Universal Horizon Research Articles

Art as the Silence of the World. An Attempt at a Phenomenological Interpretation

ABSTRACTThis paper provides an analysis of the paradoxical definition of art as the silence of the world, as presented in Maurice Blanchot’s The Space of Literature. The definition is analysed phenomenologically, by treating the world as the universal horizon of all experiences. The paper presents two possible interpretations of Blanchot’s statement. First, a possibility is considered that, according to Blanchot, in genuine artistic experience the mundane everyday life falls silent, and an autonomous fictional world opens up. The paper argues that while Blanchot does oppose art to everyday life, this interpretation is insufficient. Firstly, because on the basis of the phenomenological premise, all possible worlds fall within the universal world-horizon, and secondly, the function Blanchot attributes to art is considerably more radical, as when he speaks about the directedness of art outside of all possible worlds. While such an aim may seem impossible from the viewpoint of the phenomenological premise, the second part of the paper demonstrates that it can indeed be meaningfully interpreted on the basis of Martin Heidegger’s transcendent approach to the world. According to this interpretation, while the phenomenological premise prevents all discussion of places and experiences outside the world, a liminal experience can nevertheless be discussed. If this is true, it is not an entity within the world which opens up, but rather the world-horizon itself in the form of an anxious silence.

Holography and AdS2 gravity with a dynamical aether

We study two-dimensional Einstein-aether (or equivalently Hořava-Lifshitz) gravity, which has an AdS2 solution. We examine various properties of this solution in the context of holography. We first show that the asymptotic symmetry group is the full set of time reparametrizations, the one-dimensional conformal group. At the same time there are configurations with finite energy and temperature, which indicate a violation of the Ward identity associated with one-dimensional conformal invariance. These solutions are characterized by a universal causal horizon and we show that the associated entropy of the universal horizon scales with the logarithm of the temperature. We discuss the puzzles associated with this result and argue that the violation of the Ward identity is associated with a type of explicit breaking of time reparametrizations in the hypothetical 0 + 1 dimensional dual system.

No static black hole hairs in gravitational theories with broken Lorentz invariance

In this paper, we revisit the issue of static hairs of black holes in gravitational theories with broken Lorentz invariance in the case that the speed $c_{\phi}$ of the khronon field becomes infinitely large, $c_{\phi} = \infty$, for which the sound horizon of the khronon field coincides with the universal horizon, and the boundary conditions at the sound horizon reduce to those given normally at the universal horizons. As a result, less boundary conditions are present in this extreme case in comparison with the case $c_{\phi} = $ finite. Then, it would be expected that static hairs might exist. However, we show analytically that even in this case static hairs still cannot exist, based on a decoupling limit analysis. We also consider the cases in which $c_{\phi}$ is finite but with $c_{\phi} \gg 1$, and obtain the same conclusion.

Improved derivation of the Smarr formula for Lorentz-breaking gravity

Thermodynamical properties of black holes in gravitational theories without Local Lorentz invariance have been subject to intense investigation in the past years due to the presence of universal horizons, which are strong causal barriers even for superluminal signals. Here we present a novel general method for deriving the Smarr formula for this class of theories: in particular we show that the Smarr formulae for Einstein-Aether theory and infrared Horava gravity follow from scale invariance. We not only reproduce straightforwardly previous findings for static black hole solutions, but we are also able to generalise them to the case of stationary rotating black holes. Finally, we apply our results to the rotating black holes with universal horizon as found in three dimensions, from which we shall draw some lessons on the viability of black hole thermodynamics for black hole solutions endowed with universal horizons.

Dispersion relation and surface gravity of universal horizons

In Einstein-aether theory, violating Lorentz invariance permits some super-luminal communications, and the universal horizon can trap excitations traveling at arbitrarily high velocities. To better understand the nature of these universal horizons, we first modify the ray tracing method, and then use it to study their surface gravity in charged Einstein-aether black hole spacetime. Instead of the previous result in Ref. [Phys. Rev. D 89, 064061], our results show that the surface gravity of the universal horizon is dependent on the specific dispersion relation, $\kappa_{UH}=2(z-1)\kappa_{uh}/z$, where $z$ denotes the power of the leading term in the superluminal dispersion relation, characterizing different species of particles. And the associated Hawking temperatures also are different with $z$. These findings, which coincide with those in Ref. [Nucl. Phys. B 913, 694] derived by the tunneling method, provide some full understanding of black hole thermodynamics in Lorentz-violating theories.

