We continue a previous work on the comparison between the post-Newtonian (PN) approximation and the gravitational self-force (SF) analysis of circular orbits in a Schwarzschild background. We show that the numerical SF data contain physical information corresponding to extremely high PN approximations. We find that knowing analytically determined appropriate PN parameters helps tremendously in allowing the numerical data to be used to obtain higher order PN coefficients. Using standard PN theory we compute analytically the leading 4PN and the next-to-leading 5PN logarithmic terms in the conservative part of the dynamics of a compact binary system. The numerical perturbative SF results support well the analytic PN calculations through first order in the mass ratio, and are used to accurately measure the 4PN and 5PN non-logarithmic coefficients in a particular gauge invariant observable. Furthermore we are able to give estimates of higher order contributions up to the 7PN level. We also confirm with high precision the value of the 3PN coefficient. This interplay between PN and SF efforts is important for the synthesis of template waveforms of extreme mass ratio inspirals to be analysed by the space-based gravitational wave instrument LISA. Our work will also have an impact on efforts that combine numerical results in a quantitative analytical framework so as to generate complete inspiral waveforms for the ground-based detection of gravitational waves by instruments such as LIGO and Virgo.
With the post-Newtonian approxination, the energy of Schwarzschild spacetime in the Weinberg prescription is obtained. The energy for the first post-Newtonian approximation $E^{(1)} = m$ gives the Newtonian treatment of Schwarzschild spacetime. However, for the second post-Newtonian approximation, the erergy is shown that $E^{(1)}$ adds extra terms $E^{(2)}$ which consist of the energy stored in the configuration $E_{\rm config}$, in the gravitational field $E_{\rm field}$. and a term of surface integral. These extra terms gives post-Newtonian corrections to the Newtonian treatment.
We examine the orbital dynamics of the planar pseudo-Newtonian Copenhagen problem, in the case of a binary system of Schwarzschild-like primaries, such as super-massive black holes. In particular, we investigate how the Jacobi constant (which is directly connected with the energy of the orbits) influences several aspects of the orbital dynamics, such as the final state of the orbits. We also determine how the relativistic effects (i.e., the Schwarzschild radius) affect the character of the orbits, by comparing our results with the classical Newtonian problem. Basin diagrams are deployed for pr…
Confirming and improving post-Newtonian and effective-one-body results from self-force computations along eccentric orbits around a Schwarzschild black hole
我们解析计算，通过6.5后牛顿秩序，二阶的Detweiler-Barack-Sago规范不变红移函数的偏心率部分的小质量在偏心轨道上围绕史瓦西黑洞。利用力学第一定律求解偏心轨道[A. Le Tiec，Phys. Rev. D { \bf 92}，084021（2015）]我们将我们的结果转录为有效单体形式主义的第二径向势的相应准确知识[A. Buonanno和T. Damour，Phys. Rev. D { \bf 59}，084006（1999）]。我们比较了我们新获得的分析信息，几个不同的数值自作用力数据，并发现很好的协议，估计误差范围内。我们还获得，第一次，独立的分析检查最近导出的，比较质量的第四后牛顿阶动力学[T。Damour，P. Jaranowski和G. Shaefer，Phys. Rev. D { \bf 89}，064058（2014）]。
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.
Analytic self-force calculations in the post-Newtonian regime: eccentric orbits on a Schwarzschild background
本文提出了一种求解一阶后牛顿（PN）展开场方程的方法。我们的计算推广了Bini和Damour以及随后Kavanagh等人的工作，考虑史瓦西背景下的偏心轨道。我们推导出所有$\ell$模式的粒子位置的延迟度规扰动的表达式。我们发现，尽管第一次出现，Regge-Wheeler规范度规扰动是$C^0$在所有$\ell$的粒子。作为第一次使用我们的解决方案，我们计算规范不变量$\langle U \rangle$通过4PN，同时扩大偏心率通过$e^{10}$。通过预测每个PN阶的$e\to 1$奇异行为，我们大大提高了我们的结果的精度为大$e$。我们使用$\langle U \rangle$通过$e^{10}$和在质量比的线性顺序找到有效的单体势$\hat Q$的4PN贡献。
We study the circular orbits of charged particles around a weakly charged Schwarzschild black hole immersed in a weak, axisymmetric magnetic field. We start by reviewing the circular orbits of neutral particles and charged particles around only weakly charged and only weakly magnetized black holes. The case of a weakly magnetized and charged black hole is investigated then. In particular, we study the effect of the electromagnetic forces on the charged particles innermost stable circular orbits. We show that negative energy stable circular orbits are possible and that two bands of charged part…
We compute gravitational self-force corrections to tidal invariants for spinning particles moving along circular orbits in a Schwarzschild spacetime. In particular, we consider the square and the cube of the gravitoelectric quadrupolar tidal tensor and the square of the gravitomagnetic quadrupolar tidal tensor. Our results are accurate to first-order in spin and through the 9.5 post-Newtonian order. We also compute the associated electric-type and magnetic-type eigenvalues.
