It is highly plausible that the region of space-time far from an isolated gravitating body is, in some sense, asymptotically Minkowskian. However theoretical studies of the full nonlinear theory, initiated by Bondi et al. (1962), Sachs (1962) and Newman & Unti (1962), rely on careful, clever, a-priori choices of chart (and tetrad) and so are not readily accessible to the numerical relativist, who chooses her/his chart on the basis of quite different grounds. This paper seeks to close this gap. Starting from data available in a typical numerical evolution, we construct a chart and tetrad which is, asymptotically, sufficiently close to the theoretical ones, so that the key concepts of Bondi news function, Bondi mass and its rate of decrease can be estimated. In particular these esimates can be expressed in the numerical relativist's chart as numerical relativity recipes.
We show that the solution corresponding to the gravitational field of a point particle at rest in 2+1 nonprojectable Horava is exactly the same as its analogous in 2+1 General Relativity. This solution is well known, it is a flat cone whose deficit angle is proportional to the mass of the particle. To establish the system we couple the Horava theory to a point particle with relativistic action. As a consequence of this result, we define the condition of asymptotic flatness exactly in the same way of 2+1 General Relativity. A remarkable feature of this condition is that the dominant mode is not…
We define the asymptotic flatness and discuss asymptotic symmetry at null infinity in arbitrary dimensions using the Bondi coordinates. To define the asymptotic flatness, we solve the Einstein equations and look at the asymptotic behavior of gravitational fields. Then we show the asymptotic symmetry and the Bondi mass loss law with the well-defined definition.
This is the second part of the investigation started in [Stationary solutions and asymptotic flatness I]. We prove here that Strongly Stationary ends having cubic volume growth are Weakly Asymptotically Flat. Combined with the results of the previous paper this shows that Strongly Stationary ends are Asymptotically Flat with Schwarzschidian fall off.
In 1996, Huisken-Yau proved that every three-dimensional Riemannian manifold can be uniquely foliated near infinity by stable closed surfaces of constant mean curvature (CMC) if it is asymptotically equal to the (spatial) Schwarzschild solution. Later, their decay assumptions were weakened by Metzger, Huang, Eichmair-Metzger, and the author. In this work, we prove the reverse implication, i.e. any three-dimensional Riemannian manifold is asymptotically flat if it possesses a CMC-cover satisfying certain geometric curvature estimates, a uniqueness property, a weak foliation property, and each s…
The Standard Model Extension (SME) is a generic parametrization for Lorentz violation and the phenomenological consequences of the minimal gravity sector of the SME are usually studied using a post-Newtonian expansion that requires spacetime to be asymptotically flat. However, there is a term in this sector for which these approximations are unable to make predictions; this is known as the $t$ puzzle. The present paper studies a model of spontaneous Lorentz violation in the minimal gravity sector of the SME in a static and spherically symmetric situation, when no additional matter fields are p…
The Horava theory in 2+1 dimensions can be formulated at a critical point in the space of coupling constants where it has no local degrees of freedom. This suggests that this critical case could share many features with 2+1 general relativity, in particular its large-distance effective action that is of second order in derivatives. To deepen on this relationship, we study the asymptotically flat solutions of the effective action. We take the general definition of asymptotic flatness from 2+1 general relativity, where an asymptotically flat region with a nonfixed conical angle is approached. We…
In this article and its sequel we discuss the asymptotic structure of space-times representing isolated bodies in General Relativity. Such space-times are usually required to be asymptotically flat (AF), and thus to have a prescribed type of asymptotic. Despite all the "reasonable" that the requirement is, it seems to be against the spirit of General Relativity where the global structure of the space-time should be also considered as a variable. It is shown here that, even eliminating from the definition any a priori reference or assumption about the asymptotic, the space-times of isolated bod…
For any non-rotating effective quantum (uncharged) black hole model to be viable, its asymptotic structure of spacetime should reduce to that of a Schwarzschild black hole. After examining the asymptotic structure of quantum black holes proposed in Ashtekar et al., (2018), we find that the solution is actually not asymptotically flat. Departure from asymptotically flat spacetime is a direct consequence of the quantum parameters included in the model. Moreover, since the property of asymptotic flatness needs to be explicitly invoked, for instance, in relating the black hole and the white hole m…
