Region Of Spacetime Research Articles

Nonsingular metric for an electrically charged point-source in ghost-free infinite derivative gravity

In this paper we will construct a linearized metric solution for an electrically charged system in a {\it ghost-free} infinite derivative theory of gravity which is valid in the entire region of spacetime. We will show that the gravitational potential for a point-charge with mass $m$ is non-singular, the Kretschmann scalar is finite, and the metric approaches conformal-flatness in the ultraviolet regime where the non-local gravitational interaction becomes important. We will show that the metric potentials are bounded below one as long as two conditions involving the mass and the electric charge are satisfied. Furthermore, we will argue that the cosmic censorship conjecture is not required in this case. Unlike in the case of Reissner-Nordstr\"om in general relativity, where $|Q|\leq m/M_p$ has to be always satisfied, in {\it ghost-free} infinite derivative gravity $|Q|>m/M_p$ is also allowed, such as for an electron.

Closed trapping horizons without singularity

In gravitational collapse leading to black hole formation, trapping horizons typically develop inside the contracting matter. Classically, an ingoing trapping horizon moves towards the centre where it reaches a curvature singularity, while an outgoing horizon moves towards the surface of the star where it becomes an isolated, null horizon. However, strong quantum effects at high curvature close to the centre could modify the classical picture substantially, e.g. by deflecting the ingoing horizon to larger radii, until it eventually reunites with the outgoing horizon. We here analyse some existing models of regular "black holes" of finite lifespan formed out of ingoing null shells collapsing from $\mathscr{I}^-$, after giving general conditions for the existence of (singularity-free) closed trapping horizons. We study the energy-momentum tensor of such models by solving Einstein's equations in reverse and give an explicit form of the metric to model a Hawking radiation reaching $\mathscr{I}^+$. A major flaw of the models aiming at describing the formation of black holes (with a Vaidya limit on $\mathscr{I}^-$) as well as their evaporation is finally exhibited: they necessarily violate the null energy condition up to $\mathscr{I}^-$, i.e. in a non-compact region of spacetime.

On causality violation on a Kerr-de Sitter spacetime

The causal properties of the family of Kerr-de Sitter spacetimes are analyzed and compared to those of the Kerr family. At first we show that a Kerr-de Sitter spacetime can be viewed as an assembly of Carter's blocks i.e. four dimensional spacetime regions contained within Killing horizons or a Killing horizon and the asymptotic de Sitter region. From this perspective and leaving aside topological identifications, the causal properties of a Kerr de Sitter spacetime are determined by the causal properties of the individual Carter's blocks viewed as spacetimes in their own right. We show that any Carter's block is stably causal except for the blocks that contain the ring singularity. The latter are vicious sets: any two events within such block can be connected by a future (respectively past) directed timelike curve. This behavior is identical to the causal behavior of the Boyer-Lindquist blocks that contains the Kerr ring singularity which are also vicious sets. On the other hand, while for the case of a naked Kerr singularity the entire spacetime is a vicious set and thus closed timelike curves pass through any event including events lying in the asymptotic region, for the case of a Kerr-de Sitter spacetime the cosmological horizons imply that the asymptotic de Sitter region is causally well behaved. In that regard a positive cosmological constant appears to improve the causal behavior of the underlying spacetime.

Entanglement Entropy and TT[over ¯] Deformation.

Quantum gravity in a finite region of spacetime is conjectured to be dual to a conformal field theory (CFT) deformed by the irrelevant operator TT[over ¯]. We test this conjecture with entanglement entropy, which is sensitive to ultraviolet physics on the boundary, while also probing the bulk geometry. We find that the entanglement entropy for an entangling surface consisting of two antipodal points on a sphere is finite and precisely matches the Ryu-Takayanagi formula applied to a finite region consistent with the conjecture of McGough etal. We also consider a one-parameter family of conical entropies, which are finite and verify a conjecture due to Dong. Since ultraviolet divergences are local, we conclude that the TT[over ¯] deformation acts as an ultraviolet cutoff on the entanglement entropy. Our results support the conjecture that the TT[over ¯]-deformed CFT is the holographic dual of a finite region of spacetime.

