We study the properties of fundamental physical constants using the threefold classification of dimensional constants proposed by J.-M. L{é}vy-Leblond: constants of objects (masses, etc.), constants of phenomena (coupling constants), and "universal constants" (such as $c$ and $\hbar$). We show that all of the known "natural" systems of units contain at least one non-universal constant. We discuss the possible consequences of such non-universality, e.g., the dependence of some of these systems on the number of spatial dimensions. In the search for a "fully universal" system of units, we propose a set of constants that consists of $c$, $\hbar$, and a length parameter and discuss its origins and the connection to the possible kinematic groups discovered by L{é}vy-Leblond and Bacry. Finally, we give some comments about the interpretation of these constants.
Universal spacetimes are exact solutions to all higher-order theories of gravity. We study these spacetimes in four dimensions and provide necessary and sufficient conditions for universality for all Petrov types except of type II. We show that all universal spacetimes in four dimensions are algebraically special and Kundt. Petrov type D universal spacetimes are necessarily direct products of two 2-spaces of constant and equal curvature. Furthermore, type II universal spacetimes necessarily possess a null recurrent direction and they admit the above type D direct product metrics as a limit. Su…
Universal spacetimes are spacetimes for which all conserved symmetric rank-2 tensors, constructed as contractions of polynomials from the metric, the Riemann tensor and its covariant derivatives of arbitrary order, are multiples of the metric. Consequently, metrics of universal spacetimes solve vacuum equations of all gravitational theories with Lagrangian being a polynomial curvature invariant constructed from the metric, the Riemann tensor and its derivatives of arbitrary order. In the literature, universal metrics are also discussed as metrics with vanishing quantum corrections and as class…
We study almost universal spacetimes - spacetimes for which the field equations of any generalized gravity with the Lagrangian constructed from the metric, the Riemann tensor and its covariant derivatives of arbitrary order reduce to one single differential equation and one algebraic condition for the Ricci scalar. We prove that all d-dimensional Kundt spacetimes of Weyl type III and traceless Ricci type N are almost universal. Explicit examples of Weyl type II almost universal Kundt metrics are also given. The considerable simplification of the field equations of higher-order gravity theories…
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.
A perturbative method to compute the total travel time of both null and lightlike rays in arbitrary static spherically symmetric spacetimes in the weak field limit is proposed. The resultant total time takes a quasi-series form of the impact parameter. The coefficient of this series at a certain order $n$ is shown to be determined by the asymptotic expansion of the metric functions to the order $n+1$. To the leading order(s), the time delay, as well as the difference between the time delays of two kinds of relativistic signals, is then shown to take a universal form for all SSS spacetimes. Thi…
The Kerr spacetime is perhaps the most astrophysically important of the currently known exact solutions to the Einstein field equations. Whenever spacetimes can be put in unit-lapse form it becomes possible to identify some very straightforward timelike geodesics, (the "rain" geodesics), making the physical interpretation of these spacetimes particularly clean and elegant. The most well-known of these unit-lapse formulations is the Painleve-Gullstrand form of the Schwarzschild spacetime, though there is also a Painleve-Gullstrand form of the Lense-Thirring (slow rotation) spacetime. More radic…
We study type II universal metrics of the Lorentzian signature. These metrics simultaneously solve vacuum field equations of all theories of gravitation with the Lagrangian being a polynomial curvature invariant constructed from the metric, the Riemann tensor and its covariant derivatives of an arbitrary order. We provide examples of type II universal metrics for all composite number dimensions. On the other hand, we have no examples for prime number dimensions and we prove the non-existence of type II universal spacetimes in five dimensions. We also present type II vacuum solutions of selecte…
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…
Every spacetime is defined by its metric, the mathematical object which further defines the spacetime curvature. From the relativity principle, we have the freedom to choose which coordinate system to write our metric in. Some coordinate systems, however, are better than others. In this text, we begin with a brief introduction into general relativity, Einstein's masterpiece theory of gravity. We then discuss some physically interesting spacetimes and the coordinate systems that the metrics of these spacetimes can be expressed in. More specifically, we discuss the existence of the rather useful…
Causal set non-local wave operators allow both for the definition of an action for Causal set theory and the study of deviations from local physics that may have interesting phenomenological consequences. It was previously shown that, in all dimensions, the (unique) minimal discrete operators give averaged continuum non-local operators that reduce to $\Box-R/2$ in the local limit. Recently, dropping the constraint of minimality, it was shown that there exist an infinite number of discrete operators satisfying basic physical requirements and with the right local limit in flat spacetime. In this…
