Nishanth Gudapati
We consider 3+1 rotationally symmetric Lorentzian Einstein spacetime manifolds with $Λ>0$ and reduce the equations to 2+1 Einstein equations coupled to `shifted' wave maps. Subsequently, we prove various (explicit) positive mass-energy theorems. No smallness is assumed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Lorentzian homogeneous Ricci-flat metrics on almost abelian Lie groups
本文研究四维及以上近阿贝尔李群上的洛伦兹左不变度量，构造了推广的皮托夫解，该解为 Ricci-flat 但非平坦，并具有封闭类时曲线。
This paper is the first of three in which I study the moduli space of isometry classes of (compact) globally hyperbolic spacetimes (with boundary). I introduce a notion of Gromov-Hausdorff distance which makes this moduli space into a metric space. Further properties of this metric space are studied in the next papers. The importance of the work can be situated in fields such as cosmology, quantum gravity and - for the mathematicians - global Lorentzian geometry.
Lorentzian Cheeger-Gromov convergence and temporal functions
本文研究了洛伦兹Cheeger-Gromov收敛与时间函数的特性，提出了一种针对全局超曲面时空的特殊收敛概念，并探讨了时间函数的正则性、陡峭性及其稳定性。
Matter collineations of spherically Symmetric Lorentzian Manifolds are considered. These are investigated when the energy-momentum tensor is non-degenerate and also when it is degenerate. We have classified spacetimes admitting higher symmetries and spacetimes admitting SO(3) as the maximal isometry group. For the non-degenerate case, we obtain either {\it four}, {\it six}, {\it seven} or {\it ten} independent matter collineations in which {\it four} are isometries and the rest are proper. The results of the previous paper [1] are recovered as a special case. It is worth noting that we have al…
We undertake to show how the relativistic Finslerian Metric Function (FMF) should arise under uni-directional violation of spatial isotropy, keeping the condition that the indicatrix (mass-shell) is a space of constant negative curvature. By evaluating respective Finslerian tetrads, and treating them consistently as the bases of inertial reference frame (RF), the generalized Finslerian kinematic transformations follow in a convenient explicit form. The concomitant Finslerian relativistic relations generalize their Lorentzian prototypes through the presence of one characteristic parameter g, so…
We investigate the possibility of semigroup extensions of the isometry group of an identification space, in particular, of a compactified spacetime arising from an identification map $p: \RR^n_t \to \RR^n_t / Γ$, where $\RR^n_t$ is a flat pseudo-Euclidean covering space and $Γ$ is a discrete group of primitive lattice translations on this space. We show that the conditions under which such an extension is possible are related to the index of the metric on the subvector space spanned by the lattice vectors: If this restricted metric is Euclidean, no extensions are possible. Furthermore, we prov…
Isometries of spacetimes without observer horizons
研究了具有良好因果结构的非紧致洛伦兹流形的等距群，证明时间定向保持等距群在时空上作用良好，并推导出不变的因果时间函数及等距群的分裂结构。
The effects of SUSY on the emergent spacetime in the Lorentzian type IIB matrix model
本文研究了洛伦兹型 IIB 矩阵模型中 SUSY 对涌现时空的影响，证明此前发现的 (1+1) 维膨胀时空是洛伦兹 boost 假象，并发现包含费米子贡献后可能涌现出光滑的 (3+1) 维膨胀洛伦兹时空。
In a general Lorentzian manifold M, the past lightcone of a point is a proper subset of M that does not carry enough information to determine the rest of M. That said, if M is a globally hyperbolic Cauchy development of vacuum initial data on a Cauchy surface S and there is a point whose past lightcone contains S, then the contents of such a lightcone determines all of M (up to isometry). We show some results that describe what properties of M guarantee that past lightcones do indeed determine all or at least significant portions of M. Null lines and observer horizons, which are well known fea…
Spacetime reconstruction by order and number
本文证明两个时空的随机邻接矩阵分布相同当且仅当它们光滑等距，从而将因果集合论中仅凭“序”和“数”重建时空的范式严格化，并证实了Bombelli猜想的弱版本。
The type IIB matrix model is one of the most promising candidates for a nonperturbative formulation of superstring theory. In particular, its Lorentzian version was shown to exhibit an interesting real-time dynamics such as the spontaneous breaking of the 9-dimensional rotational symmetry to the 3-dimensional one. This result, however, was obtained after regularizing the original matrix integration by introducing "infrared" cutoffs on the quadratic moments of the Hermitian matrices. In this paper, we generalize the form of the cutoffs in such a way that it involves an arbitrary power ($2p$) of…
