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.
Orientability is an important topological property of spacetime manifolds. It is generally assumed that a test for spatial orientability requires a journey across the whole 3-space to check for orientation-reversing paths. Since such a global expedition is not feasible, theoretical arguments that combine universality of physical experiments with local arrow of time, CP violation and CPT invariance are offered to support the choosing of time- and space-orientable spacetime manifolds. We show that it is possible to access spatial orientability of Minkowski spacetime through local physical effect…
One important global topological property of a spacetime manifold is orientability. It is widely believed that spatial orientability can only be tested by global journeys around the Universe to check for orientation-reversing closed paths. Since such global journeys are not feasible, theoretical arguments that combine universality of physical experiments with local arrow of time, CP violation and CPT invariance are usually offered to support the choosing of time- and space-orientable spacetime manifolds. The nonexistence of globally defined spinor fields on a non-orientable spacetime is anothe…
Universal horizons in Hořava-Lifshitz gravity and Einstein-æther theory are the equivalent of causal horizons in general relativity and appear to have many of the same properties, including a first law of horizon thermodynamics and thermal radiation. Since universal horizons are infrared solutions of a putative power counting renormalizable quantum gravitational theory, fully understanding their thermodynamics will shed light on the interplay between black hole thermodynamics and quantum gravity. In this paper, we provide a complete classification, including asymptotic charges, of all four dim…
Violating Lorentz-invariance, and so implicitly permitting some form of superluminal communication, necessarily alters the notion of a black hole. Nevertheless, in both Einstein-Æther gravity, and Hořava-Lifshitz gravity, there is still a causally disconnected region in black-hole solutions; now being bounded by a "Universal horizon", which traps excitations of arbitrarily high velocities. To better understand the nature of these black holes, and their Universal horizons, we study ray trajectories in these spacetimes. We find evidence that Hawking radiation is associated with the Universal hor…
We show that the emergent near-horizon conformal symmetry of extremal black holes gives rise to universal behavior in perturbing fields, both near and far from the black hole horizon. The scale-invariance of the near-horizon region entails power law time-dependence with three universal features: (1) the decay off the horizon is always precisely twice as fast as the decay on the horizon; (2) the special rates of $1/t$ off the horizon and $1/\sqrt{v}$ on the horizon commonly occur; and (3) sufficiently high-order transverse derivatives grow on the horizon (Aretakis instability). The results are …
Modified gravity models such as Hořava-Lifshitz gravity or Einstein-æther theory violate local Lorentz invariance and therefore destroy the notion of a universal light cone. Despite this, in the infrared limit both models above possess static, spherically symmetric solutions with "universal horizons" - hypersurfaces that are causal boundaries between an interior region and asymptotic spatial infinity. In other words, there still exist black hole solutions. We construct a Smarr formula (the relationship between the total energy of the spacetime and the area of the horizon) for such a horizon in…
We consider universal properties that arise from a local geometric structure of a Killing horizon. We first introduce a non-perturbative definition of such a local geometric structure, which we call an asymptotic Killing horizon. It is shown that infinitely many asymptotic Killing horizons reside on a common null hypersurface, once there exists one asymptotic Killing horizon. The acceleration of the orbits of the vector that generates an asymptotic Killing horizon is then considered. We show that there exists the $\textit{diff}(S^1)$ or $\textit{diff}(R^1)$ sub-algebra on an asymptotic Killing…
Doubts have been expressed on the universality of holographic/string-inspired quantization rules for the horizon areas of stationary black holes or the products of their radii, already in simple 4-dimensional general relativity. Realistic black holes are not stationary but time-dependent. Using two examples of 4D general-relativistic spacetimes containing dynamical black holes for at least part of the time, it is shown that the quantization rules (even counting virtual horizons) cannot hold, except possibly at isolated instants of time, and do not seem to be universal.