In this paper we study space-times which evolve out of Cauchy data $(Σ,{}^3g,K)$ invariant under the action of a two-dimensional commutative Lie group. Moreover $(Σ,{}^3g,K)$ are assumed to satisfy certain completeness and asymptotic flatness conditions in spacelike directions. We show that asymptotic flatness and energy conditions exclude all topologies and group actions except for a cylindrically symmetric $R^3$, or a periodic identification thereof along the $z$-axis. We prove that asymptotic flatness, energy conditions and cylindrical symmetry exclude the existence of compact trapped surfa…
A new numerical scheme to compute 3D configurations of quasiequilibrium compact stars in general relativity -- Application to synchronously rotating binary star systems --
Shape Dynamics is a theory of gravity that waives refoliation invariance in favor of spatial Weyl invariance. It is a canonical theory, constructed from a Hamiltonian, 3+1 perspective. One of the main deficits of Shape Dynamics is that its Hamiltonian is only implicitly constructed as a functional of the phase space variables. In this paper, I write down the equations of motion for Shape Dynamics to show that over a curve in phase space representing a Minkowski spacetime, Shape Dynamics possesses Poincaré symmetry for appropriate boundary conditions. The proper treatment of such boundary condi…
Using hyperbolic temporal and spatial cut-offs to define 4d asymptotically flat spacetimes, we show that supertranslation ambiguities in the asymptotic fields can all be removed even in the presence of gravitational magnetic charges. We then show that configurations with different electric and magnetic four-momenta can be consistently considered in the Mann-Marolf variational principle. This generalizes the previous result where variations over asymptotically flat configurations with fixed magnetic four-momenta were considered. We also express Kerr Taub-NUT metric to the leading and next to le…
We point out an association between anomalies in the Hawking quasilocal mass (or, in spherical symmetry, in its better known version, the Misner-Sharp-Hernandez mass) and unphysical properties of the spacetime geometry. While anomalous behaviors show up in certain quantum-corrected black holes, they are not unique to this context and signal serious physical pathologies of isolated gravitating systems in general.
We construct a canonical quantization of the two dimensional theory of a parametrized scalar field on noncompact spatial slices. The kinematics is built upon generalized charge-network states which are labelled by smooth embedding spacetimes, unlike the standard basis states carrying only discrete labels. The resulting quantum geometry corresponds to a nondegenerate vacuum metric, which allows a consistent realization of the asymptotic conditions on the canonical fields. Although the quantum counterpart of the classical symmetry group of conformal isometries consists only of continuous global …
In this paper we establish two results concerning four-dimensional asymptotically flat spacetimes at spatial infinity. First, we show that the six conserved Lorentz charges are encoded in two unique, distinct, but mutually dual symmetric divergence free tensors that we construct from the equations of motion. Second, we show that integrability of Einstein's equations in the asymptotic expansion is sufficient to establish the equivalence between counter-term charges defined from the variational principle and charges defined by Ashtekar and Hansen. These results clarify earlier constructions of c…
Spin foam models are an approach to quantum gravity based on the concept of sum over states, which aims to describe quantum spacetime dynamics in a way that its parent framework, loop quantum gravity, has not as of yet succeeded. Since these models' relation to classical Einstein gravity is not explicit, an important test of their viabilitiy is the study of asymptotics - the classical theory should be obtained in a limit where quantum effects are negligible, taken to be the limit of large triangle areas in a triangulated manifold with boundary. In this paper we will briefly introduce the EPRL/…
Holographic RG flows in some cases are known to be related to cosmological solutions. In this paper another example of such correspondence is provided. Holographic RG flows giving rise to asymptotically-free $β$-functions have been analyzed in connection with holographic models of QCD. They are shown upon Wick rotation to provide a large class of inflationary models with logarithmically-soft inflaton potentials. The scalar spectral index is universal and depends only on the number of e-foldings. The ratio of tensor to scalar power depends on the single extra real parameter that defines this cl…
We show that, when an approximation used in this prior work is removed, the resulting improved calculation yields an alternative derivation, in the particular case studied, of the accidental curvature constraint of Hellmann and Kaminski. The result is at the same time extended to apply to almost all non-degenerate Regge-like boundary data and a broad class of face amplitudes. This resolves a tension in the literature.