Spherical harmonic modes of 5.5 post-Newtonian gravitational wave polarizations and associated factorized resummed waveforms for a particle in circular orbit around a Schwarzschild black hol
Finding Schwarzschild metric component grr and FLRW's k without solving the Einstein's equation, rather by a synergistic matching between geometric results enfranchised by Newtonian gravity
Post-Newtonian expansion of gravitational waves from a particle in circular orbits around a rotating black hole: Up to $O(v^8)$ beyond the quadrupole formula
本文推广了Sasaki在Schwarzschild情况下和Shibata，Sasaki，Tagoshi和Tanaka在Kerr情况下提出的方法，计算了从绕旋转黑洞的圆形轨道上的测试粒子到四极公式之外的$O(v^8)$的引力波光度的后牛顿展开。试验粒子的轨道被限制在赤道平面上。我们发现，自旋相关的条款出现在每个后牛顿的顺序，并在$O(v^6)$，他们有一个显着的影响轨道相的演变合并紧凑的双星。通过比较后牛顿公式和数值计算结果发现，对于$30M\lesssim r \lesssim 100M$，$O(v^6)$和$O(v^7)$处的自旋相关项显著提高了后牛顿公式的精度，而$O(v^8)$处的自旋相关项没有提高.
In this paper we investigate circular orbits for test particles around Schwarzschild-de Sitter (dS) black hole surrounded by perfect fluid dark matter. We determine the region of circular orbits bounded by innermost and outermost stable circular orbits. We show that the impact of the perfect fluid dark matter shrinks the region where circular orbits can exist as the values of both innermost and outermost stable circular orbits decrease. We find that for specific lower and upper values of dark matter parameter there exist double matching values for inner and outermost stable circular orbits. It…
In the first and second post-Newtonian approximation of the Schwarzschild metric, I obtain the energy component of the Einstein and Møller energy-momentum complex. Both energies involve the rest-mass energy $m$, the energy stored in the configuration and that in the gravitational field, but the energies of Schwarzschild spacetime in the Einstein and Møller prescriptions are the total mass-energy $M$. First, for general relativity, the rest-mass energy $m$ in the flat spacetime behaves like the bare mass, and the total mass-energy $M$ in the curved spacetime behaves like the experimentally obse…
Analytic self-force effects on radial infalling particles in the Schwarzschild spacetime: the radiated energy
Istituto per le Applicazioni del Calcolo “M. Picone,” CNR（意大利国家研究委员会计算应用研究所）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（杭州高等研究院基础物理与数学科学学院，中国科学院大学）
We study the dynamics of test particle and stability of circular geodesics in the gravitational field of a non-commutative geometry inspired Schwarzschild black hole spacetime (NCSBH). The coordinate time Lyapunov exponent ($λ_{c}$) is crucial to investigate the stability of equatorial circular geodesics of massive and massless test particles. The stability or instability of circular orbits are discussed by analysing the variation of Lyapunov exponent with radius of these orbits for different values of non-commutative parameter ($α$). In the case of null circular orbits, the instability expone…
We study the metric perturbations induced by a classical spinning particle moving along a circular orbit on a Schwarzschild background, limiting the analysis to effects which are first order in spin. The particle is assumed to move on the equatorial plane and has its spin aligned with the $z$-axis. The metric perturbations are obtained by using two different approaches, i.e., by working in two different gauges: the Regge-Wheeler gauge (using the Regge-Wheeler-Zerilli formalism) and a radiation gauge (using the Teukolsky formalism). We then compute the linear-in-spin contribution to the first-o…
We compute the first-order self-force contribution to Detweiler's redshift invariant for extended bodies endowed with both dipolar and quadrupolar structure (with spin-induced quadrupole moment) moving along circular orbits on a Schwarzschild background. Our analysis includes effects which are second order in spin, generalizing previous results for purely spinning particles. The perturbing body is assumed to move on the equatorial plane, the associated spin vector being orthogonal to it. The metric perturbations are obtained by using a standard gravitational self-force approach in a radiation …
Taming the post-Newtonian expansion: Simplifying the modes of the gravitational wave energy flux at infinity for a point particle in a circular orbit around a Schwarzschild black hole