Horava 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 Horava 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 a…
In this paper, we first show that the definition of the universal horizons studied recently in the khrononmetric theory of gravity can be straightforwardly generalized to other theories that violate the Lorentz symmetry, by simply considering the khronon as a probe field and playing the same role as a Killing vector field. As an application, we study static charged ($D+1$)-dimensional spacetimes in the framework of the healthy (non-projectable) Horava-Lifshitz (HL) gravity in the infrared limit, and find various solutions. Some of them represent Lifshitz space-times with hyperscaling violation…
Motion of a particle near a horizon of a spherically symmetric black hole is shown to possess a universal Lyapunov exponent of a chaos provided by its surface gravity. To probe the horizon, we introduce electromagnetic or scalar force to the particle so that it does not fall into the horizon. There appears an unstable maximum of the total potential where the evaluated maximal Lyapunov exponent is found to be independent of the external forces and the particle mass. The Lyapunov exponent is universally given by the surface gravity of the black hole. Unless there are other sources of a chaos, th…
In Hořava and Einstein-Æther theories of modified gravity, in spite of the violation of Lorentz invariance, spherically-symmetric stationary black hole solutions possess an inner universal horizon which separates field configurations into two disconnected classes. We compute the late time radiation emitted by a dispersive field propagating in such backgrounds. We fix the initial conditions on stationary modes by considering a regular collapsing geometry, and imposing that the state inside the infalling shell is vacuum. We find that the mode pasting across the shell is adiabatic at late time (l…
Holography grew out of black hole thermodynamics, which relies on the causal structure and general covariance of general relativity. In Einstein-æther theory, a generally covariant theory with a dynamical timelike unit vector, every solution breaks local Lorentz invariance, thereby grossly modifying the causal structure of gravity. However, there are still absolute causal boundaries, called "universal horizons", which are not Killing horizons yet obey a first law of black hole mechanics and must have an entropy if they do not violate a generalized second law. We couple a scalar field to the ti…
It may be a common understanding at present that, once event horizons are in thermal equilibrium, the entropy-area law holds inevitably. However, no rigorous verification is given to such a very strong universality of the law in multi-horizon spacetimes. In this article, based on thermodynamically consistent and rigorous discussion, we investigate thermodynamics of Schwarzschild-deSitter spacetime in which the temperatures of two horizons are different. We recognize that three independent state variables exist in thermodynamics of the horizons. One of the three variables represents the effect …
Lorentz-violating gravity theories with a preferred foliation can have instantaneous propagation. Nonetheless, it has been shown that black holes can still exist in such theories and the relevant notion of an event horizon has been dubbed `universal horizon'. In stationary spacetimes the universal horizon has to reside in a region of spacetime where the Killing vector associated with stationarity is spacelike. This raises the question of what happens to the universal horizon in the extremal limit, where no such region exists anymore. We use a decoupling limit approximation to study this proble…
We investigate thermodynamic behaviors of the $D$-dimensional gravity coupled to a dynamical unit timelike vector, the aether, present two kinds of exact charged solutions and study the linearized wave spectrum of this theory. There is an universal horizon behind the Killing horizon in these aether black holes. It is interesting that there exist $D$-dimensional Schwarzschild, Reissner-Nordström and charged Schwarzschild black holes but now with an universal horizon inside. We find that in the uncharged case for both kinds, or charged case but the charge $\bar Q\ll \bar r_0/2$ for the first kin…
We make use of the fact that the optical geometry near a static non-degenerate Killing horizon is asymptotically hyperbolic to investigate universal features of black hole physics. We show how the Gauss-Bonnet theorem allows certain lensing scenarios to be ruled in or out. We find rates for the loss of scalar, vector and fermionic `hair' as objects fall quasi- statically towards the horizon. In the process we find the Lienard-Wiechert potential for hyperbolic space and calculate the force between electrons mediated by neutrinos, extending the flat space result of Feinberg and Sucher. We use th…
We investigate highly damped quasinormal mode of single-horizon black holes motivated by its relation to the loop quantum gravity. Using the WKB approximation, we show that the real part of the frequency approaches the value $T_{\rm H}\ln 3$ for dilatonic black hole as conjectured by Medved et al. and Padmanabhan. It is surprising since the area specrtum of the black hole determined by the Bohr's correspondence principle completely agrees with that of Schwarzschild black hole for any values of the electromagnetic charge or the dilaton coupling. We discuss its generality for single-horizon blac…
We show by explicit computations that the product of all the horizon areas is independent of the mass, regardless of the topology of the horizons. The universal character of this relation holds for all known five dimensional asymptotically flat black rings, and for black strings. This gives further evidence for the crucial role that the thermodynamic properties at each horizon play in understanding the entropy at the microscopic level. To this end we propose a "first law" for the inner Cauchy horizons of black holes. The validity of this formula, which seems to be universal, was explicitly che…
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 {\em 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…
In this paper, we study the existence of universal horizons in a given static spacetime, and find that the test khronon field can be solved explicitly when its velocity becomes infinitely large, at which point the universal horizon coincides with the sound horizon of the khronon. Choosing the timelike coordinate aligned with the khronon, the static metric takes a simple form, from which it can be seen clearly that the metric is free of singularity at the Killing horizon, but becomes singular at the universal horizon. Applying such developed formulas to three well-known black hole solutions, th…
It is shown that a non-rotating macroscopic black hole with very large horizon area can remain in stable thermal equilibrium with Hawking radiation provided {\it its mass, as a function of horizon area, exceeds its microcanonical entropy, i.e., its entropy when isolated, without thermal radiation or accretion, and having a constant horizon area} (in appropriate units). The analysis does not use properties of specific classical spacetimes, but depends only on the plausible assumption that the mass is a function of the horizon area for large areas.
