crowding out effect occurs. Using data from a quasi-experiment in Quzhou, China, this study has tested crowding out in a local incentive program for household recycling and evaluated the causal mechanisms and boundary conditions of crowding out. The reward program reduced residents’ inclination to conform to their neighbors’ recycling behaviors and persuasion, which was driven by the lowering of the first- and second-order beliefs underlying norm conformity. The crowding out effect and pathways were particularly salient among people with high levels of environmental self-identity or community social embeddedness. Moreover, framing the incentivized behavior in an environmentally beneficial way could not mitigate crowding out. Overall, the results contribute to refined theories of crowding out and have important implications for the design of environmental policies.

On the Resilience of Black Hole Evaporation: Gravitational Tunneling through Universal Horizons

Using a quantum tunneling derivation, we show the resilience of Hawking radiation in Lorentz violating gravity. In particular, we show that the standard derivation of the Hawking effect in relativistic quantum field theory can be extended to Lorentz breaking situations thanks to the presence of universal horizons (causal boundaries for infinite speed signals) inside black hole solutions. Correcting previous studies, we find that such boundaries are characterized by a universal temperature governed by their surface gravity. We also show that within the tunneling framework, given the pole structure and the tunneling path, only a vacuum state set in the preferred frame provides a consistent picture. Our results strongly suggest that the robustness of black hole thermodynamics is ultimately linked to the consistency of quantum field theories across causal boundaries.

Causality Extraction Cascade Model Based on Dual Labeling

Causal relation extraction is a crucial task in natural language processing. Current extraction methods have problems, including low accuracy of causal-event division and incorrect extraction of important semantic features. This study uses the bidirectional long short-term memory (BiLSTM) and attentive convolutional neural network (ACNN) models to construct a cascaded causal relationship extraction model to improve the precision of the extraction. The model uses two kinds of labels and then divides the causal event boundary after determining the relationship between the front and rear causal events. It automatically learns semantic features from sentences, reducing the dependence on external knowledge and improving the precision of extraction. The experimental results demonstrate that the precision of causality extraction can reach 81.67% and the F1 value can reach 83.2%.

Globally hyperbolic spacetimes: slicings, boundaries and counterexamples

The Cauchy slicings for globally hyperbolic spacetimes and their relation with the causal boundary are surveyed and revisited, starting at the seminal conformal boundary constructions by R. Penrose. Our study covers: (1) adaptive possibilities and techniques for their Cauchy slicings, (2) global hyperbolicity of sliced spacetimes, (3) critical review on the conformal and causal boundaries for a globally hyperbolic spacetime, and (4) procedures to compute the causal boundary of a Cauchy temporal splitting by using isocausal comparison with a static product. New simple counterexamples on $\mathbb{R}^2$ illustrate a variety of possibilities related to these splittings, such as the logical independence (for normalized sliced spacetimes) between the completeness of the slices and global hyperbolicity, the necessity of uniform bounds on the slicings in order to ensure global hyperbolicity, or the insufficience of these bounds for the computation of the causal boundary. A refinement of one of these examples shows that the space of all the (normalized, conformal classes of) globally hyperbolic metrics on a smooth product manifold $\mathbb{R}\times S$ is not convex, even though it is path connected by means of piecewise convex combinations.

Gravitational tunneling in Lorentz violating gravity

Black holes in Lorentz violating gravity, such as Einstein--Aether or Horava--Lifshitz Gravity, are drastically different from their general relativistic siblings. Although they allow for superluminal motion in their vicinity, they still exhibit an absolute causal boundary in the form of a universal horizon. By working in the tunneling picture for a gravitating scalar field, we show that universal horizons emit Hawking radiation in a manner akin to standard results in General Relativity, with a temperature controlled by the high-energy behavior of the dispersion relation of the gravitating field, and in agreement with alternative derivations in the literature. Our results substantiate the link between the universal horizon and thermodynamics in Lorentz violating theories.

