Region Of Spacetime Research Articles

Particle motion near high-spin black holes

General relativity predicts that the Kerr black hole develops qualitatively new and surprising features in the limit of maximal spin. Most strikingly, the region of spacetime near the event horizon stretches into an infinitely long throat and displays an emergent conformal symmetry. Understanding dynamics in this NHEK (near-horizon extreme Kerr) geometry is necessary for connecting theory to upcoming astronomical observations of high-spin black holes. We review essential properties of NHEK and its relationship to the rapidly rotating Kerr black hole. We then completely solve the geodesic equation in the NHEK region and describe how the resulting trajectories transform under the action of its enhanced symmetries. In the process, we derive explicit expressions for the angular integrals appearing in the Kerr geodesic equation and obtain a useful formula, valid at arbitrary spin, for a particle’s polar angle in terms of its radial motion. These results will aid in the analytic computation of astrophysical observables relevant to ongoing and future experiments.

Opacity and effective field theory in anti–de Sitter backgrounds

We consider quantum field theory in a five-dimensional anti-de Sitter background, possibly truncated by four-dimensional (4D) branes. In the Euclidian version of this space, it is known that propagators exponentially decay when they go far enough toward the Poincar\'e horizon, i.e. deep enough into the IR region of the AdS bulk. In this note, we show that an analogous property exists in Lorentzian AdS. The exponential suppression is found to occur in the presence of bulk interactions dressing the AdS propagators. We calculate one-loop gravitational dressing and find that the suppression effect comes from the scalar component of the 5D graviton. We then argue that, at least at strong coupling, this exponential decay censors the region of spacetime where the 5D effective field theory would become invalid. As an application we estimate the rate for the cascade decay of bulk fields---which are known to produce soft spherical events with high multiplicity---and find this rate to be exponentially suppressed.

Reversible time travel with freedom of choice

General relativity allows for the existence of closed time-like curves, along which a material object could travel back in time and interact with its past self. This possibility raises the question whether certain initial conditions, or more generally local operations, lead to inconsistencies and should thus be forbidden. Here we consider the most general deterministic dynamics connecting classical degrees of freedom defined on a set of bounded space-time regions, requiring that it is compatible with arbitrary operations performed in the local regions. We find that any such dynamics can be realised through reversible interactions. We further find that consistency with local operations is compatible with non-trivial time travel: three parties can interact in such a way to be all both in the future and in the past of each other, while being free to perform arbitrary local operations.

Entropy and Gravitation—From Black Hole Computers to Dark Energy and Dark Matter

We show that the concept of entropy and the dynamics of gravitation provide the linchpin in a unified scheme to understand the physics of black hole computers, spacetime foam, dark energy, dark matter and the phenomenon of turbulence. We use three different methods to estimate the foaminess of spacetime, which, in turn, provides a back-door way to derive the Bekenstein-Hawking formula for black hole entropy and the holographic principle. Generalizing the discussion for a static spacetime region to the cosmos, we find a component of dark energy (resembling an effective positive cosmological constant of the correct magnitude) in the current epoch of the universe. The conjunction of entropy and gravitation is shown to give rise to a phenomenological model of dark matter, revealing the natural emergence, in galactic and cluster dynamics, of a critical acceleration parameter related to the cosmological constant; the resulting mass profiles are consistent with observations. Unlike ordinary matter, the quanta of the dark sector are shown to obey infinite statistics. This property of dark matter may lead to some non-particle phenomenology and may explain why dark matter particles have not been detected in dark matter search experiments. We also show that there are deep similarities between the problem of “quantum gravity” (more specifically, the holographic spacetime foam) and turbulence.

Localizing and excluding quantum information; or, how to share a quantum secret in spacetime

When can quantum information be localized to each of a collection of spacetime regions, while also excluded from another collection of regions? We answer this question by defining and analyzing the localize-exclude task, in which a quantum system must be localized to a collection of authorized regions while also being excluded from a set of unauthorized regions. This task is a spacetime analogue of quantum secret sharing, with authorized and unauthorized regions replacing authorized and unauthorized sets of parties. Our analysis yields the first quantum secret sharing scheme for arbitrary access structures for which the number of qubits required scales polynomially with the number of authorized sets. We also study a second related task called state-assembly, in which shares of a quantum system are requested at sets of spacetime points. We fully characterize the conditions under which both the localize-exclude and state-assembly tasks can be achieved, and give explicit protocols. Finally, we propose a cryptographic application of these tasks which we call party-independent transfer.