Nuclear processes in other universes: Varying the strength of the weak force

Motivated by the possibility that the laws of physics could be different in other regions of space-time, we consider nuclear processes in universes where the weak interaction is either stronger or weaker than observed. We focus on the physics of both Big Bang Nucleosynthesis (BBN) and stellar evolution. For sufficiently ineffective weak interactions, neutrons do not decay during BBN, and the baryon-to-photon ratio $\eta$ must be smaller in order for protons to survive without becoming incorporated into larger nuclei. For stronger weak interactions, neutrons decay before the onset of BBN, and the early universe is left with nearly a pure hydrogen composition. We then consider stellar structure and evolution for the different nuclear compositions resulting from BBN, a wide range of weak force strengths, and the full range of stellar masses for a given universe. We delineate the range of this parameter space that supports working stars, along with a determination of the dominant nuclear reactions over the different regimes. Deuterium burning dominates the energy generation in stars when the weak force is sufficiently weak, whereas proton-proton burning into helium-3 dominates for the regime where the weak force is much stronger than in our universe. Although stars in these universes are somewhat different, they have comparable surface temperatures, luminosities, radii, and lifetimes, so that a wide range of such universes remain potentially habitable.

Path length distribution in two-dimensional causal sets

We study the distribution of maximal-chain lengths between two elements of a causal set and its relationship with the embeddability of the causal set in a region of flat spacetime. We start with causal sets obtained from uniformly distributed points in Minkowski space. After some general considerations we focus on the 2-dimensional case and derive a recursion relation for the expected number of maximal chains n_k as a function of their length k and the total number of points N between the maximal and minimal elements. By studying these theoretical distributions as well as ones generated from simulated sprinklings in Minkowski space we identify two features, the most probable path length or peak of the distribution k_0 and its width varDelta , which can be used both to provide a measure of the embeddability of the causal set as a uniform distribution of points in Minkowski space and to determine its dimensionality, if the causal set is manifoldlike in that sense. We end with a few simple examples of n_k distributions for non-manifoldlike causal sets.

The Poisson brackets of free null initial data for vacuum general relativity

A hypersurface composed of two null sheets, or ‘light fronts’, swept out by the two congruences of future null normal geodesics emerging from a spacelike 2-disk can serve as a Cauchy surface for a region of spacetime. Already in the 1960s free (unconstrained) initial data for vacuum general relativity were found for hypersurfaces of this type. Here the Poisson brackets of such free initial data are calculated from the Hilbert action. The brackets obtained can form the starting point for a constraint free canonical quantization of general relativity and may be relevant to holographic entropy bounds for vacuum gravity. Several of the results of the present work have been presented in abbreviated form in the letter (Reisenberger 2008 Phys. Rev. Lett. 101 211101).

Classical mechanics via general relativity and Maxwell’s theory: a bit of magic

In the 1950’s Herman Bondi observed that a very effective way to study gravitational radiation was to use null surfaces as part of the coordinate system for analyzing the Einstein (Einstein–Maxwell) equations. A particular class of such surfaces, (referred to as Bondi null surfaces) with their associated null tetrad, has now been the main tool for this analysis for many years; their use—until recently—has been almost ubiquitous. Several years ago we realized that there was an attractive alternative to the use of Bondi coordinates, namely to use coordinates (in the asymptotic null future space–time region) that were as close to ordinary flat-space light-cones as possible—very different from Bondi surfaces. There were initially serious impediments to this program: these new null surfaces (referred to as asymptotically shear-free surfaces, ASF) were determined by solving a non-linear differential equation (the “good-cut” equation) whose solutions were most often complex. Eventually these problems were overcome and the program was implemented. In a series of papers, using the ASF null surfaces to study the asymptotically flat Einstein (or Einstein–Maxwell) equations, a variety of surprising (strange) results were obtained. Using only the Einstein and Maxwell equations, we found a large number of the basic relations of classical mechanics. They included very detailed conservation laws, well know kinematic relations and dynamic equations and even the Abraham–Lorentz–Dirac radiation reaction force and the rocket force. As interesting as these were, they came with a serious enigma. These relations from classical mechanics had no relationship with the physical space–time. The space for the action of these relations was the parameter space of solutions of the good-cut equation—a complex space, known as H-space. The enigma—what possible relationship did these standard appearing classical relations have with physical space–time? It is the purpose of this work to establish such a relationship—objects in H-space are related to structures in physical space–time. For example, a complex world-line in H-space becomes in physical space–time an asymptotically shear-free null geodesic congruence where its twist describes its intrinsic spin and if charged, its magnetic dipole.