Symmetries at causal boundaries in 2D and 3D gravity

We study 2d and 3d gravity theories on spacetimes with causal (timelike or null) codimension one boundaries while allowing for variations in the position of the boundary. We construct the corresponding solution phase space and specify boundary degrees freedom by analysing boundary (surface) charges labelling them. We discuss Y and W freedoms and change of slicing in the solution space. For D dimensional case we find D + 1 surface charges, which are generic functions over the causal boundary. We show that there exist solution space slicings in which the charges are integrable. For the 3d case there exists an integrable slicing where charge algebra takes the form of Heisenberg ⊕ mathcal{A} 3 where mathcal{A} 3 is two copies of Virasoro at Brown-Henneaux central charge for AdS3 gravity and BMS3 for the 3d flat space gravity.

To do or not to do? Cost-sensitive causal classification with individual treatment effect estimates

Individual treatment effect models allow optimizing decision-making by predicting the effect of a treatment on an outcome of interest for individual instances. These predictions allow selecting instances to treat in order to optimize the overall efficiency and net treatment effect. In this article, we extend upon the expected value framework and introduce a cost-sensitive causal classification boundary for selecting instances to treat based on predictions of individual treatment effects and for the case of a binary outcome. The boundary is a linear function of the estimated individual treatment effect, the positive outcome probability and the cost and benefit parameters of the problem setting. It allows causally classifying instances in the positive and negative treatment class in order to maximize the expected causal profit, which is introduced as the objective at hand in cost-sensitive causal classification. We present the expected causal profit ranker which ranks instances for maximizing the expected causal profit at each possible threshold that results from a constraint on the number of positive treatments and which differs from the conventional ranking approach based on the individual treatment effect. The proposed ranking approach is experimentally evaluated on synthetic and marketing campaign data sets. The results indicate that the presented ranking method outperforms the cost-insensitive ranking approach.

The Cosmological Constant as Event Horizon

General Relativity allows for a cosmological constant (Λ) which has inspired models of cosmic Inflation and Dark Energy. We show instead that rΛ=3/Λ corresponds to an event horizon: a causal boundary term in the action. Our Universe is expanding inside its Schwarzschild radius rS=rΛ=2GM, which could have originated from a uniform free falling cloud of mass M that collapsed as a Black Hole (BH) 25 Gyrs ago. Such a BH Universe allows for large-scale structure formation without the need of Inflation or Dark Energy.

Forward scattering amplitudes in the imaginary time formalism

We study, in the imaginary time formalism, the relation between loops and on-shell forward scattering tree amplitudes in thermal field theories. This allows for an efficient evaluation, at all temperatures, of Green's functions with causal retarded boundary conditions. We present an application of this relation in quantum gravity coupled to scalar matter fields. We show that at one or two loops, involving planar diagrams, the 1PI retarded thermal Green's functions may respectively be expressed in terms of connected forward scattering tree amplitudes of one or two on-shell particles.

Relation between general relativity and a class of Hořava gravity theories

Violations of Lorentz (and specifically boost) invariance can make gravity renormalizable in the ultraviolet, as initially noted by Ho\v{r}ava, but are increasingly constrained in the infrared. At low energies, Ho\v{r}ava gravity is characterized by three dimensionless couplings, $\alpha$, $\beta$ and $\lambda$, which vanish in the general relativistic limit. Solar system and gravitational wave experiments bound two of these couplings ($\alpha$ and $\beta$) to tiny values, but the third remains relatively unconstrained ($0\leq\lambda\lesssim 0.01-0.1$). Moreover, demanding that (slowly moving) black-hole solutions are regular away from the central singularity requires $\alpha$ and $\beta$ to vanish {\it exactly}. Although a canonical constraint analysis shows that the class of khronometric theories resulting from these constraints ($\alpha=\beta=0$ and $\lambda\neq0$) cannot be equivalent to General Relativity, even in vacuum, previous calculations of the dynamics of the solar system, binary pulsars and gravitational-wave generation show perfect agreement with General Relativity. Here, we analyze spherical collapse and compute black-hole quasinormal modes, and find again that they behave {\it exactly} as in General Relativity, as far as {\it observational} predictions are concerned. Nevertheless, we find that spherical collapse leads to the formation of a regular {\it universal} horizon, i.e. a causal boundary for signals of arbitrary propagation speeds, inside the usual event horizon for matter and tensor gravitons. Our analysis also confirms that the additional scalar degree of freedom present alongside the spin-2 graviton of General Relativity remains strongly coupled at low energies, even on curved backgrounds. These puzzling results suggest that any further bounds on Ho\v{r}ava gravity will probably come from cosmology.

