Questions tagged [post-newtonian]
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58 questions
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Lagrangian of a system of relativistic charged particles
I was studying Landau's Classical Field Theory: Volume 2 and came across the Lagrangian for a system of charged particles, up to first-order post-Newtonian corrections ($65), which can be expressed as:...
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Formulating the dynamics of mass distribution in Newton-Cartan gravity
I am a mathematician following the lectures of Schuller about General Relativity, in particular this lecture. My main motivation is to understand how do we use Einstein field equation to model a ...
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Does General Relativity predict Mercury's orbital precession without other planets?
From Newtonian mechanics, the precession of Mercury can be calculated by taking into account the gravitational pull of other planets. From that, I assume that in the absence of external planets, ...
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Special relativity in PPN formalism
It is known that in the parameterized post-Newtonian formalism, the effective force (centripetal) can be expressed as
$$F=-\frac{GMm}{r^2}$$
multiplied by a factor of
$$1+(2+2\gamma-\beta)(v/c)^2,$$
...
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Extreme Mass Ratio Inspirals and GWs cycles
I was reading through the following paper GRMHD study of accreting massive black hole binaries in astrophysical environment: A review. Therein, we have the following image
It is not quite clear how ...
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How do we interpret measurements of Mercury's position?
When scientists measured the position of Mercury in the 18th century, they interpreted the results assuming a Euclidean background, because they did not know general relativity. So they measured $r$ ...
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Confusion about Post-Newtonian orbital motion (Damour-Deruelle)
In their famous paper in 1985 (link), Damour&Deruelle describe the orbital motion for a binary system taking into account first-order post-Newtonian corrections (1PN). The solution is given in ...
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Help to approximately invert Post Newtonian expression [closed]
Can anyone advice how to perform some sort of Taylor series approximation to compute the inverse of the following expression for $t(v)$ i.e. to obtain $v(t)$. Thanks!
$$
t(v) = t_0 - \frac{5M}{256\eta ...
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GR correction to perihelion precession comparing with newtonian orbit
My professor did the following derivation of the formula for the perihelion precession $\delta \phi = \frac{6\pi G M}{a(1-e^2)}$, but I am missing a factor of 2. I would appreciate if someone can help ...
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Order of magnitude of time derivatives of gravitational potential and gravitational vector potential on Earth
[This question is connected with this one. Since the estimation and measurement of spatial gradients and time derivatives have very different levels of difficulties, I thought it best to ask two ...
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Order of magnitude of gravitational vector potential & its gradient on Earth
In post-Newtonian approximation of gravitation, the metric on and around the Earth is taken to have the expression
$$
\begin{bmatrix}
-1+\frac{2}{c^2}U+ \frac{2}{c^4}(\psi-U^2) + \mathrm{O}(c^{-5})
&...
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Post-Newtonian Stress-Energy tensor
I am currently studying Michele Maggiore's book - 'Gravitational Waves: Volume 1: Theory and Experiments'. On pages 245 and 246, each order --- until the second order --- of the stress-energy tensor. ...
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Newtonian 2-Body problem
The Newtonian equations of motion for two-point masses $m$ and $m^{\prime}$ are derived from the following Lagrangian:
$$L = \frac{1}{2}m\mathbf{v}^{2} + \frac{1}{2}m^{\prime}\mathbf{v}^{\prime \, 2} +...
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Relativistic Corrections to orbital elements
Given a massive compact object $M$ and a smaller object $m$ orbiting it in an elliptical orbit where $M \gg m$, Newtonian gravity describes the orbital elements $(a, e, i, \omega, \Omega, T)$, such as ...
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Question about integral with second derivative of Newtonian potential (Weinberg 9.9)
I have a question about an integration that i found in Weinberg-Gravitation (1972), specifically in 9.9 about Post-Newtonian approximation of Brans-Dicke theory. We need to solve at order $O(2)$ an ...
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How to do taylor expansion of metric tensor to get Lagrangian for first Post-Newtonian order? [closed]
For the two-body compact object system how to write Lagrangian after obtaining first post-Newtonian metric tensor(just gravitational field)? Considering the perturbation in the metric as $$gαβ=ηαβ+hαβ,...
