A definition of asymptotic flatness at spatial infinity in $d$ dimensions ($d\geq 4$) is given using the conformal completion approach. Then we discuss asymptotic symmetry and conserved quantities. As in four dimensions, in $d$ dimensions we should impose a condition at spatial infinity that the "magnetic" part of the $d$-dimensional Weyl tensor vanishes at faster rate than the "electric" part does, in order to realize the Poincare symmetry as asymptotic symmetry and construct the conserved angular momentum. However, we found that an additional condition should be imposed in $d>4$ dimensions.
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…
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…
Asymptotic Flatness, Taub-NUT, and Variational Principle
使用双曲的时间和空间截止定义四维渐近平坦时空，我们表明，超平移的模糊性，即使在存在引力磁荷的渐近场都可以被删除。然后，我们表明，具有不同的电和磁四动量的配置可以一致地认为在曼-马罗夫变分原理。这推广了以前的结果，其中的变化与固定的磁四动量的渐近平坦的配置被认为是。我们还将Kerr Taub-NUT度量表示为Beig-Schmidt形式的首阶和次首阶，并将其渐近形式与3d de Sitter空间上的张量调和函数进行了比较.
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…
We propose a definition of asymptotic flatness at timelike infinity in four spacetime dimensions. We present a detailed study of the asymptotic equations of motion and the action of supertranslations on asymptotic fields. We show that the Lee-Wald symplectic form $Ω(g, δ_1 g, δ_2 g)$ does not get contributions from future timelike infinity with our boundary conditions. As a result, the "future charges" can be computed on any two-dimensional surface surrounding the sources at timelike infinity. We present expressions for supertranslation and Lorentz charges.
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.
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…
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…
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.
本文及其续篇讨论了广义相对论中代表孤立体的时空的渐近结构。这样的时空通常要求是渐近平坦的（AF），因此具有规定的渐近类型。尽管这个要求是“合理的”，但它似乎违背了广义相对论的精神，即时空的整体结构也应该被视为一个变量。这里表明，即使从定义中消除任何先验参考或关于渐近的假设，孤立体的时空是可证明的和后验的AF。在这两篇文章之间，证明了任何真空严格静止时空的结束，（商）流形同构于R^3减去一个球，并且其Killing场的范数有界远离零，则它必然是AF，且具有Schwarzschidian fall off。“切除”的球将包含（如果有的话）实际的物质体，但这一信息或任何其他信息对于得出结论是不必要的。物理和数学的影响也进行了讨论。
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…
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/…
Large gauge symmetries in Minkowski spacetime are often studied in two distinct regimes: either at asymptotic (past or future) times or at spatial infinity. By working in harmonic gauge, we provide a unified description of large gauge symmetries (and their associated charges) that applies to both regimes. At spatial infinity the charges are conserved and interpolate between those defined at the asymptotic past and future. This explains the equality of asymptotic past and future charges, as recently proposed in connection with Weinberg's soft photon theorem.
We present a new set of asymptotic conditions for gravity at spatial infinity that includes gravitational magnetic-type solutions, allows for a non-trivial Hamiltonian action of the complete $BMS_4$ algebra, and leads to a non-divergent behaviour of the Weyl tensor as one approaches null infinity. We then extend the analysis to the coupled Einstein-Maxwell system and obtain as canonically realized asymptotic symmetry algebra a semi-direct sum of the $BMS_4$ algebra with the angle dependent $u(1)$ transformations. The Hamiltonian charge-generator associated with each asymptotic symmetry element…
Explicit boundary conditions are given at spatial infinity for four-dimensional supergravity, which provide a realization of the super-BMS algebra of Awada, Gibbons and Shaw. The results are then generalized to the $N$- extended super-BMS algebras.