We construct a generalized Smarr formula which could provide a thermodynamic route to derive the covariant field equation of general theories of gravity in dynamic spacetimes. Combining some thermodynamic variables and a new chemical potential conjugated to the number of degree of freedom on the holographic screen, we find a universal Cardy-Verlinde formula and give its braneworld interpretation. We demonstrate that the associated AdS-Bekenstein bound is tighten than the previous expression for multi-charge black holes in the gauged supergravities. The Cardy-Verlinde formula and the AdS-Bekens…
We calculate Sorkin's spacetime entanglement entropy of a Gaussian scalar field for complementary regions in the 2d cylinder spacetime and show that it has the Calabrese-Cardy form. We find that the cut-off dependent term is universal when we use a covariant UV cut-off. In addition, we show that the relative size-dependent term exhibits complementarity. Its coefficient is however not universal and depends on the choice of pure state. It asymptotes to the universal form within a natural class of pure states.
Light rings (LRs) play an important role in gravitational wave observations and black hole photographs. In this paper, we investigate general features of LRs in stationary, axisymmetric, asymptotically flat spacetimes with or without horizons. For a nonextremal black hole, we show explicitly that there always exist at least two LRs propagating in opposite directions, where the outermost one is radially unstable. For an extremal black hole, we show that there exists at least one retrograde LR. We find that there is at least one LR which is angularly stable. The stability analysis does not invol…
Spacetime must be foliable by spacelike surfaces for the quantum mechanics of matter fields to be formulated in terms of a unitarily evolving state vector defined on spacelike surfaces. When a spacetime cannot be foliated by spacelike surfaces, as in the case of spacetimes with closed timelike curves, a more general formulation of quantum mechanics is required. In such generalizations the transition matrix between alternatives in regions of spacetime where states {\it can} be defined may be non-unitary. This paper describes a generalized quantum mechanics whose probabilities consistently obey …
We analyse the extent of possible computations following Hogarth in Malament-Hogarth (MH) spacetimes, and Etesi and Németi in the special subclass containing rotating Kerr black holes. Hogarth had shown that any arithmetic statement could be resolved in a suitable MH spacetime. Etesi and Nemeti had shown that some \forall \exists relations on natural numbers which are neither universal nor co-universal, can be decided in Kerr spacetimes, and had asked specifically as to the extent of computational limits there. The purpose of this note is to address this question, and further show that MH spac…
We present a new ``universal property'' of entropy, that is the ``entropy sum'' relation of black holes in four dimensional (anti-)de-Sitter asymptotical background. They depend only on the cosmological constant with the necessary effect of the un-physical ``virtual'' horizon included in the spacetime where only the cosmological constant, mass of black hole, rotation parameter and Maxwell field exist. When there is more extra matter field in the spacetime, one will find the ``entropy sum'' is also dependent of the strength of these extra matter field. For both cases, we conclude that the ``ent…
In this paper, the following two propositions are proven under the dominant energy condition for the matter field in the higher-dimensional spherically symmetric spacetime in Einstein-Gauss-Bonnet gravity in the presence of a cosmological constant $Λ$. First, for $Λ\le 0$ and $α\ge 0$ without a fine-tuning to give a unique anti-de Sitter vacuum, where $α$ is the Gauss-Bonnet coupling constant, vanishing generalized Misner-Sharp mass is equivalent to the maximally symmetric spacetime. Under the fine-tuning, it is equivalent to the vacuum class I spacetime. Second, under the fine-tuning with $α>…
Free-fall is only approximately universal in general relativity. Different extended bodies can fall in different ways, depending on their internal dynamics. Nevertheless, certain aspects of their motion are universal. This paper examines the universal constraints on extended-body motion in vacuum type D spacetimes. Working in the quadrupole approximation, we show that in addition to the (previously-known) constraints imposed by Killing vectors, two components of the gravitational torque must vanish. Furthermore, of the ten components of a body's quadrupole moment, four are found to be irreleva…
We study universal electromagnetic (test) fields, i.e., p-forms fields F that solve simultaneously (virtually) any generalized electrodynamics (containing arbitrary powers and derivatives of F in the field equations) in n spacetime dimensions. One of the main results is a sufficient condition: any null F that solves Maxwell's equations in a Kundt spacetime of aligned Weyl and traceless-Ricci type III is universal (in particular thus providing examples of p-form Galileons on curved Kundt backgrounds). In addition, a few examples in Kundt spacetimes of Weyl type II are presented. Some necessary …
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 explicitly confirm the expectation that generic Lovelock gravity in D dimensions has a unitary massless spin-2 excitation around any one of its constant curvature vacua just like the cosmological Einstein gravity. The propagator of the theory reduces to that of Einstein's gravity, but scattering amplitudes must be computed with an effective Newton's constant which we provide. Tree-level unitarity imposes a single constraint on the parameters of the theory yielding a wide range of unitary region. As an example, we explicitly work out the details of the cubic Lovelock theory.