Closed timelike curves and ‘effective’ superluminal travel with naked line singularities

We examine closed timelike curves (CTCs) and ‘effective’ superluminal travel in a spacetime containing naked line singularities, which we call ‘wires’. Each wire may be straight-line singularity or a ring singularity. The weak energy condition (WEC) is preserved in all well-defined regions of the spacetime. (The singularities themselves are not well-defined, so the WEC is undefined there, but it is never explicitly violated.) Parallel to the wire, ‘effective’ superluminal travel is possible, in that the wire may be used as a shortcut between distant regions of spacetime. Our purpose in presenting the superluminal aspects of the wire is to dispel the commonly held view that explicit WEC violation is necessary for effective superluminal travel, whereas in truth the strictures against superluminal travel are more complicated. We also demonstrate how the existence of such ‘wires’ could create CTCs. We present a model spacetime which contains two wires which are free to move relative to each other. This spacetime is asymptotically flat: it becomes a Minkowski spacetime a finite distance away from each of the wires. The CTCs under investigation do not need to enter the wires’ singularities, and can be confined to regions that are weak-field: this means that if these wires were physically possible, they would present causality problems even in nonsingular, energetically realistic regions of the spacetime. We conclude that the weak energy condition alone is not sufficient to prevent superluminal travel in asymptotically flat spacetimes.

Spatio-Temporal Segmentation Applied to Optical Remote Sensing Image Time Series

The availability of a large amount of remote sensing data made Earth Observation increasingly accessible and detailed. High temporal and spatial resolution sensors are responsible for making available data sets of time series in unprecedented proportions. Within this context, the use of efficient segmentation algorithms of remote sensing imagery represents an important role in this scenario, because they provide homogeneous regions in space-time and hence simplify the data set. In addition, the spatio-temporal segmentation can bring a new way of interpreting data by means of analyzing contiguous regions in time. This letter describes a method for image segmentation applied to time series of the Earth Observation data. We adapted the traditional region growing method to detect homogeneous regions in space and time. Study cases were conducted by considering the dynamic time warping algorithm as the homogeneity criterion to grow regions. Tests on high temporal resolution image sequences from Moderate Resolution Imaging Spectroradiometer and Landsat-8 Operational Land Imager vegetation indices and comparisons with other distance measurements provided satisfactory outcomes.

A time machine for free fall into the past

Inspired by some recent works of Tippett–Tsang and Mallary–Khanna–Price, we present a new spacetime model containing closed timelike curves (CTCs). This model is obtained postulating an ad hoc Lorentzian metric on , which differs from the Minkowski metric only inside a spacetime region bounded by two concentric tori. The resulting spacetime is topologically trivial, free of curvature singularities and is both time and space orientable; besides, the inner region enclosed by the smaller torus is flat and displays geodesic CTCs. Our model shares some similarities with the time machine of Ori and Soen but it has the advantage of a higher symmetry in the metric, allowing for the explicit computation of a class of geodesics. The most remarkable feature emerging from this computation is the presence of future-oriented timelike geodesics starting from a point in the outer Minkowskian region, moving to the inner spacetime region with CTCs, and then returning to the initial spatial position at an earlier time; this means that time travel to the past can be performed by free fall across our time machine. The amount of time travelled into the past is determined quantitatively; this amount can be made arbitrarily large keeping non-large the proper duration of the travel. An important drawback of the model is the violation of the classical energy conditions, a common feature of many time machines. Other problems emerge from our computations of the required (negative) energy densities and of the tidal accelerations; these are small only if the time machine is gigantic.