A measure for quantum paths, gravity and spacetime microstructure

The number of classical paths of a given length, connecting any two events in a (pseudo) Riemannian spacetime is, of course, infinite. It is, however, possible to define a useful, finite, measure [Formula: see text] for the effective number of quantum paths [of length [Formula: see text] connecting two events [Formula: see text]] in an arbitrary spacetime. When [Formula: see text], this reduces to [Formula: see text] giving the measure for closed quantum loops of length [Formula: see text] containing an event [Formula: see text]. Both [Formula: see text] and [Formula: see text] are well-defined and depend only on the geometry of the spacetime. Various other physical quantities like, for e.g. the effective Lagrangian, can be expressed in terms of [Formula: see text]. The corresponding measure for the total path length contributed by the closed loops, in a spacetime region [Formula: see text], is given by the integral of [Formula: see text] over [Formula: see text]. Remarkably enough [Formula: see text], the Ricci scalar; i.e. the measure for the total length contributed by infinitesimal closed loops in a region of spacetime gives us the Einstein–Hilbert action. Its variation, when we vary the metric, can provide a new route towards induced/emergent gravity descriptions. In the presence of a background electromagnetic field, the corresponding expressions for [Formula: see text] and [Formula: see text] can be related to the holonomies of the field. The measure [Formula: see text] can also be used to evaluate a wide class of path integrals for which the action and the measure are arbitrary functions of the path length. As an example, I compute a modified path integral which incorporates the zero-point-length in the spacetime. I also describe several other properties of [Formula: see text] and outline a few simple applications.

Propagation and heterogeneous steady states in a delayed nonlocal R-D equation without spatial translation-invariance

We consider a delayed reaction-diffusion equation that models the population dynamics of a single species with the mature population living in the 1-D whole space R while the immature population only living in the half space R+, with homogeneous Dirichlet condition for the immatures at the boundary point. One of the important features of this model system is that it does have the translational-invariance. By linking the non-translational-invariant solution map for this equation to travelling wave maps for another related 1-D spatial homogeneous delay reaction-diffusion equation, we obtain some traveling-like a priori estimates for nontrivial solutions. We then establish the existence, uniqueness, and attractivity of heterogeneous steady states. As a result, we are able to describe the traveling-like asymptotic behaviours of nontrivial solutions in space-time region. These enable us to develop a new method for exploring the spreading speeds and asymptotic propagation phenomena for a class of non-translation-invariant delay reaction-diffusion equations on R. As a corollary, we also recover some results on the asymptotic spreading speeds and traveling waves for monostable and spatial homogeneous delay reaction-diffusion equations in R.

Particle and energy cost of entanglement of Hawking radiation with the final vacuum state

A semiclassical analysis shows that in the process of black hole formation and evaporation, an initial pure state will evolve to a mixed state, i.e., information will be lost. One way of avoiding this conclusion without invoking drastic modifications of the local laws of physics in a low curvature regime would be for the information to be restored at the very end of the evaporation process. It is normally envisioned that this would require a final burst of particles entangled with the early time Hawking radiation. This would imply the emission of an extremely large number of particles from an object of Planck size and mass and would appear to be blatantly ruled out by energy considerations. However, Hotta, Schutzhold, and Unruh have analyzed a $(1+1)$-dimensional moving mirror analog of the Hawking process and have found that, in this model, information is restored via entanglement of the early time Hawking radiation with vacuum fluctuations in the spacetime region to the future of the event where the mirror returns to inertial motion. We analyze their model here and give a precise formulation of this entanglement by introducing the notion of "Milne particles." We then analyze the inertial particle and energy cost of such an entanglement of Hawking radiation with vacuum fluctuations. We show that that, in fact, the entanglement of early time Hawking radiation with vacuum fluctuations requires the emission of at least as many late time inertial particles as Hawking particles. Although the energy cost can be made small in the $(1+1)$-dimensional mirror system, this should not be the case for the $(3+1)$-dimensional evaporating black hole system. Thus, vacuum entanglement has the same difficulties as the more usual burst scenarios for attempting to avoid information loss.

