scholarly journals PHENOMENOLOGICAL CONSTRAINTS ON THE KEHAGIAS–SFETSOS SOLUTION IN THE HOŘAVA–LIFSHITZ GRAVITY FROM SOLAR SYSTEM ORBITAL MOTIONS

2010 ◽  
Vol 25 (29) ◽  
pp. 5399-5408 ◽  
Author(s):  
L. IORIO ◽  
M. L. RUGGIERO
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Solar System ◽  
Slow Motion ◽  
Analytical Form ◽  
Weak Field ◽  
Schwarzschild Black Hole ◽  
Anomalous Acceleration ◽  
Motion Approximation ◽  
General Relativistic

We focus on Hořava–Lifshitz (HL) theory of gravity, and, in particular, on the Kehagias and Sfetsos's solution that is the analog of Schwarzschild black hole of General Relativity. In the weak-field and slow-motion approximation, we analytically work out the secular precession of the longitude of the pericentre ϖ of a test particle induced by this solution. Its analytical form is different from that of the general relativistic Einstein's pericentre precession. Then, we compare it to the latest determinations of the corrections [Formula: see text] to the standard Newtonian/Einsteinian planetary perihelion precessions recently estimated by E. V. Pitjeva with the EPM2008 ephemerides. It turns out that the planets of the solar system, taken singularly one at a time, allow one to put lower bounds on the adimensional HL parameter ψ0 of the order of 10-12(Mercury)-10-24 (Pluto). They are not able to account for the Pioneer anomalous acceleration for r > 20 AU.

On claims that general relativity differs from Newtonian physics for self-gravitating dusts in the low velocity, weak field limit

2015 ◽  
Vol 24 (08) ◽  
pp. 1550065 ◽  
Author(s):  
David R. Rowland
Keyword(s):  
General Relativity ◽  
Solar System ◽  
Relativistic Effects ◽  
Weak Field ◽  
Newtonian Gravity ◽  
Galactic Rotation ◽  
Low Velocity ◽  
Rotation Curves ◽  
Newtonian Physics ◽  
General Relativistic

Galaxy rotation curves are generally analyzed theoretically using Newtonian physics; however, two groups of authors have claimed that for self-gravitating dusts, general relativity (GR) makes significantly different predictions to Newtonian physics, even in the weak field, low velocity limit. One group has even gone so far as to claim that nonlinear general relativistic effects can explain flat galactic rotation curves without the need for cold dark matter. These claims seem to contradict the well-known fact that the weak field, low velocity, low pressure correspondence limit of GR is Newtonian gravity, as evidenced by solar system tests. Both groups of authors claim that their conclusions do not contradict this fact, with Cooperstock and Tieu arguing that the reason is that for the solar system, we have test particles orbiting a central gravitating body, whereas for a galaxy, each star is both an orbiting body and a contributor to the net gravitational field, and this supposedly makes a difference due to nonlinear general relativistic effects. Given the significance of these claims for analyses of the flat galactic rotation curve problem, this article compares the predictions of GR and Newtonian gravity for three cases of self-gravitating dusts for which the exact general relativistic solutions are known. These investigations reveal that GR and Newtonian gravity are in excellent agreement in the appropriate limits, thus supporting the conventional use of Newtonian physics to analyze galactic rotation curves. These analyses also reveal some sources of error in the referred to works.

scholarly journals A GRAVITOMAGNETIC EFFECT ON THE ORBIT OF A TEST BODY DUE TO THE EARTH'S VARIABLE ANGULAR MOMENTUM

2002 ◽  
Vol 11 (05) ◽  
pp. 781-787 ◽  
Author(s):  
LORENZO IORIO
Keyword(s):  
Angular Momentum ◽  
Test Particle ◽  
Equations Of Motion ◽  
Time Derivative ◽  
Slow Motion ◽  
Weak Field ◽  
Test Body ◽  
Angular Velocity Vector ◽  
Motion Approximation ◽  
General Relativistic

The well known general relativistic Lense–Thirring drag of the orbit of a test particle in the stationary field of a central slowly rotating body is generated, in the weak-field and slow-motion approximation of General Relativity, by a gravitomagnetic Lorentz-like acceleration in the equations of motion of the test particle. In it the gravitomagnetic field is due to the central body's angular momentum supposed to be constant. In the context of the gravitational analogue of the Larmor theorem, such acceleration looks like a Coriolis inertial term in an accelerated frame. In this paper the effect of the variation in time of the central body's angular momentum on the orbit of a test mass is considered. It can be shown that it is analogue to the inertial acceleration due to the time derivative of the angular velocity vector of an accelerated frame. The possibility of detecting such effect in the gravitational field of the Earth with LAGEOS-like satellites is investigated. It turns out that the orbital effects are far too small to be measured.