Hořava gravity at a Lifshitz point: A progress report

Hořava’s quantum gravity at a Lifshitz point is a theory intended to quantize gravity by using traditional quantum field theories. To avoid Ostrogradsky’s ghosts, a problem that has been facing in quantization of general relativity since the middle of 1970’s, Hořava chose to break the Lorentz invariance by a Lifshitz-type of anisotropic scaling between space and time at the ultra-high energy, while recovering (approximately) the invariance at low energies. With the stringent observational constraints and self-consistency, it turns out that this is not an easy task, and various modifications have been proposed, since the first incarnation of the theory in 2009. In this review, we shall provide a progress report on the recent development of Hořava gravity. In particular, we first present four so far most-studied versions of Hořava gravity, by focusing first on their self-consistency and then their consistency with experiments, including the solar system tests and cosmological observations. Then, we provide a general review on the recent development of the theory in three different but also related areas: (i) universal horizons, black holes and their thermodynamics, (ii) nonrelativistic gauge/gravity duality and (iii) quantization of the theory. The studies in these areas can be easily generalized to other gravitational theories with broken Lorentz invariance.

«Гоголь, или Провинциал в столице»: от Малороссии к Петербургу

The article is devoted to the problem of the uniqueness of creativity of N. V. Gogol and his place in literature. The relevance of the work is determined by pendency of the issue, which literature researchers repeatedly addressed to. The author uses an interdisciplinary approach. The study is based on extensive literary material. Problem of finding the “key” to understanding the creativity and fate of N. V. Gogol rises from the lore point of view. A review of literature on the subject is given. It is shown that in the spiritual and creative fracture of the writer, and hence his growth, a significant role was played by moving from the Ukraine to Petersburg. The author dwells on the universality of Gogol as one of the national corollaries of duality, which became a fruitful imperative of his creativity, the key breakthrough - through Russian language and Russian themes - from the “provincial Dikanka” to the universal horizon. The article proves the idea that Petersburg in contrast with the Little Russia breaks (and forms) Gogol’s optics. It is noted that the writer did not remain in debt: there was “invasion of the Ukrainian wave with Gogol on the crest” in Russian culture (in the words of N. Piksanov). It is shown that the regional approach applicable to the figure of the writer allows to expand the possibilities of literary analysis. Also the question is raised about the relationship of reality and artistic fiction in the works by N. Gogol.

New asymptotically Lifshitz black holes in Hořava gravity

We study asymptotically Lifshitz solutions with critical exponent $z \neq 1$ in Horava gravity in three and four spacetime dimensions. For $z=2$ and $z=3/2$, we find a novel class of numerical solutions with regular universal horizon, but are characterized by non-analytic behavior near infinity. In the interior, inside the universal horizon, the unit timelike vector field associated with the preferred time foliation exhibits oscillatory behavior, qualitatively similar to that found earlier in asymptotically flat solutions. For $z>2$ no solutions of this type appear to exist. We comment on potential applications to holographic Lifshitz dualities.

Three-dimensional charged Einstein-aether black holes and the Smarr formula

We investigate the three-dimensional behavior of gravity coupled to a dynamical unit timelike vector: the aether, and present two new classes of exact charged solutions. When c_{13}=0,\Lambda'=0$, we find the solutions is the usual BTZ black hole but now with an universal horizon. In the frame of black hole chemistry, we then calculate the temperature of the universal horizons and, construct the Smarr formulas and first law in the three cases: quasi-asymptotically flat, aether asymptotically flat and quasi-BTZ black hole spacetime. We found these universal horizons obey an exact (or slightly modified) first law of black hole mechanics and may have an entropy and, black hole mass can be interpreted as enthalpy of spacetime. Then the holography may be extended to these horizons under violating Lorentz symmetry.

Causality and black holes in spacetimes with a preferred foliation

We develop a framework that facilitates the study of the causal structure of spacetimes with a causally preferred foliation. Such spacetimes may arise as solutions of Lorentz-violating theories, e.g. Hořava gravity. Our framework allows us to rigorously define concepts such as black/white holes and to formalize the notion of a ‘universal horizon’, that has been previously introduced in the simpler setting of static and spherically symmetric geometries. We also touch upon the issue of development and prove that universal horizons are Cauchy horizons when evolution depends on boundary data or asymptotic conditions. We establish a local characterisation of universal horizons in stationary configurations. Finally, under the additional assumption of axisymmetry, we examine under which conditions these horizons are cloaked by Killing horizons, which can act like usual event horizons for low-energy excitations.