Inhomogeneous cosmology in an anisotropic Universe

This thesis presents computer simulations of the formation of super-structures in the Universe by solving the equations of Einstein’s theory of gravity: General Relativity. This differs from the usual approach which uses Newton’s law of gravity. We find that different regions of spacetime expand at different rates, but the effect is not sufficient to explain the measured accelerating expansion of the Universe, currently attributed to dark energy. Local differences are also not sufficient to explain the recently measured discrepancy between small-scale and large-scale expansion rates of the Universe. However, they could affect our observations as our instruments become more precise.

The Vacuum as a Lagrangian subspace

We unify and generalize the notions of vacuum and amplitude in linear quantum field theory in curved spacetime. Crucially, the generalized notion admits a localization in spacetime regions and on hypersurfaces. The underlying concept is that of a Lagrangian subspace of the space of complexified germs of solutions of the equations of motion on hypersurfaces. Traditional vacua and traditional amplitudes correspond to the special cases of definite and real Lagrangian subspaces respectively. Further, we introduce both infinitesimal and asymptotic methods for vacuum selection that involve a localized version of Wick rotation. We provide examples from Klein-Gordon theory in settings involving different types of regions and hypersurfaces to showcase generalized vacua and the application of the proposed vacuum selection methods. A recurrent theme is the occurrence of mixed vacua, where propagating solutions yield definite Lagrangian subspaces and evanescent solutions yield real Lagrangian subspaces. The examples cover Minkowski space, Rindler space, Euclidean space and de Sitter space. A simple formula allows for the calculation of expectation values for observables in the generalized vacua.

Black Holes are a Mathematical Fantasy, not a Physical Reality

With recent detection of black hole mergers by LIGO, the 'Black Holes' and 'Neutron Stars' have become common house-hold names, albeit fanciful names in public domain. However, for the scientific community black holes are the ultimate paradoxes of nature. The claimed observations of black hole mergers are in fact interpretations of certain observations under the spacetime model of Relativity. These interpretations can change significantly with the change in operating model of the phenomenon. A black hole is believed to be a ‘region of spacetime’ exhibiting such strong gravitational effects that nothing, not even light can escape from it. We demonstrate in this paper that this conviction is based on erroneous derivation for the gravitational redshift and the correct derivation shows that a photon cannot be prevented from escaping a gravitating body of any mass and size. Due to erroneous depiction of spacetime as a physical entity in GR, a mathematical singularity predicted by Schwarzschild metric solution of EFE has been projected as a physical possibility in the form of Black Holes. To strengthen the physical basis of Black Hole creation, the observations of Super Nova explosions are being interpreted under core collapse models. The core collapse models are now regarded as the physical foundation of Black Holes and Neutron stars. In this paper we have established the invalidity of current core collapse models on the grounds of treating electrons, ions and nuclei as non-interacting particles and using kinetic theory of gases for analyzing compressive stresses in solid iron core.

A spacetime area law bound on quantum correlations

Area laws are a far-reaching consequence of the locality of physical interactions, and they are relevant in a range of systems, from black holes to quantum many-body systems. Typically, these laws concern the entanglement entropy or the quantum mutual information of a subsystem at a single time. However, when considering information propagating in spacetime, while carried by a physical system with local interactions, it is intuitive to expect area laws to hold for spacetime regions. In this work, we prove such a law for quantum lattice systems. We consider two agents interacting in disjoint spacetime regions with a spin-lattice system that evolves in time according to a local Hamiltonian. In their respective spacetime regions, the two agents apply quantum instruments to the spins. By considering a purification of the quantum instruments, and analyzing the quantum mutual information between the ancillas used to implement them, we obtain a spacetime area law bound on the amount of correlation between the agents’ measurement outcomes. Furthermore, this bound applies both to signaling correlations between the choice of operations on the side of one agent, and the measurement outcomes on the side of the other; as well as to the entanglement they can harvest from the spins by coupling detectors to them.