On the viability of regular black holes

The evaporation of black holes raises a number of conceptual issues, most of them related to the final stages of evaporation, where the interplay between the central singularity and Hawking radiation cannot be ignored. Regular models of black holes replace the central singularity with a nonsingular spacetime region, in which an effective classical geometric description is available. It has been argued that these models provide an effective, but complete, description of the evaporation of black holes at all times up to their eventual disappearance. However, here we point out that known models fail to be self-consistent: the regular core is exponentially unstable against perturbations with a finite timescale, while the evaporation time is infinite, therefore making the instability impossible to prevent. We also discuss how to overcome these difficulties, highlighting that this can be done only at the price of accepting that these models cannot be fully predictive regarding the final stages of evaporation.

Solvation in Space-time: Pretransition Effects in Trajectory Space.

We demonstrate pretransition effects in space-time in trajectories of systems in which the dynamics displays a first-order phase transition between distinct dynamical phases. These effects are analogous to those observed for thermodynamic first-order phase transitions, most notably the hydrophobic effect in water. Considering the (infinite temperature) East model as an elementary example, we study the properties of "space-time solvation" by examining trajectories where finite space-time regions are conditioned to be inactive in an otherwise active phase. We find that solvating an inactive region of space-time within an active trajectory shows two regimes in the dynamical equivalent of solvation free energy: an "entropic" small solute regime in which uncorrelated fluctuations are sufficient to evacuate activity from the solute, and an "energetic" large solute regime which involves the formation of a solute-induced inactive domain with an associated active-inactive interface bearing a dynamical interfacial tension. We also show that as a result of this dynamical interfacial tension there is a dynamical analog of the hydrophobic collapse that drives the assembly of large hydrophobes in water. We discuss the general relevance of these results to the properties of dynamical fluctuations in systems with slow collective relaxation such as glass formers.

Causal set generator and action computer

The causal set approach to quantum gravity has gained traction over the past three decades, but numerical experiments involving causal sets have been limited to relatively small scales. The software suite presented here provides a new framework for the generation and study of causal sets. Its efficiency surpasses previous implementations by several orders of magnitude. We highlight several important features of the code, including the compact data structures, the O(N2) causal set generation process, and several implementations of the O(N3) algorithm to compute the Benincasa–Dowker action of compact regions of spacetime. We show that by tailoring the data structures and algorithms to take advantage of low-level CPU and GPU architecture designs, we are able to increase the efficiency and reduce the amount of required memory significantly. The presented algorithms and their implementations rely on methods that use CUDA, OpenMP, x86 Assembly, SSE/AVX, Pthreads, and MPI. We also analyze the scaling of the algorithms’ running times with respect to the problem size and available resources, with suggestions on how to modify the code for future hardware architectures. Program summaryProgram Title: Causal Set Generator and Action ComputerProgram Files doi:http://dx.doi.org/10.17632/5k8wjrhgwh.1Licensing Provisions: MITProgramming Language: C++/CUDA, x86 AssemblyNature of Problem: Generate causal sets and compute the Benincasa–Dowker action.Solution Method: We generate causal sets sprinkled on a Lorentzian manifold by randomly sampling element coordinates using OpenMP and linking elements using CUDA. Causal sets are stored in a minimal binary representation via the FastBitset class. We measure the action in parallel using OpenMP, SSE/AVX and x86 Assembly. When multiple computers are available, MPI and POSIX threads are also incorporated.Additional Comments: The program runs most efficiently with an Intel processor supporting AVX2 and an NVIDIA GPU with compute capability greater than or equal to 3.0.

Hawking radiation in the spacetime of white holes

A white hole (WH) is a time-reversed black hole (BH) solution in General relativity with a spacetime region to which cannot be entered from the outside. Recently they have been proposed as a possible solution to the information loss problem [Haggard and Rovelli, 2015]. In particular it has been argued that the quantization of the gravitational field may prevent a BH from collapsing entirely with an exponential decay law associated to the black-hole-to-white-hole (BHWH) tunneling scenario [Barcelo, Carballo, and Garay, 2017]. During this period of BHWH transition the Hawking radiation should take place. Taking this possibility into account, we utilize the Hamilton-Jacobi and Parkih-Wilczek methods to study the Hawking radiation viewed as a quantum tunneling effect to calculate the tunneling rate of vector particles tunneling inside (outside) the horizon of a WH (BH), respectively. We show that there is a Hawking radiation associated to a WH spacetime equal to the BH Hawking temperature when viewed from the outside region of the WH geometry. In the framework of Parkih-Wilczek method, surprisingly, we show that Hawking temperature is affected by the initial radial distance at which the gravitational collapse starts.