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 partic…
In relativistic gravity, requiring a spacetime hypersurface be a Killing horizon breaks the general covariance of general relativity. The residual algebra of horizon preserving diffeomorphisms can be extended to a Virasoro algebra near the horizon, the central charge of which yields the Bekenstein-Hawking entropy via the Cardy formula. This near horizon symmetry approach provides an argument for why black hole entropy computations in various quantum gravity models all agree. An exception may be Hořava-Lifshitz gravity, where causal horizons are not Killing horizons but rather universal horizon…
The paper deals with universal thermodynamics for FRW model of the universe bounded by apparent (or event) horizon. Assuming Hawking temperature on the horizon, the unified first law is examined on the horizon for different gravity theories. The results show that equilibrium configuration is preserved with a modification to Bekenstein entropy on the horizon.
In this paper, we first generalize the definition of stationary universal horizons to dynamical ones, and then show that (dynamical) universal horizons can be formed from realistic gravitational collapse. This is done by constructing analytical models of a collapsing spherically symmetric star with finite thickness in Einstein-aether theory.
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 Hořava gravity with an extra U(1) symmetry in (2+1)-dimensions, which, by construction, is power-counting renormalizable.
We derive universal properties of the near-horizon geometry of spherically symmetric black holes that follow from the observability of a regular apparent horizon. Only two types of solutions are admissible. After reviewing their properties we show that only a special form of the solutions of the second type is consistent. We describe how these results extend to modified theories of gravity, including Einstein--Cartan theories. Then we describe the unique black hole formation scenario that necessarily involves both types of solutions. The generalized surface gravity is infinite at the apparent …
It is shown that a massless scalar probe reveals a universal near-horizon conformal structure for a wide class of black holes, including the BTZ. The central charge of the corresponding Virasoro algebra contains information about the black hole. With a suitable quantization condition on the central charge, the CFT associated with the black hole in our approach is consistent with the recent observation of Witten, where the dual theory for the BTZ in the AdS/CFT framework has been identified with the construction of Frenkel, Lepowsky and Meurman. This CFT admits the Fischer-Griess monster group …
It seems to be a common understanding at present that, once event horizons are in thermal equilibrium, the entropy-area law holds inevitably. However no rigorous verification is given to such a very strong universality of the law in multi-horizon spacetimes. Then, based on thermodynamically consistent and rigorous discussion, this paper suggests an evidence of breakdown of entropy-area law for horizons in Schwarzschild-de Sitter spacetime, in which the temperatures of the horizons are different. The outline is as follows: We construct carefully "two thermal equilibrium systems" individually fo…
Universal thermodynamics for FRW model of the Universe bounded by apparent/event horizon has been considered for massive gravity theory. Assuming Hawking temperature and using the unified first law of thermodynamics on the horizon, modified entropy on the horizon has been determined. For simple perfect fluid with constant equation of state, generalized second law of thermodynamics and thermodynamical equilibrium have been examined on both the horizons.
In Lorentz violating theories of gravitation with a preferred foliation a notion of black hole is still possible, despite the presence of infinitely fast propagating modes. Such event horizons are known as universal horizons. Their discovery poses the question of whether they satisfy mechanical laws, analogous to the ones of Killing horizons in Lorentz symmetric theories, and whether they admit a thermodynamical interpretation. In this paper we study the viability of the first law for several exact universal horizon solutions previously derived in the literature. Our results show that a simple…
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.
This thesis explores two avenues into understanding the physics of black holes and horizons beyond general relativity, via analogue models and Lorentz violating theories. Analogue spacetimes have wildly different dynamics to general relativity; this allows the possibility of non-Killing horizons in stationary solutions. In the case of non-Killing horizons different definitions of surface gravity are truly different quantities. This also has application to modified theories of gravity, where there is no reason to expect all horizons to be Killing horizons. In Lorentz violating theories, the sit…
We prove that for sub-extremal axisymmetric and stationary black holes with arbitrary surrounding matter the inequality $8π|J|<A$ holds, where $J$ is the angular momentum and $A$ the horizon area of the black hole.