Generalized no-hair theorems without horizons

The simplicity of black holes, as characterized by no-hair theorems, is one of the most important mathematical results in the framework of general relativity. Are these theorems unique to black hole spacetimes, or do they also constrain the geometry around regions of spacetime with arbitrarily large (although finite) redshift? This paper presents a systematic study of this question and illustrates that no-hair theorems are not restricted to spacetimes with event horizons but are instead characteristic of spacetimes with deep enough gravitational wells, extending Israel’s theorem to static spacetimes without event horizons that contain small deviations from spherical symmetry. Instead of a uniqueness result, we obtain a theorem that constrains the allowed deviations from the Schwarzschild metric and guarantees that these deviations decrease with the maximum redshift of the gravitational well in the external vacuum region. Israel’s theorem is recovered continuously in the limit of infinite redshift. This result provides a first extension of no-hair theorems to ultracompact stars, wormholes, and other exotic objects, and paves the way for the construction of similar results for stationary spacetimes describing rotating objects.

A stable finite-difference time-domain scheme for local time-stepping on an adaptive mesh

Physical effects driven by strong electromagnetic fields often occur in regions of highly localized fields on a scattering object. Unfortunately, the most common numerical technique for simulating time-domain electromagnetics, known as Finite-Difference Time-Domain (FDTD), is ill-equipped to handle such problems. A common solution to capture physics across many spatial scales is to use an adaptive mesh, which resolves temporal or spatial features exactly when and where they are needed, avoiding extra computation in space-time regions where it is unnecessary. We present a minimal modification to the FDTD algorithm that allows for a stable late-time solution to Maxwell's equations on an adaptive mesh with a Courant-Friedrichs-Levy limit of 5/6. An emphasis is placed on creating a simple, flexible, and easy to understand algorithm. The algorithm is implemented in 1D, 2D and 3D for geometries which are dynamic or possess large disparities in spatial or temporal scales. An example is presented which demonstrates the use of the algorithm in a resonant dielectric disc with a small slot.

Charged wormholes in f(R,T)-extended theory of gravity

Wormholes (WHs) are a solution for General Relativity field equations which characterize a passage or tunnel that connects two different regions of spacetime and is filled by some sort of exotic matter that does not satisfy the energy conditions. On the other hand, it is known that in extended theories of gravity, the extra degrees of freedom once provided may allow the energy conditions to be obeyed and, consequently, the matter content of the WH to be nonexotic. In this work, we obtain, as a novelty in the literature, solutions for charged WHs in the [Formula: see text]-extended theory of gravity. We show that the presence of charge in these objects may be a possibility to respect some stability conditions for their metric. Also, remarkably, the energy conditions are respected in the present approach. In addition, we argue that our framework can be very useful to study the possibility of evolving [Formula: see text] and [Formula: see text]-dimensional WH spacetime within the context of nonlinear electrodynamics, which open a new window to probe the physical quantities in a WH-type solution.

Cosmological consequences of Omnia Sequestra

Vacuum energy sequestering is a mechanism for cancelling off the radiative corrections to vacuum energy. The most comprehensive low energy model, proposed in [1], has the ability to cancel off radiative corrections to vacuum energy for loops of both matter and gravitons, in contrast to earlier proposals. Here we explore the framework and cosmological consequences of this model, which we call Omnia Sequestra, owing to its ability to sequester all. A computation of historic integrals on a cosmological background reveals some subtleties with UV sensitivity not seen in earlier models, but which are tamed in a Universe that grows sufficiently old. For these old Universes, we estimate the size of the radiatively stable residual cosmological constant and show that it does not exceed the critical density of our Universe today. We also study the effect of phase transitions, both homogeneous and inhomogeneous, and find that generically spacetime regions with a small cosmological constant do not need to be fine-tuned against the scale of the transition, a result which is now seen to hold across all models of sequestering. The model is developed in other ways, from its compatibility with inflation, to the correct inclusion of boundaries and the geometric consequences of certain choices of boundary data.