It has been long known that in spacetimes with a positive cosmological constant $Λ>0$ the area of spatially stable marginally trapped surfaces (MTSs) has a finite upper bound given by $4π/Λ$. In this paper I show that any such spacetime containing spatially stable MTSs with area approaching indefinitely that bound acquire universal properties generically. Specifically, they all possess {\em generalized} `holographic screens' (i.e. marginally trapped tubes) foliated by MTSs of spherical topology, composed of a dynamical horizon portion and a timelike membrane portion that meet at a distinguishe…
If universal quantum interaction is really connected with the coset structure of deformations of quantum states then the curvature of projective Hilbert state space should be observable. I discuss some approach to the measurement of curvature-dependent values.
In general relativity the parallel transfer of a vector around a closed curve in spacetime, or along two curves which together form a closed loop, usually results in a nonzero deficit angle between the vector's initial and final positions. We show that such holonomy in the McVittie spacetime, which represents a gravitating object imbedded in an expanding universe, can in principle be used to directly detect the expansion of the universe, for example by measuring changes in the components of a gyroscopic spin axis. Although such changes are of course small, they are large enough (\D S \sim 10^{…
In this paper, we present all $[(d+1)+1]$-dimensional static diagonal vacuum solutions of the non-projectable Hořava-Lifshitz gravity in the IR limit, and show that they give rise to very rich Lifshitz-type structures, depending on the choice of the free parameters of the solutions. These include the Lifshitz spacetimes with or without hyperscaling violation, Lifshitz solitons, and black holes. Remarkably, even the theory breaks explicitly the Lorentz symmetry and allows generically instantaneous propagations, universal horizons still exist, which serve as one-way membranes for signals with an…
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…
Recently, a coherent picture of the quantum mechanics of an evaporating black hole has been presented which reconciles unitarity with the predictions of the equivalence principle. The thermal nature of a black hole as viewed in a distant reference frame arises from entanglement between the hard and soft modes, generated by the chaotic dynamics at the string scale. In this paper, we elaborate on this picture, particularly emphasizing the importance of the chaotic nature of the string (UV) dynamics across all low energy species in generating large (IR) spacetime behind the horizon. Implications …
In this paper, we have studied the thermodynamics of Gauss-Bonnet black holes in D-dimensional $AdS$ spacetime. Here, the cosmological constant ($Λ$), Newton's gravitational constant ($G$) and the Gauss-Bonnet parameter ($α$) are varied in the bulk, and a mixed first law is rewritten considering central charge ($C$) (of dual boundary conformal theory) and its conjugate variable utilising the gauge-gravity duality. A novel universal nature of central charge near the critical point of black hole phase transition in Einstein's gravity has been observed in \cite{mann1}. We observe that this univer…
It is well known that 4-dimensional Kerr-NUT-AdS spacetime possesses the hidden symmetry associated with the Killing-Yano tensor. This tensor is "universal" in the sense that there exist coordinates where it does not depend on any of the free parameters of the metric. Recently the general higher dimensional Kerr-NUT-AdS solutions of the Einstein equations were obtained. We demonstrate that all these metrics with arbitrary rotation and NUT parameters admit a universal Killing-Yano tensor. We give an explicit presentation of the Killing-Yano and Killing tensors and briefly discuss their properti…
We investigated the light propagation by means of the Robertson-McVittie solution which is considered to be the spacetime around the gravitating body embedded in the FLRW (Friedmann-Lema{î}tre-Robertson-Walker) background metric. We concentrated on the time delay and derived the correction terms with respect to the Shapiro's formula. To relate with the actual observation and its reduction process, we also took account of the time transformations; coordinate time to proper one, and conversely, proper time to coordinate one. We applied these results to the problem of increase of astronomical uni…