Complex Spacetimes and the Newman-Janis Trick

2021 ◽  
Author(s):  
◽  
Del Rajan
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Mathematical Theory ◽  
Kerr Black Hole ◽  
Complex Variables ◽  
Complex Manifolds ◽  
Schwarzschild Black Hole ◽  
The Subject ◽  
Short Method

<p>In this thesis, we explore the subject of complex spacetimes, in which the mathematical theory of complex manifolds gets modified for application to General Relativity. We will also explore the mysterious Newman-Janis trick, which is an elementary and quite short method to obtain the Kerr black hole from the Schwarzschild black hole through the use of complex variables. This exposition will cover variations of the Newman-Janis trick, partial explanations, as well as original contributions.</p>

scholarly journals A precise extragalactic test of General Relativity

Science ◽  
2018 ◽  
Vol 360 (6395) ◽  
pp. 1342-1346 ◽  
Author(s):  
Thomas E. Collett ◽  
Lindsay J. Oldham ◽  
Russell J. Smith ◽  
Matthew W. Auger ◽  
Kyle B. Westfall ◽  
...  
Keyword(s):  
General Relativity ◽  
Solar System ◽  
Long Range ◽  
Weak Field ◽  
Gravitational Lens ◽  
Stellar Kinematics ◽  
Spatial Curvature ◽  
Spatially Resolved ◽  
Consistent Model ◽  
Self Consistent

Einstein’s theory of gravity, General Relativity, has been precisely tested on Solar System scales, but the long-range nature of gravity is still poorly constrained. The nearby strong gravitational lens ESO 325-G004 provides a laboratory to probe the weak-field regime of gravity and measure the spatial curvature generated per unit mass, γ. By reconstructing the observed light profile of the lensed arcs and the observed spatially resolved stellar kinematics with a single self-consistent model, we conclude that γ = 0.97 ± 0.09 at 68% confidence. Our result is consistent with the prediction of 1 from General Relativity and provides a strong extragalactic constraint on the weak-field metric of gravity.

scholarly journals The Gravitomagnetism in the Solar System

2017 ◽  
Vol 45 ◽  
pp. 1760052
Author(s):  
Flavia Rocha ◽  
Manuel Malheiro ◽  
Rubens Marinho
Keyword(s):  
Mass Density ◽  
Slow Motion ◽  
Weak Field ◽  
Einstein Equations ◽  
Dipole Potential ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Perihelion Advance ◽  
Motion Approximation

In 1918, Joseph Lense and Hans Thirring discovered the gravitomagnetic (GM) effect of Einstein field equations in weak field and slow motion approximation. They showed that Einstein equations in this approximation can be written as in the same form as Maxwell’s equation for electromagnetism. In these equations the charge and electric current are replaced by the mass density and the mass current. Thus, the gravitomagnetism formalism in astrophysical system is used with the mass assuming the role of the charge. In this work, we present the deduction of gravitoelectromagnetic equations and the analogue of the Lorentz force in the gravitomagnetism. We also discuss the problem of Mercury’s perihelion advance orbit, we propose solutions using GM formalism using a dipole-dipole potential for the Sun-Planet interaction.

scholarly journals ENERGY ASSOCIATED WITH SCHWARZSCHILD BLACK HOLE IN A MAGNETIC UNIVERSE

2000 ◽  
Vol 15 (19) ◽  
pp. 2979-2986 ◽  
Author(s):  
S. S. XULU
Keyword(s):  
Magnetic Field ◽  
Black Hole ◽  
Uniform Magnetic Field ◽  
Relativistic Effect ◽  
Rest Mass ◽  
Mass Energy ◽  
Schwarzschild Black Hole ◽  
General Relativistic ◽  
The Magnetic Field ◽  
General Relativistic Effect