Does It Matter How We Speak About Social Kinds? A Large, Preregistered, Online Experimental Study of How Language Shapes the Development of Essentialist Beliefs

A problematic way to think about social categories is to essentialize them-to treat particular differences between people as marking fundamentally distinct social kinds. From where do these beliefs arise? Language that expresses generic claims about categories elicits some aspects of essentialism, but the scope of these effects remains unclear. This study (N=204, ages 4.5-8years, 73% White; recruited predominantly from the United States and the United Kingdom to participate online in 2019) found that generic language increases two critical aspects of essentialist thought: Beliefs that (a) category-related properties arise from intrinsic causal mechanisms and (b) category boundaries are inflexible. These findings have implications for understanding the spread of essentialist beliefs across communities and the development of intergroup behavior.

The cosmological constant as a zero action boundary

ABSTRACT The cosmological constant Λ is usually interpreted as Dark Energy (DE) or modified gravity (MG). Here, we propose instead that Λ corresponds to a boundary term in the action of classical General Relativity. The action is zero for a perfect fluid solution and this fixes Λ to the average density ρ and pressure p inside a primordial causal boundary: Λ = 4πG <ρ+3p >. This explains both why the observed value of Λ is related to the matter density today and also why other contributions to Λ, such as DE or MG, do not produce cosmic expansion. Cosmic acceleration results from the repulsive boundary force that occurs when the expansion reaches the causal horizon. This universe is similar to the ΛCDM universe, except on the largest observable scales, where we expect departures from homogeneity/isotropy, such as CMB anomalies and variations in cosmological parameters indicated by recent observations.

Structure of globally hyperbolic spacetimes-with-timelike-boundary

Globally hyperbolic spacetimes-with-timelike-boundary (\overline{M} = M \cup \partial M, g) are the natural class of spacetimes where regular boundary conditions (eventually asymptotic, if \partial M is obtained by means of a conformal embedding) can be posed. \partial M represents the naked singularities and can be identified with a part of the intrinsic causal boundary. Apart from general properties of \partial M , the splitting of any globally hyperbolic (\overline{M},g) as an orthogonal product \mathbb{R}\times \bar\Sigma with Cauchy slices-with-boundary \{t\}\times \bar\Sigma is proved. This is obtained by constructing a Cauchy temporal function \tau with gradient \nabla \tau tangent to \partial M on the boundary. To construct such a \tau , results on stability of both global hyperbolicity and Cauchy temporal functions are obtained. Apart from having their own interest, these results allow us to circumvent technical difficulties introduced by \partial M . The techniques also show that \overline{M} is isometric to the closure of some open subset in a globally hyperbolic spacetime (without boundary). As a trivial consequence, the interior M both splits orthogonally and can be embedded isometrically in some \mathbb{L}^N , extending so properties of globally spacetimes without boundary to a class of causally continuous ones.

Hausdorff closed limits and the c-boundary II: null infinity and black holes

We have shown in a companion paper (e Silva et al (2019)) that when a spacetime is globally hyperbolic with a (possibly empty) smooth timelike boundary , then a metrizable topology, the closed limit topology (CLT), can be advantageously adopted on the Geroch–Kronheimer–Penrose causal completion (or c-completion for short) of . The CLT retains essentially all the good properties of other topologies previously defined in the literature, such as the well-known chronological topology. In this paper we prove that if a globally hyperbolic spacetime admits a conformal boundary, defined in such broad terms as to include all the standard examples in the literature, then the latter is homeomorphic to the causal boundary endowed with the CLT. Then, we revisit the new definitions of (future) null infinity and black hole as given in terms of the c-boundaries in another recent work Costa e Silva et al (2018 J. High Energy Phys. JHEP(2018)123). We show that a number of the attending technicalities can be simplified for globally hyperbolic spacetimes when the CLT is considered.