Universal Horizon Research Articles

Is Birkhoff's theorem valid in Einstein-Aether theory?

We attempt to answer whether Birkhoff's theorem (BT) is valid in the Einstein-Aether (EA) theory. The BT states that any spherically symmetric solution of the vacuum field equations must be static, unique, and asymptotically flat. For a general spherically symmetric metric with metric functions A(r,t) &B(r,t), and aether components a(r,t) &b(r,t), we prove the conditions for the staticity of spacetime using two different methods. We point out that BT is valid in EA theory only for special values of c1+c3, c1+c4, and c2, where we can show that all these special cases are asymptotically flat. In particular, when the aether has only a temporal component i.e., b(r,t)=0, the c14≠0 case gives us spherically symmetric static solutions with singularities without Killing nor universal horizons, at least for special values of c14. However, when we have an aether vector with temporal and radial components, we prove that the staticity and the flatness at infinity hold for only a special metric and a particular combination of the aether parameters. These solutions have universal horizons.

Hawking radiation in Lorentz violating gravity: a tale of two horizons

Since their proposal, Lorentz violating theories of gravity have posed a potential threat to black hole thermodynamics, as superluminal signals appeared to be incompatible with the very black hole notion. Remarkably, it was soon realized that in such theories causally disconnected regions of space-time can still exist thanks to the presence of universal horizons: causal barriers for signals of arbitrary high speed. Several investigations, sometimes with contrasting results, have been performed so to determine if these horizons can be associated with healthy thermodynamic properties similar to those associated with Killing horizons in General Relativity. In this work we offer what we deem to be the final picture emerging from this and previous studies. In summary we show that: 1) there is a thermal, and most of all species-independent, emission associated to universal horizons, determined by their surface gravity; 2) due to the modified dispersion relation of the matter fields, the low energy part of the emitted spectrum is affected by the presence of the Killing horizon, in a way similar to an effective refractive index, leading at low energies (w.r.t. the Lorentz breaking scale) to an emission that mimics a standard Hawking spectrum (i.e. one determined by the Killing horizon surface gravity); 3) the whole picture is compatible with a globally well defined vacuum state i.e. an Unruh state associated with preferred observers, which however at very low energies it is basically indistinguishable from the standard Unruh vacuum associated to metric free-falling observers. One can then conclude that Hawking radiation is remarkably resilient even within the context of gravitational theories entailing the breakdown of local Lorentz invariance.

Well-posed evolution of field theories with anisotropic scaling: the Lifshitz scalar field in a black hole space-time

Partial differential equations exhibiting an anisotropic scaling between space and time — such as those of Hořava-Lifshitz gravity — have a dispersive nature. They contain higher-order spatial derivatives, but remain second order in time. This is inconvenient for performing long-time numerical evolutions, as standard explicit schemes fail to maintain convergence unless the time step is chosen to be very small. In this work, we develop an implicit evolution scheme that does not suffer from this drawback, and which is stable and second-order accurate. As a proof of concept, we study the numerical evolution of a Lifshitz scalar field on top of a spherically symmetric black hole space-time. We explore the evolution of a static pulse and an (approximately) ingoing wave-packet for different strengths of the Lorentz-breaking terms, accounting also for the effect of the angular momentum eigenvalue and the resulting effective centrifugal barrier. Our results indicate that the dispersive terms produce a cascade of modes that accumulate in the region in between the Killing and universal horizons, indicating a possible instability of the latter.

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.

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.

Regular black holes and horizonless ultra-compact objects in Lorentz-violating gravity

There is growing evidence that Hořava gravity may be a viable quantum theory of gravity. It is thus legitimate to expect that gravitational collapse in the full, non-projectable version of the theory should result in geometries that are free of space-time singularities. Previous analyses have shown that such geometries must belong to one of the following classes: simply connected regular black holes with inner horizons; non-connected black holes “hiding” a wormhole mouth (black bounces); simply connected or non-connected horizonless compact objects. Here, we consider a singular black hole in the low-energy limit of non-projectable Hořava gravity, i.e. khronometric theory, and describe examples of its possible “regularisations”, covering all of the viable classes. To our knowledge, these examples constitute the first instances of black holes with inner universal horizons, of black bounces and of stars with a de Sitter core in the context of Lorentz-violating theories of gravity.