In this paper we obtain the energy distribution associated with the Ernst space–time (geometry describing Schwarzschild black hole in Melvin's magnetic universe) in Einstein's prescription. The first term is the rest-mass energy of the Schwarzschild black hole, the second term is the classical value for the energy of the uniform magnetic field and the remaining terms in the expression are due to the general relativistic effect. The presence of the magnetic field is found to increase the energy of the system.

scholarly journals RELXILL_NK: A Black Hole Relativistic Reflection Model for Testing General Relativity

Proceedings ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 7 ◽  
Author(s):  
Askar B. Abdikamalov ◽  
Dimitry Ayzenberg ◽  
Cosimo Bambi  ◽  
Sourabh Nampalliwar
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Relativistic Effects ◽  
Asymptotically Flat ◽  
X Ray ◽  
Black Hole Accretion ◽  
Reflection Model ◽  
Black Hole Spacetime ◽  
General Relativistic ◽  
Hole Accretion

In this paper, we briefly present RELXILL_NK, the first and currently only readily available model of the relativistic reflection spectrum of black hole accretion disks that includes non-Kerr solutions for the black hole spacetime, thus allowing for tests of the Kerr hypothesis and general relativity (GR). RELXILL_NK makes use of a general relativistic ray-tracing code to calculate the relativistic effects of any well-behaved, stationary, axisymmetric, and asymptotically flat black hole spacetime, while the disk physics is handled through the non-relativistic X-ray reflection code XILLVER. A number of different flavors are available within RELXILL_NK; we summarize and compare these flavors using the Johannsen metric for the black hole spacetime.

scholarly journals On the foundations of general relativistic celestial mechanics

2017 ◽  
Vol 32 (26) ◽  
pp. 1730022 ◽  
Author(s):  
Emmanuele Battista ◽  
Giampiero Esposito ◽  
Simone Dell’Agnello
Keyword(s):  
General Relativity ◽  
Solar System ◽  
Celestial Mechanics ◽  
Body Problem ◽  
Equations Of Motion ◽  
Modern Science ◽  
N Body Problem ◽  
General Relativistic ◽  
New Perspective ◽  
Three Body

Towards the end of nineteenth century, Celestial Mechanics provided the most powerful tools to test Newtonian gravity in the solar system and also led to the discovery of chaos in modern science. Nowadays, in light of general relativity, Celestial Mechanics leads to a new perspective on the motion of satellites and planets. The reader is here introduced to the modern formulation of the problem of motion, following what the leaders in the field have been teaching since the nineties, in particular, the use of a global chart for the overall dynamics of N bodies and N local charts describing the internal dynamics of each body. The next logical step studies in detail how to split the N-body problem into two sub-problems concerning the internal and external dynamics, how to achieve the effacement properties that would allow a decoupling of the two sub-problems, how to define external-potential-effacing coordinates and how to generalize the Newtonian multipole and tidal moments. The review paper ends with an assessment of the nonlocal equations of motion obtained within such a framework, a description of the modifications induced by general relativity on the theoretical analysis of the Newtonian three-body problem, and a mention of the potentialities of the analysis of solar-system metric data carried out with the Planetary Ephemeris Program.

scholarly journals Wave properties of plasma surrounding the event horizon of a nonrotating black hole

2008 ◽  
Vol 86 (11) ◽  
pp. 1265-1285 ◽  
Author(s):  
M Sharif ◽  
G Mustafa
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Schwarzschild Black Hole ◽  
Magnetohydrodynamics Equations ◽  
Normal Dispersion ◽  
Isothermal Plasma ◽  
General Relativistic ◽  
Relativistic Magnetohydrodynamics ◽  
Wave Properties ◽  
Complex Dispersion

We study the wave properties of a cold isothermal plasma in the vicinity of a Schwarzschild black-hole event horizon. The Fourier-analyzed perturbed 3+1 general relativistic magnetohydrodynamics equations are examined such that the complex dispersion relations are obtained for nonrotating, rotating nonmagnetized, and rotating magnetized backgrounds. The propagation and attenuation vectors along with the refractive index are obtained (shown graphically) to study the dispersive properties of the medium near the event horizon. The results show that no information can be obtained from the Schwarzschild magnetosphere. Further, the pressure stops the existence of normal dispersion of waves.PACS Nos.: 95.30.Sf, 95.30.Qd, 04.30.Nk

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