A Lorentzian manifold endowed with a time function, $τ$, can be converted into a metric space using the null distance, $\hat{d}_τ$, defined by Sormani and Vega. We show that if the time function is a proper regular cosmological time function as studied by Andersson, Galloway and Howard, and also by Wald and Yip, or if, more generally, it satisfies the anti-Lipschitz condition of Chruściel, Grant and Minguzzi, then the causal structure is encoded by the null distance in the following sense: $$ \hat{d}_τ(p,q)=τ(q)-τ(p) \iff q \textrm{ lies in the causal future of } p. $$ As a consequence, in dim…
In 4 spacetime dimensions there is a well known proof that for any asymptotically flat, stationary, and axisymmetric vacuum solution of Einstein's equation there exists a "$t$-$ϕ$" reflection isometry that reverses the direction of the timelike Killing vector field and the direction of the axial Killing vector field. However, this proof does not generalize to higher spacetime dimensions. Here we consider asymptotically flat, stationary, and axisymmetric (i.e., having one or more commuting rotational isometries) black hole spacetimes in vacuum general relativity in $d \geq 4$ spacetime dimensio…
A crucial step in the history of General Relativity was Einstein's adoption of the principle of general covariance which demands a coordinate independent formulation for our spacetime theories. General covariance helps us to disentangle a theory's substantive content from its merely representational artifacts. It is an indispensable tool for a modern understanding of spacetime theories. Motivated by quantum gravity, one may wish to extend these notions to quantum spacetime theories (whatever those are). Relatedly, one might want to extend these notions to discrete spacetime theories (i.e., lat…
Spacetime symmetries and geometric diffusion
通过Lorentzian流形的标架丛和观察者丛研究相对论性扩散，详细探讨具有非平凡等距群的时空中对称解的条件，分析Killing向量场的守恒律及其对测地线喷洒和垂直Laplacian的影响，并给出相关对称时空例子。
On the structure of big bang singularities in spatially homogenous solutions to the Einstein non-linear scalar field equations
本文研究空间齐次Einstein非线性标量场方程解中大爆炸奇点的结构，证明奇点初始数据与发展间存在双射，且两者的等距类集合具有光滑结构并由Einstein流生成微分同胚，同时证明了一类解的全局非线性稳定性。
The Harmonic Einstein equation is the vacuum Einstein equation supplemented by a gauge fixing term which we take to be that of DeTurck. For static black holes analytically continued to Riemannian manifolds without boundary at the horizon this equation has previously been shown to be elliptic, and Ricci flow and Newton's method provide good numerical algorithms to solve it. Here we extend these techniques to the arbitrary cohomogeneity stationary case which must be treated in Lorentzian signature. For stationary spacetimes with globally timelike Killing vector the Harmonic Einstein equation is …
"Ends of hyperbolic 3-manifolds should support canonical Wick Rotations, so they realize effective interactions of their ending globally hyperbolic spacetimes of constant curvature." We develop a consistent sector of WR-rescaling theory in 3D gravity, that, in particular, concretizes the above guess for many geometrically finite manifolds. ML(H2)-spacetimes are solutions of pure Lorentzian 3D gravity encoded by measured geodesic laminations of the hyperbolic plane H2, possibly invariant by any given torsion-free discrete isometry group G. The rescalings which correlate spacetimes of different …
We present in detail the Einstein equations in the Baumgarte-Shapiro-Shibata-Nakamura formulation for the case of $D$ dimensional spacetimes with $SO(D-d)$ isometry based on a method originally introduced in Ref.1. Regularized expressions are given for a numerical implementation of this method on a vertex centered grid including the origin of the quasi-radial coordinate that covers the extra dimensions with rotational symmetry. Axisymmetry, corresponding to the value $d=D-2$, represents a special case with fewer constraints on the vanishing of tensor components and is conveniently implemented …
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。