Thermodynamics of Einstein-Aether black holes

We analyze several spherically symmetric exterior vacuum solutions allowed by the Einstein-Aether (EA) theory with a non-static aether and study the thermodynamics of their Killing and universal horizons. We show that there are five classes of solutions corresponding to different values of a combination of the free parameters, c_{2}, c_{13}=c_1+c_3 and c_{14}=c_1+c_4, which are: (A) c_2 ne 0 and c_{13} ne 0 and c_{14}=0, (B) c_2 ne 0 and c_{13} = 0 and c_{14} = 0, (C) c_2 = 0 and c_{13} ne 0 and c_{14} = 0, (D) c_2 = 0, c_{13} = 0 and c_{14} ne 0, and (E) c_2 = - c_{13} ne 0 and c_{14} ne 0. We present explicit analytical solutions for these five cases. All these cases have singularities at r=0 and are asymptotically flat spacetimes and possess both Killing and universal horizons with the universal horizons always being inside the Killing horizons. Finally, we compute the surface gravity, the temperature, the entropy and the first law of thermodynamics for the universal horizons.

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.

Смысловые основания ценностей культуры в зеркале майевтики Сократа (на примере диалога «Лахет»)

The article examines the semantic foundations of values that define cultural norms and patterns, as well as the culturality of the person himself, his identity. It is argued that reflection on personal identity consists in distinguishing between the authenticity and the imaginary of one's own existence through reflection on traditional values. Such reflection was a mayeutics, an ontological procedure in its essence, helping the birth of human virtues. The analysis of the dialogue "Lakhet", the participants of which are trying to define courage, allows us to identify the apophatic integrity of the semantic content of traditional values. Such a value, on the one hand, has an intuitive self-evidence that allows you to recognize courageous actions. On the other hand, it carries the possibility of different interpretations, giving priority to certain substantive features. However, such interpretations are not able to contain the full meaning of the value and conceptual certainty can lead to distortion of its content. The conceptualisation of value aims at juxtaposing the concreteness of human existence and the universal horizon of human existence.

Time orientability and particle production from universal horizons

We discuss particle production in spacetimes endowed with a universal horizon in Einstein--Aether and Horava gravity. We argue that continuity and differentiability of the lapse function require the orientation of the foliation in the interior of the horizon to be reversed with respect to the exterior one. Unless this is allowed, interaction of gravitating scalar fields with the universal horizon leads to unitarity violations in the quantum theory. This property is responsible for particle production by the universal horizon, as we show by computing explicitly its Hawking temperature for all stationary and spherically symmetric spacetimes. We particularize our result to known analytic solutions, including those compatible with observational constraints.

Geodesically complete black holes in Lorentz-violating gravity

We present a systematic study of the geometric structure of non-singular spacetimes describing black holes in Lorentz-violating gravity. We start with a review of the definition of trapping horizons, and the associated notions of trapped and marginally trapped surfaces, and then study their significance in frameworks with modified dispersion relations. This leads us to introduce the notion of universally marginally trapped surfaces, as the direct generalization of marginally trapped surfaces for frameworks with infinite signal velocities (Hořava-like frameworks), which then allows us to define universal trapping horizons. We find that trapped surfaces cannot be generalized in the same way, and discuss in detail why this does not prevent using universal trapping horizons to define black holes in Hořava-like frameworks. We then explore the interplay between the kinematical part of Penrose’s singularity theorem, which implies the existence of incomplete null geodesics in the presence of a focusing point, and the existence of multiple different metrics. This allows us to present a complete classification of all possible geometries that neither display incomplete physical trajectories nor curvature singularities. Our main result is that not all classes that exist in frameworks in which all signal velocities are realized in Hořava-like frameworks. However, the taxonomy of geodesically complete black holes in Hořava-like frameworks includes diverse scenarios such as evaporating regular black holes, regular black holes bouncing into regular white holes, and hidden wormholes.