Hawking radiation of charged Einstein-aether black holes at both Killing and universal horizons

We study analytically quantum tunneling of relativistic and non-relativistic particles at both Killing and universal horizons of Einstein–Maxwell-aether black holes, after high-order curvature corrections are taken into account, for which the dispersion relation of the particles becomes nonlinear. Our results at the Killing horizons confirm the previous ones, i.e., at high frequencies the corresponding radiation remains thermal and the nonlinearity of the dispersion does not alter the Hawking radiation significantly. In contrary, non-relativistic particles are created at universal horizons and are radiated out to infinity. The radiation also has a thermal spectrum, and the corresponding temperature takes the form, TUHz=2κUH(z−1)/(2πz), where z (z≥2) denotes the power of the leading term in the nonlinear dispersion relation, κUH is the surface gravity of the universal horizon, defined by peering behavior of ray trajectories at the universal horizon. We also study the Smarr formula by assuming that: (a) the entropy is proportional to the area of the universal horizon, and (b) the first law of black hole thermodynamics holds, whereby we derive the Smarr mass, which in general is different from the total mass obtained at infinity. This indicates that one or both of these assumptions must be modified.

Analogue black holes in relativistic BECs: Mimicking Killing and universal horizons

Relativistic Bose-Einstein condensates (rBECs) have recently become a well-established system for analogue gravity. Indeed, while such relativistic systems cannot be yet realized experimentally, they provide an interesting framework for mimicking metrics for which no analogue is yet available, so paving the way for further theoretical and numerical explorations. In this vein, we here discuss black holes in rBECs and explore how their features relate to the bulk properties of the system. We then propose the coupling of external fields to the rBEC as a way to mimic non-metric features. In particular, we use a Proca field to simulate an aether field, as found in Einstein-Aether or Horava-Lifshitz gravity. This allows us to mimic a universal horizon, the causal barrier relevant for superluminal modes in these modified gravitational theories.

FRANTZ FANON EN EL PENSAMIENTO DE FAUSTO REINAGA: CULTURA, REVOLUCIÓN Y NUEVO HUMANISMO

This article explores links that can be established among indigenous and Afro-descendent thought developed in Latin America during the 20th century. By drawing a comparison between the Caribbean and Andean regions, we specifically concentrate on the intellectual work of an indigenous Bolivian and an Afro-Caribbean from Martinique: Fausto Reinaga and Frantz Fanon. Reinaga‘s inaugural writings on indianista thought reveal several references to the work of Fanon, providing material for our analysis. We argue that such allusions are not mere accessories, but rather fundamental elements for the kind of indianismo that the Quechua-Aymara author develops; that is, an anticolonial thought in which universal and human horizons are present.

Static and rotating universal horizons and black holes in gravitational theories with broken Lorentz invariance

In this paper, we show the existence of static and rotating universal horizons and black holes in gravitational theories with the broken Lorentz invariance. We pay particular attention on the ultraviolet regime, and show that universal horizons and black holes exist not only in low energy scales but also in the UV scales. This is realized by presenting various static and stationary exact solutions of the full theory of the projectable Ho\v{r}ava gravity with an extra U(1) symmetry in (2+1)-dimensions, which, by construction, is power-counting renormalizable.

Quasilocal approach to general universal horizons

Theories of gravity with a preferred foliation usually display arbitrarily fast signal propagation, changing the black hole definition. A new inescapable barrier, the universal horizon, has been defined and many static and spherically symmetric examples have been studied in the literature. Here, we translate the usual definition of the universal horizon in terms of an optical scalar built with the preferred flow defined by the preferred spacetime foliation. The new expression has the advantages of being of quasilocal nature and independent of specific spacetime symmetries in order to be well defined. Therefore, we propose it as a definition for general quasilocal universal horizons. Using the new formalism we show that there are no universal analog of cosmological horizons for FLRW models for any scale factor function, and we also state that quasilocal universal horizons are restricted to trapped regions of the spacetime. Using the evolution equation, we analyze the formation of universal horizons under a truncated Horava-Lifshitz theory, in spherical symmetry, showing the existence of regions in parameter space where the universal horizon formation cannot be smooth from the center, under some physically reasonable assumptions. We conclude with our view on the next steps for the understanding of black holes in nonrelativistic gravity theories.

