Gravitation

About: Gravitation is a research topic. Over the lifetime, 29306 publications have been published within this topic receiving 821510 citations.

Introduction to Modified Gravity and Gravitational Alternative for Dark Energy

Abstract: We review various modified gravities considered as gravitational alternative for dark energy. Specifically, we consider the versions of $f(R)$, $f(G)$ or $f(R,G)$ gravity, model with non-linear gravitational coupling or string-inspired model with Gauss-Bonnet-dilaton coupling in the late universe where they lead to cosmic speed-up. It is shown that some of such theories may pass the Solar System tests. On the same time, it is demonstrated that they have quite rich cosmological structure: they may naturally describe the effective (cosmological constant, quintessence or phantom) late-time era with a possible transition from decceleration to acceleration thanks to gravitational terms which increase with scalar curvature decrease. The possibility to explain the coincidence problem as the manifestation of the universe expansion in such models is mentioned. The late (phantom or quintessence) universe filled with dark fluid with inhomogeneous equation of state (where inhomogeneous terms are originated from the modified gravity) is also described.

Superrotation Charge and Supertranslation Hair on Black Holes

Abstract: It is shown that black hole spacetimes in classical Einstein gravity are characterized by, in addition to their ADM mass M, momentum $$ \overrightarrow{P} $$ , angular momentum $$ \overrightarrow{J} $$ and boost charge $$ \overrightarrow{K} $$ , an infinite head of supertranslation hair. The distinct black holes are distinguished by classical superrotation charges measured at infinity. Solutions with super-translation hair are diffeomorphic to the Schwarzschild spacetime, but the diffeomorphisms are part of the BMS subgroup and act nontrivially on the physical phase space. It is shown that a black hole can be supertranslated by throwing in an asymmetric shock wave. A leading-order Bondi-gauge expression is derived for the linearized horizon supertranslation charge and shown to generate, via the Dirac bracket, supertranslations on the linearized phase space of gravitational excitations of the horizon. The considerations of this paper are largely classical augmented by comments on their implications for the quantum theory.

Celestial mechanics, conformal structures, and gravitational waves.

Abstract: Newton's equations for the motion of $N$ nonrelativistic point particles attracting according to the inverse square law may be cast in the form of equations for null geodesics in a ($3N+2$)-dimensional Lorentzian spacetime which is Ricci flat and admits a covariantly constant null vector. Such a spacetime admits a Bargmann structure and corresponds physically to a plane-fronted gravitational wave (generalized pp wave). Bargmann electromagnetism in five dimensions actually comprises the two distinct Galilean electromagnetic theories pointed out by Le Bellac and L\'evy-Leblond. At the quantum level, the $N$-body Schr\"odinger equation may be cast into the form of a massless wave equation. We exploit the conformal symmetries of such spacetimes to discuss some properties of the Newtonian $N$-body problem, in particular, (i) homographic solutions, (ii) the virial theorem, (iii) Kepler's third law, (iv) the Lagrange-Laplace-Runge-Lenz vector arising from three conformal Killing two-tensors, and (v) the motion under time-dependent inverse-square-law forces whose strength varies inversely as time in a manner originally envisaged by Dirac in his theory of a time-dependent gravitational constant $G(t)$. It is found that the problem can be reduced to one with time-independent inverse-square-law forces for a rescaled position vector and a new time variable. This transformation (Vinti and Lynden-Bell) is shown to arise from a particular conformal transformation of spacetime which preserves the Ricci-flat condition originally pointed out by Brinkmann. We also point out (vi) a Ricci-flat metric representing a system of $N$ nonrelativistic gravitational dyons. Our results for a general time-dependent $G(t)$ are also applicable by suitable reinterpretation to the motion of point particles in an expanding universe. Finally we extend these results to the quantum regime.

Viking relativity experiment - Verification of signal retardation by solar gravity

Abstract: Analysis of 14 months of data obtained from radio ranging to the Viking spacecraft verified, to an estimated accuracy of 0.1%, the prediction of the general theory of relativity that the round-trip times of light signals traveling between the earth and Mars are increased by the direct effect of solar gravity. The corresponding value for the metric parameter gamma is 1.000 plus or minus 0.002, where the quoted uncertainty, twice the formal standard deviation, allows for possible systematic errors.