Erratum: Neutron star sensitivities in Hořava gravity after GW170817 [Phys. Rev. D 100 , 084053 (2019)

Hořava gravity breaks boost invariance in the gravitational sector by introducing a preferred time foliation. The dynamics of this preferred slicing is governed, in the low-energy limit suitable for most astrophysical applications, by three dimensionless parameters α, β and λ. The first two of these parameters are tightly bound by Solar System and gravitational-wave propagation experiments, but λ remains relatively unconstrained (0≤λ≲0.01–0.1). We restrict here to the parameter-space region defined by α=β=0 (with λ kept generic), which in a previous paper we showed to be the only one where black hole solutions are nonpathological at the universal horizon, and we focus on possible violations of the strong equivalence principle in systems involving neutron stars. We compute neutron star “sensitivities,” which parametrize violations of the strong equivalence principle at the leading post-Newtonian order, and find that they vanish identically, like in the black hole case, for α=β=0 and generic λ≠0. This implies that no violations of the strong equivalence principle (neither in the conservative sector nor in gravitational-wave fluxes) can occur at the leading post-Newtonian order in binaries of compact objects, and that data from binary pulsars and gravitational interferometers are unlikely to further constrain λ.

The Incarnation: Classical Christology and Public Theology

Classical christology matters for public theology. In the Gospel of John, the Logos who creates the cosmos became flesh. Chalcedon (451 CE) clarified the divine/human union in Jesus of Nazareth. Jesus the creating Logos enlightens every human, Aquinas taught, with the capacity for thought and agency in social existence, the light of reason. The public sphere is a free space for discussion of matters bearing on human flourishing. Public theology is attentive to both the historical particularity of belief in Jesus the Messiah and the universal horizon of the Logos in creation and conscience. Promoting social justice, public theology addresses topics, structures, dynamics and meanings in the public sphere of liberal democracies.

Paternoster, or Invective by paradigm

The poem Apostrofa (na czas stanu wojennego) by Father Kazimierz Wójtowicz was published in the collection of poems Odpisy Nadziei in Vienna in 1982. The artist is a Catholic monk (a Resurrectionist) and a poet with considerable achievements, acknowledged in the so-called priestly poetry (Krzysztof Dybciak, Bożena Chrząstowska), but going beyond the features of its style through the connection with linguistic poetry and the New Wave poetics. The author of the article attempts to recognize the phenomenon of the text, which belongs to the realm of martial law literature and in which the poet expresses a politically and morally motivated reprimand addressed to General Jaruzelski through the pattern of Pater noster — the most important Christian prayer. The foundations of the strategy implemented in Apostrofa are: the shift of meanings (“Our Stepfather” as an invective), the reference to the language of values, the use of several rhetorical figures (including figures of thought and aversio), as well as the reference to the Lord’s Prayer in the form of reactivating a separate literary genre (pacierz — Lord’s prayer) in its serious and exhorting variant (paternoster — ‘scolding’ prayer). With such an approach, the text of Our Father cannot be perceived as the subject of occasional intertextual stylization (parody, travesty or burlesque), the matrix of a pamphlet or a pasquil, but rather as the root paradigm (“the cultural model of behavior”; Victor Turner’s concept) defining a universal ethical horizon for Wójtowicz’s poem.

Energy-entropy relation for asymptotically Lifshitz spacetimes with universal horizons

We numerically solve for 2+1 asymptotically Lifshitz universal horizon solutions in Horava-Lifshitz gravity for dynamical exponents $z=2$ through $z=8$. We find that for all $z$ there is a thermodynamical first law and Smarr formula. Furthermore, we find that the energy-entropy relation expected for a thermal state in a two dimensional Lifshitz field theory, $E=\frac{2}{z+2}TS$, is also satisfied for universal horizons, including the correct $z$ scaling.

Hawking radiation from universal horizons

The persistence of a suitable notion of black hole thermodynamics in Lorentz breaking theories of gravity is not only a non-trivial consistency test for such theories, it is also an interesting investigation per se, as it might help us identifying the crucial features at the root of these surprising laws governing such purely gravitational objects. In past investigations, controversial findings were presented in this sense. With the aim of settling this issue, we present here two complementary derivations of Hawking radiation in geometries endowed with universal horizons: a novel feature of back holes in Lorentz breaking theories of gravity which reproduces several properties normally characterizing Killing horizons. We find that both the derivations agree on the fact that the Hawking temperature associated to these geometries is set by the generalized universal horizon peeling surface gravity, as required for consistency with extant derivations of the first law of thermodynamics for these black holes. We shall also comment on the compatibility of our results with previous alternative derivations and on their significance for the survival of the generalized second law of black hole thermodynamics in Lorentz breaking theories of gravity.