Cosmic censorship in Lorentz-violating theories of gravity

Is Cosmic Censorship special to General Relativity, or can it survive a violation of equivalence principle? Recent studies have shown that singularities in Lorentz violating Einstein-Aether (or Horava-Lifhsitz) theories can lie behind a universal horizon in simple black hole spacetimes. Even infinitely fast signals cannot escape these universal horizons. We extend this result, for an incompressible aether, to 3+1d dynamical or spinning spacetimes which possess inner killing horizons, and show that a universal horizon always forms in between the outer and (would-be) inner horizons. This finding suggests a notion of Cosmic Censorship, given that geometry in these theories never evolves beyond the universal horizon (avoiding potentially singular inner killing horizons). A surprising result is that there are 3 distinct possible stationary universal horizons for a spinning black hole, only one of which matches the dynamical spherical solution. This motivates dynamical studies of collapse in Einstein-Aether theories beyond spherical symmetry, which may reveal instabilities around the spherical solution.

Asymptotically Lifshitz spacetimes with universal horizons in (1+2) dimensions

Ho\ifmmode \check{r}\else \v{r}\fi{}ava gravity theory possesses global Lifshitz space as a solution and has been conjectured to provide a natural framework for Lifshitz holography. We derive the conditions on the two-derivative Ho\ifmmode \check{r}\else \v{r}\fi{}ava gravity Lagrangian that are necessary for static, asymptotically Lifshitz spacetimes with flat transverse dimensions to contain a universal horizon, which plays a similar thermodynamic role as the Killing horizon in general relativity. Specializing to $z=2$ in $1+2$ dimensions, we then numerically construct such regular solutions over the whole spacetime. We calculate the mass for these solutions and show that, unlike the asymptotically anti--de Sitter case, the first law applied to the universal horizon is straightforwardly compatible with a thermodynamic interpretation.

Evolution and spherical collapse in Einstein-Æther theory and Hořava gravity

We compare the initial value formulation of the low-energy limit of (non-projectable) Horava gravity to that of Einstein-aether theory when the aether is assumed to be hypersurface orthogonal at the level of the field equations. This comparison clearly highlights a crucial difference in the causal structure of the two theories at the non-perturbative level: in Horava gravity evolution equations include an elliptic equation that is not a constraint relating initial data but needs to be imposed on each slice of the foliation. This feature is absent in Einstein-aether theory. We discuss its physical significance in Horava gravity. We also focus on spherical symmetry and we revisit existing collapse simulations in Einstein-aether theory. We argue that they have likely already uncovered the dynamical formation of a universal horizon and that they can act as evidence that this horizon is indeed a Cauchy horizon in Horava gravity.

Slowly rotating black holes in Einstein-æther theory

We study slowly rotating, asymptotically flat black holes in Einstein-aether theory and show that solutions that are free from naked finite area singularities form a two-parameter family. These parameters can be thought of as the mass and angular momentum of the black hole, while there are no independent aether charges. We also show that the aether has non-vanishing vorticity throughout the spacetime, as a result of which there is no hypersurface that resembles the universal horizon found in static, spherically symmetric solutions. Moreover, for experimentally viable choices of the coupling constants, the frame-dragging potential of our solutions only shows percent-level deviations from the corresponding quantities in General Relativity and Horava gravity. Finally, we uncover and discuss several subtleties in the correspondence between Einstein-aether theory and Horava gravity solutions in the $c_\omega\to\infty$ limit.

“Our Loyalties Must Become Ecumenical”: Martin Luther King, Jr., as a Pluralist Theologian

This essay presents how “theologian” and “pluralist” are contested categories in religious-studies scholarship to such a degree that the pluralist theologies of people of color have been thwarted from many ecumenical discourses. While Martin Luther King, Jr.’s credentials as a theologian have been questioned, he should, nevertheless, be interpreted not only as a theologian but also as a pluralist theologian par excellence . To this end, King’s primary sources are used to reconstruct dimensions of his pluralist theology. His pluralist views and values are placed in critical conversation with contemporary pluralism scholarship. It is shown that King’s universal horizon transcended Jewish, Christian, and Muslim relationships. He did not believe in the metaphysical unity of religions. He identified both similar and dissimilar teachings across religions. He preached that Christian and non-Christian traditions provided resources for sharing and learning—especially for ethical values. Overall, King’s ecumenism contributes to debates about ethnocentric biases and admiration for different faiths.