This thesis is concerned with formulations of the Einstein equations in axisymmetric spacetimes which are suitable for numerical evolutions. We develop two evolution systems based on the (2+1)+1 formalism. The first is a (partially) constrained scheme with elliptic gauge conditions arising from maximal slicing and conformal flatness. The second is a strongly hyperbolic first-order formulation obtained by combining the (2+1)+1 formalism with the Z4 formalism. A careful study of the behaviour of regular axisymmetric tensor fields enables us to cast the equations in a form that is well-behaved on…
The concepts of isolated self-gravitating system, asymptotic flatness and asymptotic simplicity are reconsidered, various related results are discussed and put into perspective, basic open questions are posed.
In this short review we present some recently obtained traversable wormhole models in the framework of general relativity (GR) in four and six dimensions that somehow widen our common ideas on wormhole existence and properties. These are, first, rotating cylindrical wormholes, asymptotically flat in the radial direction and existing without exotic matter. The topological censorship theorems are not violated due to lack of asymptotic flatness in all spatial directions. Second, these are cosmological wormholes constructed on the basis of the Lemaitre-Tolman-Bondi solution. They connect two copie…
By using Stationary-to-Randers correspondence (SRC), a characterization of light and time-convexity of the boundary of a region of a standard stationary (n+1)-spacetime is obtained, in terms of the convexity of the boundary of a domain in a Finsler n or (n+1)-space of Randers type. The latter convexity is analyzed in depth and, as a consequence, the causal simplicity and the existence of causal geodesics confined in the region and connecting a point to a stationary line are characterized. Applications to asymptotically flat spacetimes include the light-convexity of stationary hypersurfaces whi…
All known solutions to the Einstein equations describing rotating cylindrical wormholes lack asymptotic flatness and therefore cannot describe wormhole entrances as local objects in our Universe. To overcome this difficulty, wormhole solutions are joined to flat asymptotic regions at some surfaces $Σ_-$ and $Σ_+$. The whole configuration thus consists of three regions, the internal one containing a wormhole throat, and two flat external ones, considered in rotating reference frames. Using a special kind of anisotropic fluid respecting the Weak Energy Condition (WEC) as a source of gravity in t…
We examine current numerical relativity computations of gravitational waves, which typically determine the asymptotic waves at infinity by extrapolation from finite (small) radii. Using simulations of a black hole binary with accurate wave extraction at $r=1000M$, we show that extrapolations from the near-zone are self-consistent in approximating measurements at this radius, although with a somewhat reduced accuracy. We verify that $ψ_4$ is the dominant asymptotic contribution to the gravitational energy (as required by the peeling theorem) but point out that gauge effects may complicate the i…
We discuss, without assuming asymptotic flatness, a gravitational lens for an observer and source that are within a finite distance from a lens object. The proposed lens equation is consistent with the deflection angle of light that is defined for nonasymptotic observer and source by Takizawa et al. [Phys. Rev. D 101, 104032 (2020)] based on the Gauss-Bonnet theorem with using the optical metric. This lens equation, though it is shown to be equivalent to the Bozza lens equation[Phys. Rev. D 78, 103005 (2008)], is linear in the deflection angle. Therefore, the proposed equation is more convenie…
We present a new study of remnant black hole properties from 13 binary black hole systems, numerically evolved using the Spectral Einstein Code. The mass, spin, and recoil velocity of each remnant were determined quasi-locally from apparent horizon data and asymptotically from Bondi data $(h, ψ_4, ψ_3, ψ_2, ψ_1)$ computed at future null infinity using SpECTRE's Cauchy characteristic evolution. We compare these independent measurements of the remnant properties in the bulk and on the boundary of the spacetime, giving insight into how well asymptotic data are able to reproduce local properties o…
Given a collection of N asymptotically Euclidean ends with zero scalar curvature, we construct a Riemannian manifold with zero scalar curvature and one asymptotically Euclidean end, whose boundary has a neighborhood isometric to the disjoint union of a specified collection of sub-regions of the given ends. An application is the construction of time-symmetric solutions of the constraint equations which model N-body initial data.