Locality and multi-level sampling with fermions

Multi-level Monte Carlo sampling techniques exploit the locality of quantum field theory to provide a solution in purely-bosonic quantum field theories to the signal-to-noise ratio problem that affects the lattice determination of a large class of quantities. However, it is not straightforward to generalize multi-level sampling to lattice theories with fermionic content, such as QCD, due to the loss of manifest locality after the fermion path integral is performed. We discuss how the decrease of the fermion propagator with Euclidean distance induces a systematic approximation of the fermion propagator and the fermion determinant, in which the gauge field dependence of distant spacetime regions is completely factorized. This allows us to apply multi-level sampling to the lattice QCD computation of hadronic observables, such as mesonic and baryonic correlators. In particular, we show an application of this strategy to the disconnected contribution to the correlator of two flavour-singlet pseudoscalar densities, which results in a significant increase of the signal-to-noise ratio when a two-level sampling scheme is used.

Gravitational perturbations of nonsingular black holes in conformal gravity

It is believed that in the near future, gravitational wave detections will become a promising tool not only to test gravity theories, but also to probe extremely curved spacetime regions in our universe, such as the surroundings of black holes. In this paper, we investigate the quasinormal modes (QNMs) of the axial gravitational perturbations of a class of non-singular black holes conformally related to the Schwarzschild black hole. These non-singular black holes can be regarded as the vacuum solution of a family of conformal gravity theories which are invariant under conformal transformations. After conformal symmetry is broken, these black holes produce observational signatures different from those of the Schwarzschild black hole, such as their QNM frequencies. We assume that the spacetime is described by the Einstein equation with the effective energy momentum tensor of an anisotropic fluid. The master equation describing the QNMs is derived, and the QNM frequencies are evaluated with the Wentzel-Kramers-Brillouin (WKB) method up to the 6th order. As expected, the QNM spectra of these non-singular black holes deviate from those of the Schwarzschild black hole, indicating the possibility of testing these black hole solutions with the help of future gravitational wave detections.

Restricted Maximin surfaces and HRT in generic black hole spacetimes

The AdS/CFT understanding of CFT entanglement is based on HRT surfaces in the dual bulk spacetime. While such surfaces need not exist in sufficiently general spacetimes, the maximin construction demonstrates that they can be found in any smooth asymptotically locally AdS spacetime without horizons or with only Kasner-like singularities. In this work, we introduce restricted maximin surfaces anchored to a particular boundary Cauchy slice C∂ . We show that the result agrees with the original unrestricted maximin prescription when the restricted maximin surface lies in a smooth region of spacetime. We then use this construction to extend the existence theorem for HRT surfaces to generic charged or spinning AdS black holes whose mass-inflation singularities are not Kasner-like. We also discuss related issues in time-independent charged wormholes.

Persistent gravitational wave observables: General framework

The gravitational wave memory effect is characterized by the permanent relative displacement of a pair of initially comoving test particles that is caused by the passage of a burst of gravitational waves. Recent research on this effect has clarified the physical origin and the interpretation of this gravitational phenomenon in terms of conserved charges at null infinity and "soft theorems." In this paper, we describe a more general class of effects than the gravitational wave memory that are not necessarily associated with these charges and soft theorems, but that are, in principle, measurable. We shall refer to these effects as persistent gravitational wave observables. These observables vanish in non-radiative regions of a spacetime, and their effects "persist" after a region of spacetime which is radiating. We give three examples of such persistent observables, as well as general techniques to calculate them. These examples, for simplicity, restrict the class of non-radiative regions to those which are exactly flat. Our first example is a generalization of geodesic deviation that allows for arbitrary acceleration. The second example is a holonomy observable, which is defined in terms of a closed loop. It contains the usual "displacement" gravitational wave memory; three previously identified, though less well known memory effects (the proper time, velocity, and rotation memories); and additional new observables. Finally, the third example we give is an explicit procedure by which an observer could measure a persistent effect using a spinning test particle. We briefly discuss the ability of gravitational wave detectors (such as LIGO and Virgo) to measure these observables.