Commutative geometry for non-commutative D-branes by tachyon condensation

There is a difficulty in defining the positions of the D-branes when the scalar fields on them are non-abelian. We show that we can use tachyon condensation to determine the position or the shape of D0-branes uniquely as a commutative region in spacetime together with non-trivial gauge flux on it, even if the scalar fields are non-abelian. We use the idea of the so-called coherent state method developed in the field of matrix models in the context of the tachyon condensation. We investigate configurations of noncommutative D2-brane made out of D0-branes as examples. In particular, we examine a Moyal plane and a fuzzy sphere in detail, and show that whose shapes are commutative $\mathbb{R}^2$ and $S^2$, respectively, equipped with uniform magnetic flux on them. We study the physical meaning of this commutative geometry made out of matrices, and propose an interpretation in terms of K-homology.

Localized non-Abelian gauge fields in non-compact extra dimensions

Dynamical localization of non-Abelian gauge fields in non-compact flat $D$ dimensions is worked out. The localization takes place via a field-dependent gauge kinetic term when a field condenses in a finite region of spacetime. Such a situation typically arises in the presence of topological solitons. We construct four-dimensional low-energy effective Lagrangian up to the quadratic order in a universal manner applicable to any spacetime dimensions. We devise an extension of the $R_\xi$ gauge to separate physical and unphysical modes clearly. Out of the D-dimensional non-Abelian gauge fields, the physical massless modes reside only in the four-dimensional components, whereas they are absent in the extra-dimensional components. The universality of non-Abelian gauge charges holds due to the unbroken four-dimensional gauge invariance. We illustrate our methods with models in $D=5$ (domain walls), in $D=6$ (vortices), and in $D=7$.

Unruh effect for inertial observers through vacuum correlations

We study a dynamic version of the Unruh effect in a two dimensional collapse model forming a black hole. In this two-dimensional collapse model a scalar field coupled to the dilaton gravity, moving leftwards, collapses to form a black hole. There are two sets of asymptotic (trightarrow infty ) observers, around xrightarrow infty and xrightarrow -infty . The observers at the right null infinity witness a thermal flux of radiation associated with time dependent geometry leading to a black hole formation and its subsequent Hawking evaporation, in an expected manner. We show that even the observers at left null infinity find themselves in thermal ambiance, without experiencing any change of spacetime geometry all along their trajectories. They remain as inertial observers in a flat region of spacetime where curvature tensor identically vanishes in a portion of full spacetime. These observers find the state of the quantum field in a late time thermal configuration, with exactly the same temperature as measured by the observers at right null infinity, despite being inertial in flat spacetime region throughout their history. This is very closely related to the standard Unruh effect in the flat spacetime, except for a key difference – since they are inertial throughout and have no causally connected source in the past light cone to account for what they see. The result arises from quantum correlations which extend outside the past light cone and is conceptually similar to the EPR correlations.

Toward Entanglement Entropy with UV-Cutoff in Conformal Nets

We consider the entanglement entropy for a spacetime region and its spacelike complement in the framework of algebraic quantum field theory. For a M\"obius covariant local net satisfying a certain nuclearity property, we consider the von Neumann entropy for type I factors between local algebras and introduce an entropic quantity. Then we implement a cutoff on this quantity with respect to the conformal Hamiltonian and show that it remains finite as the distance of two intervals tends to zero. We compare our definition to others in the literature.

Energy emission from a high curvature region and its backreaction

A strong gravity naked singular region can give important clues towards understanding classical as well as spontaneous nature of General Relativity. We propose here a model for energy emission from a naked singular region in a self-similar dust spacetime by gluing two self-similar dust solutions at the Cauchy horizon. The energy is defined and evaluated as a surface energy of a null hypersurface, the null shell. Also included are scenarios of spontaneous creation or disappearance of a singularity, end of inflation, black hole formation and bubble nucleation. Our examples investigated here explicitly show that one can model unlimitedly luminous and energetic objects in the framework of General Relativity.