On gravitational instability of the interstellar gas

Bertotti, B.; Cavaliere, A.

doi:10.1007/bf00653940

“…In Ashby and Bertotti (1986) the transformation X p + ( t , r ' ) and the metric h' was explicitly constructed in the important, but particular case in which there is only one external body (the Sun) and one point-like local body (the Earth); with the aim of studying the general properties of the non-linear interaction term Shoo we generalise the procedure of Ashby and Bertotti (1984) to solve the appropriate field equation for Shoo. In this way we can consider finite bodies and avoid the problem of the singularity; we also include the effect of the Moon and a generic external curvature, for example, one produced by gravitational waves (see, e.g., Bertotti 1973).…”

Section: -+ ~ ~ ( T ) R ~R ~+ ~( R ' )mentioning

confidence: 99%

The strong equivalence principle

Bertotti¹,

Grishchuk²

1990

Class. Quantum Grav.

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Consider C n spaces where the exterior differentiation of a vector basis of C2 functions leads to a Cartan matrix of exterior differential 1-forms. A second exterior differentiation leads to a Cartan matrix of curvature 2forms, which must evaluate to zero, by the Poincare lemma. The Cartan connection matrix can be decomposed in to two parts, one part based on a metric (Christoffel) connection, and the other part on a residue matrix of 1-forms such that [C] = [Γ]+[T ]. The exterior differential of the composite connection must vanish such that the curvature 2-forms produced by the metric component must be balanced by all other matrices of 2-forms coming from the Residue connection and interaction 2-forms generated by exterior products of the [Γ] and [Γ]. The result must balance to zero. If the curvature 2-forms generated by the metric based connection are associated with Gravity, and the rest of the curvature 2-forms are associated with-Inertia, the result is a strong principle of equivalence: Gravity curvature 2-forms equal Inertial curvature 2-forms.

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“…Concerning the possible existence of a background of gravitational waves dating back to the origin of the universe, see, e.g., Weber [42]; Wheeler [43]; Zel'dovich and Novikov [44]; Carr [45], and the discussion in Mashhoon et al [46]. The effects of incident gravitational waves on the orbital motion of gravitationally bound systems were inspected by several authors with a variety of approaches and approximations pertaining various features of both the waves and the orbits themselves [46,[47][48][49][50][51][52][53][54][55][56][57][58][59][60][61]. The idea of using the solar system to try to detect a stochastic background of gravitational waves of wavelengths much larger than about 1 au was first suggested by Bertotti [47].…”

Section: Introductionmentioning

confidence: 99%

“…The effects of incident gravitational waves on the orbital motion of gravitationally bound systems were inspected by several authors with a variety of approaches and approximations pertaining various features of both the waves and the orbits themselves [46,[47][48][49][50][51][52][53][54][55][56][57][58][59][60][61]. The idea of using the solar system to try to detect a stochastic background of gravitational waves of wavelengths much larger than about 1 au was first suggested by Bertotti [47]. At first sight, the calculations presented here may be regarded just as an academic exercise with respect to empirical celestial mechanics, although such an allegation may sound somewhat bizarre in view of the large amount of more or less analogous studies existing in literature concerning all sort of putative modified models of gravity based on much less solid theoretical and/or empirical support with respect to a GTR prediction like gravitational waves.…”

Section: Introductionmentioning

confidence: 99%

Orbital effects of a monochromatic plane gravitational wave with ultra-low frequency incident on a gravitationally bound two-body system

2014

ScienceOpen Astronomy &Amp; Astrophysics

0

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show abstract

“…Concerning the possible existence of a background of gravitational waves dating back to the origin of the universe, see, e.g., Weber [42]; Wheeler [43]; Zel'dovich and Novikov [44]; Carr [45], and the discussion in Mashhoon et al [46]. The effects of incident gravitational waves on the orbital motion of gravitationally bound systems were inspected by several authors with a variety of approaches and approximations pertaining various features of both the waves and the orbits themselves [46,[47][48][49][50][51][52][53][54][55][56][57][58][59][60][61]. The idea of using the solar system to try to detect a stochastic background of gravitational waves of wavelengths much larger than about 1 au was first suggested by Bertotti [47].…”

mentioning

confidence: 99%

“…The effects of incident gravitational waves on the orbital motion of gravitationally bound systems were inspected by several authors with a variety of approaches and approximations pertaining various features of both the waves and the orbits themselves [46,[47][48][49][50][51][52][53][54][55][56][57][58][59][60][61]. The idea of using the solar system to try to detect a stochastic background of gravitational waves of wavelengths much larger than about 1 au was first suggested by Bertotti [47]. At first sight, the calculations presented here may be regarded just as an academic exercise with respect to empirical celestial mechanics, although such an allegation may sound somewhat bizarre in view of the large amount of more or less analogous studies existing in literature concerning all sort of putative modified models of gravity based on much less solid theoretical and/or empirical support with respect to a GTR prediction like gravitational waves.…”

mentioning

confidence: 99%

Orbital effects of a monochromatic plane gravitational wave with ultra-low frequency incident on a gravitationally bound two-body system

Efroimsky¹

2014

ScienceOpen Research

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We analytically compute the long-term orbital variations of a test particle orbiting a central body acted upon by an incident monochromatic plane gravitational wave. We assume that the characteristic size of the perturbed two-body system is much smaller than the wavelength of the wave. Moreover, we also suppose that the wave's frequency n g is much smaller than the particle's orbital one n b . We make neither a priori assumptions about the direction of the wavevector b k nor on the orbital configuration of the particle. While the semi-major axis a is left unaffected, the eccentricity e, the inclination I, the longitude of the ascending node Ω, the longitude of pericenter ϖ and the mean anomaly M undergo non-vanishing long-term changes of the form dW=dt ¼ FðK ij ; e; I; X; xÞ; W ¼ e; I; X; -; M, where K ij ; i; j ¼ 1; 2; 3 are the coefficients of the tidal matrix K. Thus, in addition to the variations of its orientation in space, the shape of the orbit would be altered as well. Strictly speaking, such effects are not secular trends because of the slow modulation introduced by K and by the orbital elements themselves: they exhibit peculiar long-term temporal patterns which would be potentially of help for their detection in multidecadal analyses of extended data records of planetary observations of various kinds. In particular, they could be useful in performing independent tests of the inflation-driven ultra-low gravitational waves whose imprint may have been indirectly detected in the Cosmic Microwave Background by the Earthbased experiment BICEP2. Our calculation holds, in general, for any gravitationally bound two-body system whose orbital frequency n b is much larger than the frequency n g of the external wave, like, e.g., extrasolar planets and the stars orbiting the Galactic black hole. It is also valid for a generic perturbation of tidal type with constant coefficients over timescales of the order of the orbital period of the perturbed particle.

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On gravitational instability of the interstellar gas

Cited by 4 publications

References 14 publications

The strong equivalence principle

The strong equivalence principle

Orbital effects of a monochromatic plane gravitational wave with ultra-low frequency incident on a gravitationally bound two-body system

Orbital effects of a monochromatic plane gravitational wave with ultra-low frequency incident on a gravitationally bound two-body system

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