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 s…
Using $\star$-calculus on the dual of the Borchers-Uhlmann algebra endowed with a combinatorial co-product, we develop a method to calculate a unitary transformation relating the GNS representations of a non-quasifree and a quasifree state of the free hermitian scalar field. The motivation for such an analysis and a further result is the fact that a unitary transformation of this kind arises naturally in scattering theory on non-stationary backgrounds. Indeed, employing the perturbation theory of the Yang-Feldman equations with a free CCR field in a quasifree state as an initial condition and …
Ideal rods and clocks are defined as an infinitesimal symmetry of the spacetime. Since no a priori geometric structure is considered, all the possible models of spacetime are obtained.
We study exact solutions of the infinite derivative gravity with null radiation which belong to the class of almost universal Weyl type III/N Kundt spacetimes. This class is defined by the property that all rank-2 tensors ${B_{ab}}$ constructed from the Riemann tensor and its covariant derivatives have traceless part of type N of the form $\mathcal{B}(\square)S_{ab}$ and the trace part constantly proportional to the metric. Here, $\mathcal{B}(\square)$ is an analytic operator and $S_{ab}$ is the traceless Ricci tensor. We show that the convoluted field equations reduce to a single non-local bu…
A special class of metrics, called universal metrics, solve all gravity theories defined by covariant field equations purely based on the metric tensor. Since we currently lack the knowledge of what the full of quantum-corrected field equations of gravity are at a given microscopic length scale, these metrics are particularly important in understanding quantum fields in curved backgrounds in a consistent way. But, finding explicit universal metrics has been a hard problem as there does not seem to be a procedure for it. In this work, we overcome this difficulty and give a construction of unive…
We describe what can be called the "universal" phase space of AdS3 gravity, in which the moduli spaces of globally hyperbolic AdS spacetimes with compact spatial sections, as well as the moduli spaces of multi-black-hole spacetimes are realized as submanifolds. The universal phase space is parametrized by two copies of the Universal Teichmüller space T(1) and is obtained from the correspondence between maximal surfaces in AdS3 and quasisymmetric homeomorphisms of the unit circle. We also relate our parametrization to the Chern-Simons formulation of 2+1 gravity and, infinitesimally, to the holo…
Modern advances in transformation optics and electromagnetic metamaterials made possible experimental demonstrations of highly unusual curvilinear optical spaces, such as various geometries necessary for electromagnetic cloaking. Recently we demonstrated that mapping light intensity in a hyperbolic metamaterial may also model the flow of time in an effective (2+1) dimensional Minkowski spacetime. Curving such an effective spacetime creates experimental model of a toy big bang. Here we demonstrate that at low light levels this model may be used to emulate a fully covariant version of quantum me…
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…
Within quantum-gravity approaches and beyond, different mechanisms for singularity resolution in black holes exist. Under a set of assumptions that we spell out in detail, these mechanisms leave their imprint in shadow images of spherically symmetric black holes. We find that even current EHT accuracy is sufficient to place nontrivial constraints on the scale of new physics within one modified spacetime, if the EHT measurement of M87* is combined with an independent measurement of the black-hole mass. In other spacetimes, increased accuracy is required that the next-generation EHT may deliver.…
One parameter quantization ambiguity is existed in Loop quantum gravity which is called the Immirzi parameter. In this paper, we fix this free paremater by considering the quasinormal mode spectrum of black holes in four and higher spacetime dimensions. As a consequence, our result consistents with Bekenstein-Hawking entropy of a black hole. Moreover, we also give a possible quantum gravity explanation of the universal $\ln(3)$ behavior of the quasinormal mode spectrum.