We show that the asymptotic charges associated with Lorentz symmetries on past and future null infinity match in the limit to spatial infinity in a class of asymptotically-flat spacetimes. These are spacetimes that obey the Ashtekar-Hansen definition of asymptotic flatness at null and spatial infinity and satisfy an additional set of conditions which we lay out explicitly. Combined with earlier results on the matching of supertranslation charges, this shows that all Bondi-Metzner-Sachs (BMS) charges on past and future null infinity match in the limit to spatial infinity in this class of spacet…
By studying the notion of a fundamentally minimal length scale in asymptotically safe gravity we find that a specific version of deformed special relativity (DSR) naturally arises in this approach. We then consider two thought experiments to examine the interpretation of the scenario and discuss similarities and differences to other approaches to DSR.
We propose a general framework to describe Planckian deviations from Special Relativity (SR) compatible with a relativistic principle. They are introduced as the leading corrections in an asymptotic approach to SR going beyond the energy power expansion of effective field theories. We discuss the conditions in which these Planckian effects might be experimentally observable in the near future, together with the non-trivial limits of applicability of this asymptotic approach that such a situation would produce, both at the very high (ultraviolet) and the very low (infrared) energy regimes.
In this work the asymptotic structure of space-time and the main properties of the Bondi-Metzner-Sachs (BMS) group, which is the asymptotic symmetry group of asymptotically flat space-times, are analysed. Every chapter, except the fourth, begins with a brief summary of the topics that will be dealt through it and an introduction to the main concepts. The work can be divided into three principal parts. The first part includes the first two chapters and is devoted to the development of the mathematical tools that will be used throughout all of the work. In particular we will introduce the notion…
The positivity of the Bondi mass has been proven in 4 dimensions, but in higher dimensions the issue remains open. The formalism of the present paper has been developed to investigate this and is well suited to the higher dimensional case. At null infinity, we make asymptotic expansions of the metric components in conformal Gaussian null coordinates, and use the vacuum Einstein equations to solve for the expansion coefficients. We find simple coordinate formulae for the Bondi mass, news and flux in terms of the expansion coefficients of the metric components. We also make expansions of the gen…
We study the Lie group structure of asymptotic symmetry groups in General Relativity from the viewpoint of infinite-dimensional geometry. To this end, we review the geometric definition of asymptotic simplicity and emptiness due to Penrose and the coordinate-wise definition of asymptotic flatness due to Bondi et al. Then we construct the Lie group structure of the Bondi--Metzner--Sachs (BMS) group and discuss its Lie theoretic properties. We find that the BMS group is regular in the sense of Milnor, but not real analytic. This motivates us to conjecture that it is not locally exponential. Fina…
Recently some 4d asymptotically $AdS_2 \times S^2$ regular bubbling solutions written in terms of an arbitrary profile function has appeared in literature. We discuss the possibility of extending these solutions to asymptotically flat spaces, therefore building a model for an horizonless and singularity-free fuzzball with the same asymptotic charges of the associated black hole, directly in general relativity. A negative conclusion is reached within an axial-symmetric ansatz inside the IWP family.