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…
The theories of gravity which violate local Lorentz invariance do not admit a universal maximum speed of signal-propagation. Different field excitations see a different effective metric and hence a different light cone. In these theories, although one can define the Killing horizon in a conventional way, this definition does not capture the notion of a black hole. This is so because there exist modes which see a wider light cone than the one defined by the Killing Horizon and therefore can escape to infinity. However, there exist solutions of these theories which admit a special spacelike hype…
The entropy for two-dimensional black holes is obtained through the entropy function with the condition that the geometry approaches an $AdS_2$ spacetime in the near horizon limit. It is shown that the entropy is universal and proportional to the value of the dilaton field at the event horizon as expected. We find this universal behavior holds even after the inclusion of higher derivative terms, only modifying the proportional constant. More specifically, a variety of models of the dilaton gravity in two dimensions are considered, in which it is shown that the universal entropy coincides with …
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…
We show that, in a gravitational theory [in any number of dimensions greater than 3] which admits BPS branes and AdS-Reissner-Nordstrom black holes with flat event horizons, the specific [dimensionless] temperature of such a black hole is bounded below by approximately 0.156875. This confirms the recent suggestion by Hartnoll and Tavanfar, to the effect that no such black hole can be arbitrarily cold, since from the AdS/CFT dual point of view the low-temperature degrees of freedom should not be concealed by the equivalent of an event horizon.
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 d…
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, $κ_{UH}=2(z-1)κ_{uh}/z$, where $…
Using the solution phase space method, we investigate the thermodynamics of black holes in Einstein-aether-Maxwell theory, for which the traditional Wald method (covariant phase space method) fails. We show the first laws of thermodynamics and definitive entropy expressions at both Killing and universal horizons for some examples of exact black hole solutions, including 3-dimensional static charged quasi-BTZ black hole, two 4-dimensional static charged black holes and 3-dimensional rotating solution. At Killing horizons the entropies are exactly one quarter of the horizon area, but at universa…
We numerically study the gravitational collapse of a massless scalar field with spherical symmetry in Einstein-aether theory, and show that apparent, spin-0 and dynamical universal horizons (dUHs) can be all formed. The spacetime and the aether field are well-behaved and regular, including regions nearby these horizons (but away from the center of spherical symmetry). The spacetime outside the apparent and spin-0 horizons settles down to a static configuration, and some of such resulting static black holes were already found numerically in the literature. On the other hand, the proper distance…
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 fie…
Motivations for the existence of a fundamental preferred frame range from pure phenomenology to attempts to solve the non-renormalizability of quantum gravity, the problem of time (and scale), and the cosmological constant problem(s). In many explicit constructions, such as Einstein-Aether or Gravitational Aether theories, K-essence, Cuscuton theory, Shape Dynamics, or (non-projectable) Horava-Lifshitz gravity, the low energy theory contains a fluid (which defines a preferred frame) with superluminal or incompressible excitations. We study here the formation of black holes in the presence of s…
It is proposed by Cvetic et al [Phys. Rev. Lett. 106 (2011) 121301] that the product of all horizon areas for general rotating multi-change black holes has universal expressions independent of the mass. When we consider the product of all horizon entropies, however, the mass will be present in some cases, while another new universal property [JHEP 1401 (2014) 031] is preserved, which is more general and says that the sum of all horizon entropies depends only on the coupling constants of the theory and the topology of the black hole. The property has been studied in limited dimensions and the g…
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. Horava 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 as…
A study of Universal thermodynamics is done in Lanczos-Lovelock gravity. The Universe is chosen as FRW model bounded by apparent or event horizon. The unified first law is examined, assuming extended Hawking temperature on the horizon. As a result there is a modification of Bekenstein entropy on the horizons. Further the validity of generalized second law of thermodynamics and thermodynamical equilibrium are also investigated for perfect fluid (with constant equation of state), modified chaplygin gas model and holographic dark energy model.
A study of Universal thermodynamics is done in the frame work of RSII brane model and DGP brane scenario. The Universe is chosen as FRW model bounded by apparent or event horizon. Assuming extended Hawking temperature on the horizon, the unified first law is examined for perfect fluid (with constant equation of state) and modified Chaplygin gas model. As a result there is a modification of Bekenstein entropy on the horizons. Further the validity of the generalized second law of thermodynamics and thermodynamical equilibrium are also investigated.
The present work deals with a detailed study of universal thermodynamics in different modified gravity theories. The validity of the generalized second law of thermodynamics (GSLT) and thermodynamical equilibrium (TE) of the Universe bounded by a horizon (apparent/event) in f(R)-gravity, Einstein-Gauss-Bonnet gravity, RS-II brane scenario and DGP brane model has been investigated. In the perspective of recent observational evidences, the matter in the Universe is chosen as interacting holographic dark energy model. The entropy on the horizons are evaluated from the validity of the unified firs…
In this paper, we study the non-projectable 2d Hořava gravity coupled with a non-relativistic scalar field, where the coupling is in general non-minimal and of the form $f(ϕ)R$, where $f(ϕ)$ is an arbitrary function of the scalar field $ϕ$, and $R$ denotes the 2d Ricci scalar. In particular, we first investigate the Hamiltonian structure, and show that there are two-first and two-second class constraints, similar to the pure gravity case, but now the local degree of freedom is one, due to the presence of the scalar field. Then, we present various exact stationary solutions of this coupled syst…