A free hermitian conformal field theory is considered in Minkowski, de Sitter and anti-de Sitter spacetimes. The first part of the paper studies spacetime inversion and conformal inversion, wherein their role in the field quantization is elucidated in those spaces. The second part of the paper is concerned with the non-unitary evolution of detector's state. Several examples of such processes are provided with a clarification of how the unitarity is preserved with still having well-known thermal effects.
Robertson-Walker and Generalized Robertson-Walker spacetimes may be characterized by the existence of a time-like unit torse-forming vector field, with other constrains. We show that Twisted manifolds may still be characterized by the existence of such (unique) vector field, with no other constrain. Twisted manifolds generalize RW and GRW spacetimes by admitting a scale function that depends both on time and space. We obtain the Ricci tensor, corresponding to the stress-energy tensor of an imperfect fluid.
A set of simple rules for constructing the maximal (e.g. analytic) extensions for any metric with a Killing field in an (effectively) two-dimensional spacetime is formulated. The application of these rules is extremely straightforward, as is demonstrated at various examples and illustrated with numerous figures. Despite the resulting simplicity we also comment on some subtleties concerning the concept of Penrose diagrams. Most noteworthy among these, maybe, is that (smooth) spacetimes which have both degenerate and non-degenerate (Killing) horizons do not allow for globally smooth Penrose diag…
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…
We present evidence that the universal Kovtun-Son-Starinets shear viscosity to entropy density ratio of 1/4πcan be associated with a Rindler causal horizon in flat spacetime. Since there is no known holographic (gauge/gravity) duality for this spacetime, a natural microscopic explanation for this viscosity is in the peculiar properties of quantum entanglement. In particular, it is well-known that the Minkowski vacuum state is a thermal state and carries an area entanglement entropy density in the Rindler spacetime. Based on the fluctuation-dissipation theorem, we expect a similar notion of vis…
The strong cosmic censorship conjecture, introduced by Penrose five decades ago, asserts that, in self-consistent theories of gravity, Cauchy horizons inside dynamically formed black holes should be unstable to remnant perturbation fields that fall into the newly born black holes. The question of the (in)validity of this intriguing conjecture in non-asymptotically flat charged black-hole spacetimes has recently attracted much attention from physicists and mathematicians. We here provide a general proof, which is based on Bekenstein's generalized second law of thermodynamics, for the validity o…
By following the general guiding principle that nothing should be prescribed or imposed on the universal entity, spacetime, we establish that it is the homogeneity (by which we mean homogeneity and isotropy of space and homogeneity of time) that requires not only a universally constant invariant velocity but also an invariant length given by its constant curvature, $Λ$ and spacetime is completely free of dynamics. Thus $c$ and $Λ$ are the only two true constants of the spacetime structure and no other physical constant could claim this degree of fundamentalness. When matter is introduced, the …
We attempt to calculate the gravitational time delay in a time-dependent gravitational field, especially in McVittie spacetime, which can be considered as the spacetime around a gravitating body such as the Sun, embedded in the FLRW (Friedmann-Lemaître-Robertson-Walker) cosmological background metric. To this end, we adopt the time transfer function method proposed by Le Poncin-Lafitte {\it et al.} (Class. Quant. Grav. 21:4463, 2004) and Teyssandier and Le Poncin-Lafitte (Class. Quant. Grav. 25:145020, 2008), which is originally related to Synge's world function $Ω(x_A, x_B)$ and enables to ci…
It is widely known that the primordial curvature perturbation $ζ$ has several universal properties in the infrared (IR) such as the soft theorem, which is also known as the consistency relation, and the conservation in time. They are valid in rather general single clock models of inflation. It has been argued that these universal properties are deeply related to the large gauge transformations in inflationary spacetime. However, the invariance under the large gauge transformations is not sufficient to show these IR properties. In this paper, we show that the locality condition is crucial to sh…