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 investigate the behavior of null geodesics near future null infinity in asymptotically flat spacetimes. In particular, we focus on the asymptotic behavior of null geodesics that correspond to worldlines of photons initially emitted in the directions tangential to the constant radial surfaces in the Bondi coordinates. The analysis is performed for general dimensions, and the difference between the four-dimensional cases and the higher-dimensional cases is stressed. In four dimensions, some assumptions are required to guarantee the null geodesics to reach future null infinity, in addition to …
We construct a relation between the Aretakis charge of any extreme black hole and the Newman-Penrose charge. This is achieved by constructing a conformal correspondence between extreme black holes and what we call weakly asymptotically flat space-times. Under this correspondence the Newman-Penrose charge of the weakly asymptotically flat space-time maps on to the Aretakis charge of the extreme black hole. Furthermore, we generalise the conformal isometry displayed by the extreme Reissner-Nordström solution to a novel conformal symmetry that acts within a class of static STU supergravity black …
We use the formalism developed by Wald and Zoupas to derive explicit covariant expressions for the charges and fluxes associated with the Bondi-Metzner-Sachs symmetries at null infinity in asymptotically flat spacetimes in vacuum general relativity. Our expressions hold in non-stationary regions of null infinity, are local and covariant, conformally-invariant, and are independent of the choice of foliation of null infinity and of the chosen extension of the symmetries away from null infinity. While similar expressions have appeared previously in the literature in Bondi-Sachs coordinates (to wh…
Hamada and Shiu have recently shown that tree level amplitudes in QED satisfy an infinite hierarchy of soft photon theorems, the first two of which are Weinberg and Low's theorems respectively. In this paper we propose that in tree level massless QED, this entire hierarchy is equivalent to a hierarchy of (asymptotic) conservation laws. We prove the equivalence explicitly for the case of sub-subleading soft photon theorem and give substantial evidence that the equivalence continues to hold for the entire hierarchy. Our work also brings out the (complimentary) relationship between the asymptotic…
We give two double copy prescriptions which construct asymptotically flat solutions in gravity from asymptotically flat gauge fields. The first prescription applies to radiative fields, which are non-linear vacuum solutions determined by characteristic data at null infinity. For any two such radiative gauge fields (linear or non-linear), the characteristic data of a radiative metric, dilaton and axion is constructed by a simple `squaring' procedure, giving a classical double copy at the level of radiation fields. We demonstrate the procedure with several examples where the characteristic data …
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.
A new sufficient condition for photons emitted near future null infinity to reach future null infinity is derived by studying null geodesics in the Bondi coordinates in asymptotically flat spacetimes. In our previous works [arXiv:2106.03150, arXiv:2110.10917], such a condition was established for photons emitted in outward or tangential directions to constant radial surfaces. This paper improves our previous result by including photons emitted in inward directions. In four dimensions, imposing the same assumptions on the metric functions as previously, we prove that photons reach future null i…
We analyze the asymptotic symmetries and their associated charges at spatial infinity in $4$-dimensional asymptotically-flat spacetimes. We use the covariant formalism of Ashtekar and Hansen where the asymptotic fields and symmetries live on the $3$-manifold of spatial directions at spatial infinity, represented by a timelike unit-hyperboloid (or de Sitter space). Using the covariant phase space formalism, we derive formulae for the charges corresponding to asymptotic supertranslations and Lorentz symmetries at spatial infinity. With the motivation of, eventually, proving that these charges ma…
On any asymptotically-flat spacetime, we show that the asymptotic symmetries and charges of Maxwell fields on past null infinity can be related to those on future null infinity as recently proposed by Strominger. We extend the covariant formalism of Ashtekar and Hansen by constructing a 3-manifold of both null and spatial directions of approach to spatial infinity. This allows us to systematically impose appropriate regularity conditions on the Maxwell fields near spatial infinity along null directions. The Maxwell equations on this 3-manifold and the regularity conditions imply that the relev…
We show that the BMS-supertranslations and their associated supermomenta on past null infinity can be related to those on future null infinity, proving the conjecture of Strominger for a class of spacetimes which are asymptotically-flat in the sense of Ashtekar and Hansen. Using a cylindrical 3-manifold of both null and spatial directions of approach towards spatial infinity, we impose appropriate regularity conditions on the Weyl tensor near spatial infinity along null directions. The asymptotic Einstein equations on this 3-manifold and the regularity conditions imply that the relevant Weyl t…
