The metric outside an isolated object made up of ordinary matter is bound to be the classical Schwarzschild vacuum solution of General Relativity. Nevertheless, some solutions are known (e.g. Morris-Thorne wormholes) that do not match Schwarzschild asymptotically. On a phenomenological point of view, gravitational lensing in metrics falling as $1/r^q$ has recently attracted great interest. In this work, we explore the conditions on the source matter for constructing static spherically symmetric metrics exhibiting an arbitrary power-law as Newtonian limit. For such space-times we also derive the expressions of gravitational redshift and force on probe masses, which, together with light deflection, can be used in astrophysical searches of non-Schwarzschild objects made up of exotic matter. Interestingly, we prove that even a minimally coupled scalar field with a power-law potential can support non-Schwarzschild metrics with arbitrary asymptotic behaviour.
Schwarzschild black-hole immersed in an electric or magnetic background in Entangled Relativity
Artemis, Université Côte d’Azur, CNRS, Observatoire Côte d’Azur（阿耳特弥斯，蔚蓝海岸大学，法国国家科学研究中心，蔚蓝海岸天文台）；Bureau des Affaires Spatiales（空间事务局）；Departament de Física Quántica i Astrofísica (FQA), Universitat de Barcelona (UB)（巴塞罗那大学量子物理与天体物理学系）
We show that mass parameter and radial coordinate values can be indirectly measured in thought experiments performed in Schwarzschild spacetime, without using the Newtonian limit of general relativity or approximations based on Euclidean geometry. Our approach involves different proper time quantifcations as well as solutions to systems of algebraic equations, and aims to strengthen the conceptual independence of general relativity from Newtonian gravity.
Seeing relativity -- I. Ray tracing in a Schwarzschild metric to explore the maximal analytic extension of the metric and making a proper rendering of the stars
In this manuscript, we show that the external Schwarzschild metric can be a good approximation of exact black hole solutions of entangled relativity. Since entangled relativity cannot be defined from vacuum, the demonstrations need to rely on the definition of matter fields. The electromagnetic field being the easiest (and perhaps the only) existing matter field with infinite range to consider, we study the case of a charged black hole -- for which the solution of entangled relativity and a dilaton theory agree -- as well as the case of a pure radiation -- for which the solution of entangled r…
Dynamical Tidal Response of Schwarzschild Black Holes
Université Paris Cité（巴黎西岱大学）；The University of Chicago（芝加哥大学）；Utah State University（犹他州立大学）；Harvard University（哈佛大学）；Universidad Autonoma de Madrid（马德里自治大学）
From Geometry to Gravity: A Friendly Introduction to the Schwarzschild Metric
Facultad de Ciencias Básicas, Departamento de Física（基础科学学院物理系）；Centro de desarrollo de Investigación CEDI-UMCE（CEDI-UMCE研究中心）；Universidad Metropolitana de Ciencias de la Educación（教育科学都会大学）
We investigate static and spherically symmetric solutions in the Minimal Theory of Bigravity (MTBG). First, we show that a pair of Schwarzschild-de Sitter spacetimes with different cosmological constants and black hole masses written in the spatially-flat Gullstrand-Painlevé (GP) coordinates is a solution in the self-accelerating branch of MTBG, while it cannot be a solution in the normal branch. We then illustrate how Schwarzschild-de Sitter solutions can become compatible with the normal branch when using different coordinates. We also confirm that the self-accelerating branch of MTBG admits…
Symplectic integrators that preserve the geometric structure of Hamiltonian flows and do not exhibit secular growth in energy errors are suitable for the long-term integration of N-body Hamiltonian systems in the solar system. However, the construction of explicit symplectic integrators is frequently difficult in general relativity because all variables are inseparable. Moreover, even if two analytically integrable splitting parts exist in a relativistic Hamiltonian, all analytical solutions are not explicit functions of proper time. Naturally, implicit symplectic integrators, such as the midp…
Testing gravity theory in the strong field region becomes a reality due to the observations of gravitational waves and black hole shadows. In this paper, we discuss how to constrain the possible deviations of the classical general relativity with the image of M87* observed by the Event Horizon Telescope. More precisely, we want to know where is the event horizon for a non-rotating black hole. General relativity predicts the horizon is located at the Schwarzschild radius $r_\textrm{s}$, while other gravity theories may give different predictions. We propose a parameterized Schwarzschild metric …
Schwarzschild-de Sitter Metric and Inertial Beltrami Coordinates
在考虑坐标条件下，得到了具有宇宙学常数$Λ$的爱因斯坦场方程的Schwarzschild-Beltrami-deSitter（S-BdS）度规解.本文对de Sitter不变狭义相对论（dS-SR）和de Sitter广义相对论（dS-GR，或GR with a $Λ$）作了简要的评述。Beltrami度规$B_{μν}$为dS时空提供了惯性参考系。通过对1918年以来文献中的Schwarzschild-de Sitter（S-dS）度规$g_{μν}^{(M)}$的考察，发现已有的S-dS度规$g_{μν}^{(M)}$描述的是引力和惯性力的混合效应，而不是dS-GR中“太阳质量”$g_{μν}^{(M)}|_{M\rightarrow 0}=B_{μν}$引起的纯引力效应。这样，我们找到了dS-GR的S-BdS解，写在惯性Beltrami坐标中。这是S-dS度量的一种新形式。讨论了它的物理意义和可能的应用。
The two-body problem in general relativity is reduced to the problem of an effective particle (with an energy-dependent relativistic reduced mass) in an external field. The effective potential is evaluated from the Born diagram of the linearized quantum theory of gravity. It reduces to a Schwarzschild-like potential with two different `Schwarzschild radii'. The results derived in a weak field approximation are expected to be relevant for relativistic velocities.
Within the theory of General Relativity, we study the solution and range of applicability of the standard geodesic deviation equation in highly symmetric spacetimes. In the Schwarzschild spacetime, the solution is used to model satellite orbit constellations and their deviations around a spherically symmetric Earth model. We investigate the spatial shape and orbital elements of perturbations of circular reference curves. In particular, we reconsider the deviation equation in Newtonian gravity and then determine relativistic effects within the theory of General Relativity by comparison. The dev…
The binary potential technique of interpolation (by M. Riesz, Acta Math. 81, 1 (1949)) is applied to some well-known metrics of general relativity. These include Schwarzschild, de Sitter and 2+1-dimensional BTZ spacetimes. In particular, the Schwarzschild-de Sitter solution is analyzed in some detail with a finite range parameter. Reasoning by the high level of non-linearity and absence of a superposition law necessitates search for alternative approaches. We propose the method of interpolation between different spacetimes as one such possibility paving the way toward controlling the two-metri…