Spherically symmetric analytic solutions and naked singularities in Einstein\u2013Aether theory

We analyze all the possible spherically symmetric exterior vacuum solutions allowed by the Einstein–Aether theory with static aether. We show that there are three classes of solutions corresponding to different values of a combination of the free parameters, c_{14}=c_1+c_4, which are: 0< c_{14}<2, c_{14} < 0, and c_{14}=0. We present explicit analytical solutions for c_{14}=3/2, 16/9, 48/25, -16 and 0. The first case has some pathological behavior, while the rest have all singularities at r=0 and are asymptotically flat spacetimes. For the solutions c_{14}=16/9, 48/25, mathrm {, and ,}, -16 we show that there exist no horizons, neither Killing horizon nor universal horizon, thus we have naked singularities. This characteristic is completely different from general relativity. We briefly discuss the thermodynamics for the case c_{14}=0 where the horizon exists.

PHENOMENOLOGY OF CULTURE BY E. HUSSERL: COMMUNICATIVE AND COMPREGENSIVE EXPERIENCES

The article states the effectiveness of the phenomenological method in solving a wide range of current problems of modern socioculture, both applied and theoretical. It is substantiated that in intentional acts of consciousness the surrounding world acts as a boundary of subjectivity, as a correlate of intentional transformations of interaction of consciousness with the world. Differentiation of communicative and compregensive experience produces the necessary grounds for the interpretation of culture as a mechanism of formation in the mind of the spatial and semantic perspective of perception and understanding of the world. Based on this disposition, we have the opportunity to distinguish between the universality of ways of "capturing" the world, or the metaphysical plan of culture, and its paradigm, or historical and social conditionality. In the dialectic of these dimensions there is a dynamic of the existence of a universal horizon of subjectivity.Key words: culture, subjectivity, intentionality, communicative experience, compregensive experience, reflection.

Hegelian Heritage and Anti-Racist Horizons

The task of confronting Hegel with the conflicts of our present proves to be indispensable to keep alive the critical scope of dialectics. In a context marked by a new wave of movements that challenge the racist structures that inform our societies, the question of the contribution of Hegelianism to an anti-racist thought takes a significant relevance.The hypothesis of this article argues that it is possible to distinguish two different operations that shape an anti-racist critique with the resources of Hegelian dialectical thought. The first one is constituted by the exegetical practice aiming to identify, within Hegel’s own discourse, a speculative core that allows the definitive overcoming of all ethno-racial particularisms through the postulation of a normative universal horizon. Such interpretative perspective, shared by numerous scholars, seeks the absorption of Hegel’s racist and Eurocentric assertions in the larger and global scope of his system. Once the limitation of this option is shown, we will examine an alternative operation, namely, the rewritings of the dialectical thought in certain philosophical reflections arising from the concreteness of anti-racist movements. To that extent, we will revisit the proposals of W.E.B Du Bois and Frantz Fanon as peripheral enunciations of the dialectic that enable a new understanding on the subjectivation processes and liberation horizons of racialized communities.

Matter accretion onto a conformal gravity black hole

The accretion of test fluids flowing onto a black hole is investigated. Particularly, by adopting a dynamical Hamiltonian approach, we are capable to find the critical points for various cases of black hole in conformal gravity. In these cases, we have analyzed the general solutions of accretion employing the isothermal equations of state. The steady state and spherically symmetric accretion of different test fluids onto the conformal gravity black hole has been considered. Further, we have classified these flows in the context of equations of state and the cases of conformal gravity black hole. The new behavior of polytropic fluid accretion is also discussed in all three cases of black hole. Black hole mass accretion rate is the most important part of this research in which we have investigated that the Schwarzschild black hole produce a typical signature than the conformal gravity black hole and Schwarzschild–de Sitter black hole. The critical fluid flow and the mass accretion rate have been presented graphically by the impact parameters beta , gamma , k and these parameters have great significance. Additionally, the maximum mass rate of accretion fall near the universal and Killing horizons and minimum rate of accretion occurs in between these regions. Finally, the results are compared with the different cases of black hole available in the literature.