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Mass redshift degeneracy for binary black holes at all order in post-Newtonian perturbation theory
When you compute the inspiral signals of a binary black hole to lowest order in the post-Newtonian formalism, and study how this solution propagates through an expanding spacetime, you find that the ...
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Is the Laplace-Runge-Lenz vector applicable for test particle motion around black holes?
In classical mechanics , the Laplace-Runge-Lenz (LRL) vector is a characteristic feature of the Kepler problem. This enables a very simple discussion of the properties of the orbit for the problem. It ...
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Parameterized post-Newtonian formalism of Newtonian mechanics
Please kindly advise why the parameters $\gamma$ and $\beta$ are both zero for classical Newtonian mechanics (see attached screenshot of Wikipedia (the page about Binet's equation)) instead of $\gamma ...
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Approximation concerning gravitational waves from binary neutron star
I'm interested in studying two neutron stars orbiting each other and producing gravitational waves. In textbooks the calculation for the power of the radiation is done by considering the neutron stars ...
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Under PPN Formalism, would the gravity of a mass double as its velocity approaches $c$?
I'm looking at the answer Michael gave to my question. Does this imply that under parameterized post-Newtonian formalism, under the $β1$ factor for kinetic energy, the gravity of a mass doubles as it ...
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Gravitational wave radiation power from dimensional analysis
Let us try to find a formula for the power emitted through gravitational waves (GW) from a binary system in quasi circular orbit. The relevant quantities are the Newton's constant $G_N$, speed of ...
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What's wrong with Abraham's proposed force law in Nordström's first theory of gravity?
Nordström's 1912 proposed theory of relativistic gravity posited that the gravitational potential field $\phi$ and the matter density field $\rho$ are both scalar fields, simply related by the wave ...
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At the other edge beyond Newton with General Relativity? #2
The Schwarzschild solution is derived by using the static, spherically symmetric solution
$$ds^2=-B(r)dt^2 + A(r) dr^2 +\text{angular terms},$$
assuming a concentrated mass, therefore gaining $A=1/B$ ...
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Would Newton's law in the solar system be independent from a presumed different fundamental gravitational law? [closed]
A thought experiment:
Let's assume the gravitational field of a black hole without any neighbors would be stronger than the Schwarzschild metric in the Newtonian limit.
Now, we let a solar system (sun ...
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What is the current status of the convergence of the post-Newtonian approximation?
In the very well written article by C. Will, On the Unreasonable Effectiveness of the post-Newtonian Approximation in Gravitational Physics, he states:
The one question that remains open is the ...
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As of 2021 in how many binary systems has the period decrease due to gravitational waves been measured?
I am searching for data for the period decrease of binary systems due to gravitational waves. I am aware of three systems in which it was possible to measure this period decrease:
The Hulse-Taylor ...
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Gravitational waves in the post-Newtonian expansion
I have spent some time trying to understand gravitational waves in the context of the post-Newtonian expansion.
As far as I understand it, the general relativistic equation of motion can be ...
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How to calculate coordinate acceleration in general relativity (without going to the Newtonian domain)?
The below quote is from Gravitation and Cosmology by Weinberg. I don't understand the calculations leading to equation $(9.1.2)$. Any help or alternative resources will be helpful.
1 The Post-...
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The order of the time-space components of the metric tensor in post-Newtonian expansion
In the book Gravitational waves Vol.1: theory and experiment by M.Maggiore, in chapter 5, page 239, the author announces that when we expand the metric tensor by $v \over c$, the components $g_{0i}$ ...
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Does Newton's Theory with Retarded potentials give rise to the motion of perihelion of Planets
If we take into account the retarded potentials and the motion of the Sun(due to the planet), does Newton's Gravitational theory give rise to the motion of Perihelion of planets (qualitatively, not ...
user300251
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General relativity modifies Newton's inverse square law of gravity. Why do many people do experiments to test the inverse square law?
General relativity may induce the so-called post-Newtonian correction to the inverse square law of gravity. For details, please refer to chapter 9 of Weinberg's Gravitation and Cosmology.
However, ...
