Similar to the Schwarzschild coordinates for spherical black holes, the Baldwin, Jeffery and Rosen (BJR) coordinates for plane gravitational waves are often singular, and extensions beyond such singularities are necessary, before studying asymptotic properties of such spacetimes at the null infinity of the plane, on which the gravitational waves propagate. The latter is closely related to the studies of memory effects and soft graviton theorems. In this paper, we point out that in the BJR coordinates all the spacetimes are singular physically at the focused point $u = u_s$, except for the two cases: (1) $α=1/2, \; \forall \; χ_n$; and (2) $α=1, \; χ_i = 0\; (i = 1, 2, 3)$, where $χ_n$ are the coefficients in the expansion $χ\equiv \left[{\mbox{det}}\left(g_{ab}\right) \right]^{1/4} = \left(u - u_s\right)^α\sum_{n = 0}^{\infty}χ_n \left(u - u_s\right)^n$ with $χ_0 \not= 0$, the constant $α\in (0, 1]$ characterizes the strength of the singularities, and $g_{ab}$ denotes the reduced metric on the two-dimensional plane orthogonal to the propagation direction of the wave. Therefore, the hypersurfaces $u= u_s$ already represent the boundaries of such spacetimes, and the null infinity does not belong to them. As a result, they cannot be used to study properties of plane gravitational waves at null infinities, including memory effects and soft graviton theorems.
We consider the perturbation of the Schwarzschild solution by the perimeter action. The asymptotic behaviour of the solution at infinity and at the horizon are calculated and analysed in the first approximation. The perturbation is characterised by the ratio of the Plank length to the Schwarzschild radius. It is demonstrated that in the modified theory appear space-time regions of the Schwarzschild radius scale that are unreachable by test particles. These regions are located in the places where standard theory of gravity has singularities.
What happens to a massive star at the end of its life cycle is one of the most important and intriguing questions in theoretical physics. An unhindered gravitational collapse of such a sufficiently massive star can give rise to a spacetime singularity. This thesis discusses the phenomenon of such unhindered gravitational collapse and the causal structure of the singularity thus formed.
In this paper, we will investigate the consequences of loop quantum gravitational modifications on the formation of naked singularities. The loop quantum gravitational effects will be incorporated in the collapsing system using gravity's rainbow. This will be done by using rainbow functions, which are constructed from loop quantum gravitational modifications to the energy momentum dispersion. It will be observed that this modification will prevent the formation of naked singularity. Thus, such a modification can ensures that the weak cosmic censorship hypothesis will hold for any collapsing sy…
The number of strong lens systems is expected to increase significantly in ongoing and upcoming surveys. With an increase in the total number of such systems we expect to discover many configurations that correspond to unstable caustics. In such cases, the instability can be used to our advantage for constraining the lens model. We have implemented algorithms for detection of different types of singularities in gravitational lensing. We test our approach on a variety of lens models and then go on to apply it to the inferred mass distribution for Abell 697 as an example application. We propose …
This note emphasizes the role of multi-scale wave structures and junction conditions in many fields of physics, from the dynamics of fluids with non-convex equations of state to the study of gravitational singularities and bouncing cosmologies in general relativity. Concerning the definition and construction of bouncing spacetimes, we review the recent proposal in collaboration with B. Le Floch and G. Veneziano based on the notion of singularity scattering maps. We also present recent numerical investigations of small-scale phenomena arising in compressible fluid flows on FRLW or Kasner geomet…
On gravitational collapse and integrable singularities
Università di Bologna（博洛尼亚大学）；I.N.F.N., Sezione di Bologna（意大利国家核物理研究所博洛尼亚分部）；Alma Mater Research Center on Applied Mathematics (AM)（阿尔特玛母应用数学研究中心）；Universidad de Tarapacá（塔拉帕卡大学）
We derive a particular approximate solution of Einstein equations, describing the gravitational field of a mass distribution that slightly deviates from spherical symmetry. The deviation is described by means of a quadrupole parameter that is responsible for the appearance of a curvature singularity, which is not covered by a horizon. We investigate the motion of test particles in the gravitational field of this naked singularity and show that the quadrupole parameter affects the properties of Schwarzschild trajectories. By investigating radial geodesics, we find that no effects of repulsive g…
In this paper, we analyze the deflection angle of light by Brane-Dicke wormhole in the weak field limit approximation to find the effect of the Brane-Dicke coupling parameter on the weak gravitation lensing. For this purpose, we consider new geometric techniques, i.e., Gauss-Bonnet theorem and optical geometry in order to calculate the deflection angle. Furthermore, we verify our results by considering the most familiar geodesic technique. Moreover, we establish the quantum corrected metric of Brane-Dicke wormhole by replacing the classical geodesic with Bohmian trajectories, whose matter sour…
Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland（马里兰大学凝聚态理论中心与联合量子研究所）；Department of Physics and Astronomy and Rice Center for Quantum Materials, Rice University（莱斯大学物理与天文学系及量子材料中心）
The spatial modulation of the Fermi velocity for gapless Dirac electrons in quantum materials is mathematically equivalent to the problem of massless fermions on a certain class of curved spacetime manifolds. We study null geodesic lensing through these manifolds, which are dominated by curvature singularities, such as nematic singularity walls (where the Dirac cone flattens along one direction). Null geodesics lens across these walls, but do so by perfectly collimating to a local transit angle. Nevertheless, nematic walls can trap null geodesics into stable or metastable orbits characterized …
We solve a $1+5$-dimensional cylindrical gravitational-wave solution of the Einstein equation, in which there are two curvature singularities. Then we show that one of the curvature singularities can be removed by an extension of the spacetime. The result exemplifies that the curvature singularity is not always a spacetime singularity; in other words, the curvature singularity cannot serve as a criterion for spacetime singularities.
Motivated by quantum-mechanical considerations we earlier suggested an alternative action for discretised quantum gravity which measures the perimeter of the space-time and has a dimension of length. It is the so called perimeter action, since it is a "square root" of the area action in gravity and has a new constant of dimension one in front. The physical reason to introduce the perimeter/linear action was to suppress singular configurations "spikes" in the quantum-mechanical integral over geometries. Here we shall consider the continuous limit of the discretised perimeter/linear action. We s…
We explore the consequences of requiring that quantum theories of gravity be unitary, mostly focusing on simple cosmological models to illustrate the main points. We show that unitarity for a clock that encounters a classical singularity at finite time implies quantum singularity resolution, but for a clock that encounters future infinity at finite time leads to a quantum recollapse. We then find that our starting point - assuming the general covariance of general relativity - is actually incompatible with general quantum unitarity: singularity resolution in quantum gravity can always be engin…
Gravitational wave memory is an important prediction of general relativity, which has not been detected yet. Amounts of memory events can form a stochastic gravitational wave memory background. Here we find that memory background can be described as a Brownian motion in the condition that the observation time is longer than the averaged time interval between two successive memory events. We investigate, for the first time, the memory background of binary black hole coalescences. We only consider the spectrum of the memory background for a relatively low frequency range. So we can use the step …