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Adding two tensors in different coordinate systems
I have difficulties understanding the following (Everything out of the book Gravity by Poisson and Clifford): We have a quantity $\mathfrak{g}^{\alpha \beta}$ called gothic inverse metric in prior ...
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Newtonian approximation of the metric tensor
I was reading Dirac's General Theory of Relativity. In chapter 16, the Newtonian approximation, we start with
Let us consider a static gravitational field and refer it to a static coordinate system. ...
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Precession of perihelion of Mercury?
I have a few questions about precession of Mercury and GR corrections. Feel free to any that you can:
GR is used to correct precession caused by Sun on Mercury by time dilation and length contraction....
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Hyperbolic orbit to keplerian orbit
How do I model a two body system that is initially travelling on an unbound orbit (hyperbolic so negative semi major axis) but then becomes a bound orbit (eccentric elliptic, so positive semi major ...
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Gravitional Force of Mercury in General Relativity
I have been searching everywhere for the first order GR term that describes the gravitational force of a mass.
Could someone kindly show me the term that describes this?
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Why do gravitational waves circularize a binary?
I understand that a binary orbiting around one another will circularize due to the emission of GWs due to Peters equations and that highly eccentric binaries evolve faster.
But GW emission also ...
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When does the Post-Newtonian expansion break down?
In the book Gravitational waves Vol.1: theory and experiment by M.Maggiore, in chapter 5, page 236, the author discusses the Post-Newtonian (PN) expansion and says that it is valid for small speed and ...
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What's the difference between a post-Minkowskian approximation and a post-Newtonian one?
I'm studying the book Gravity by Poisson & Will. Specifically, I'm interested in the post-Newtonian and post-Minkowskian approximations showed in chapters 6-10. The problem I'm having is ...
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Taking the speed of light into account during $n$-body simulation
Currently, I compute the force between two gravitational interacting particles in a simulation with $n$ bodies according to
$$F = G\frac{m_1m_2}{r^2}.$$
Doing this, however, assumes that all bodies in ...
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How to find the terms of Post-Newtonian approximation?
I am studying the Damour paper on the Post-Minkowskian approximation to the 2 bodies problem in General Relativity (paper) but can't really understand the explanation of the previous state of the art, ...
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What does `weakly gravitating' mean?
When relativists like Bousso (see for instance https://arxiv.org/abs/hep-th/0203101) talk about `weakly gravitating systems', what sense of weak gravity is usually meant?
(1) Post-Newtonian ...
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Help with calculating the Ricci tensor for the PPN formalism
I'm trying to follow the calculation done by Will in his book Theory and experiment in gravitational physics, and I was hoping for some help in calculating the Ricci tensor components in Section 5.2 (...
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3PN and higher order post-Newtonian Schwarzschild approximation
This expression can be found in documentation from the JPL determining the relativistic acceleration under Schwarzschild conditions in the euclidean approximation they use to calculate the orbits of ...
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How to get space component of weak field (linearized) metric?
For Minkowski space with a weak gravitational field the metric takes the form
$$
ds^2 = (1+2\phi/c^2)c^2dt^2 -(1-2\phi/c^2)(dx^2+dy^2+dz^2),
$$
where $\phi$ is the Newtonian gravitational potential.
...
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Experimental limits on non-Newtonian gravitational force at length scales larger than 1 meter?
This answer from 2012 shows some information on an exponential term characterized by relative strength and range parameters $\alpha$ and $\lambda$,
One potential tested here is here
$$V(r)=-G\frac{...
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What are modern solar system applications of GR where approximation methods fail? [closed]
It is often stated that general relativity (GR) provides the most accurate description of gravitational phenomenon. In most undergraduate and even graduate textbooks this idea is reinforced by ...
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Light dispersion in gravitational theories
GR predicts no Ricci curvature in vacuum (or at least when we can ignore the cosmological constant). Would theories that violate this lead to observable light dispersion in solar system tests of ...
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How to obtain components of the metric tensor?
In coordinates given by $x^\mu = (ct,x,y,z)$ the line element is given
$$ (ds)^2 = g_{00} (cdt)^2 + 2g_{0i}(cdt\;dx^i) + g_{ij}dx^idx^j, $$
where the $g_{\mu\nu}$ are the components of the metric ...
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