Method of the Self-Consistent Field in General Relativity and its Application to the Gravitational Geon

Brill, Dieter R.; Hartle, James B.

doi:10.1103/physrev.135.b271

Cited by 207 publications

(243 citation statements)

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“…Here Γ (ℓ)α µν is the Christoffel connection at order ℓ. In accordance with the Brill-Hartle-Isaacson averaging procedure for gravitational waves of small amplitude and wavelength much shorter than any background curvature radius [62][63][64][65], one can ignore total derivatives in the stress tensor such as the first two terms in (6.1). Substituting the expression…”

Section: A Einstein-hilbert Quadratic Termsmentioning

confidence: 99%

Scalar gravitational waves in the effective theory of gravity

Mottola

2017

J. High Energ. Phys.

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As a low energy effective field theory, classical General Relativity receives an infrared relevant modification from the conformal trace anomaly of the energy-momentum tensor of massless, or nearly massless, quantum fields. The local form of the effective action associated with the trace anomaly is expressed in terms of a dynamical scalar field that couples to the conformal factor of the spacetime metric, allowing it to propagate over macroscopic distances. Linearized around flat spacetime, this semi-classical EFT admits scalar gravitational wave solutions in addition to the transversely polarized tensor waves of the classical Einstein theory. The amplitude of the scalar wave modes, as well as their energy and energy flux which are positive and contain a monopole moment, are computed. Astrophysical sources for scalar gravitational waves are considered, with the excited gluonic condensates in the interiors of neutron stars in merger events with other compact objects likely to provide the strongest burst signals.

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Section: A Einstein-hilbert Quadratic Termsmentioning

confidence: 99%

Scalar gravitational waves in the effective theory of gravity

Mottola

2017

J. High Energ. Phys.

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“…In the high-frequency approximation (ǫ ≪ 1, ε = 1) the dominant term is R (1) µν = O(ǫ −1 ) which gives the wave equation (6) for the perturbations h µν on the curved background γ µν (considering a vacuum full metric g µν ). The two terms of the order O(1), namely R (0) µν and R (2) µν , are both used to give the Einstein equation for the background non-vacuum metric, which represents the essential influence of the high-frequency gravitational waves on the background.…”

Section: High-frequency Approximation Versus Standard Linearizationmentioning

confidence: 99%

“…Interestingly, it follows that the wave equation for h µν , which arises from the linear perturbation of the Ricci tensor in vacuum for both the above limiting cases ε ≪ 1, ǫ = 1, and ǫ ≪ 1, ε = 1, is the same equation (6). In analogy with the well-known theory of massless spin-2 fields in flat space [4] we wish to impose two TT gauge conditions,…”

Section: Linear Approximationmentioning

confidence: 99%

“…Moreover, using the WKB approximation of T GW µν and the Brill-Hartle averaging procedure [6] (which guarantees the gauge invariance) Isaacson obtained for gravitational waves in the geometric optics limit the energy-momentum tensor [1]…”

Section: Gravitational Waves In the Wkb Approximationmentioning

confidence: 99%

“…The high-frequency perturbations were originally considered by Wheeler [5] and then applied to investigation of gravitational geons by Brill and Hartle [6]. Isaacson's systematic study [1] stimulated further works in which his treatment was developed and also re-formulated in various formalisms.…”

Section: Introductionmentioning

confidence: 99%

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Some High-Frequency Gravitational Waves Related to Exact Radiative Spacetimes

Podolský

Svítek

2004

General Relativity and Gravitation

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A formalism is introduced which may describe both standard linearized waves and gravitational waves in Isaacson's high-frequency limit. After emphasizing main differences between the two approximation techniques we generalize the Isaacson method to non-vacuum spacetimes. Then we present three large explicit classes of solutions for high-frequency gravitational waves in particular backgrounds. These involve non-expanding (plane, spherical or hyperboloidal), cylindrical, and expanding (spherical) waves propagating in various universes which may contain a cosmological constant and electromagnetic field. Relations of high-frequency gravitational perturbations of these types to corresponding exact radiative spacetimes are described.

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High‐frequency Waves in Gravitational Theories with Fourth‐order Derivative Equations

Borzeszkowski

1981

Annalen der Physik

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For Einstein's gravitational equations with fourth-order corrections being proportional to the square of an elementary length I, we discuss the behaviour of high-frequency waves. It is shown that (1) only waves with lengths 1 2 I can generate a macroscopic avarage background (for 1 < I, only the terms aP are decisive such that one has the same situation as in a pure fourth-order theory without Einstein term which cannot be interpreted as gravitational theory), (2) for 1 2 I, the background metric is purely determined via the second-order derivative Einstein tensor (formally one obtains the same equations for the background as in the non-modified Einsteinian theory), and (3) only waves correaponding to the massless and the massive spin-two gravitons contribute to background curvature; in the geometrical-optic8 approximation, these both particle sorts are moving independent of each other and satisfy a conservation law for the total number of m = 0 and massive spin-two gravitons, respectively.The results obtained in this paper corroborate partly the conclusions drawn in the weak-field approximation [ll, 15,181. Hochfrequente Wellen in aravitationstheorien mit Feldgleichungen vierter OrdnungInhaltsiibersicht. Das Verhalten hochfrequenter Wellen wird im Rahmen von Gravitationsfeldgleichungen diskutiert, die neben dem Einstein-Tensor Terme enthalten, welche einer elementaren Gnge 1 proportional sind und dritte und vierte Ableitungen der Metrik enthalten. Es wird gezeigt,(1) daB nur Wellen der Litnge 1 2 1 ein makroskopisches Hintergrundfeld eneugen (fiir 1 < I sind die Terme -Z2 in den Feldgleichungen entacheidend, so da8 sich dieselbe Situation wie in einer Theorie vierter Ordnung ohne Einstein-Term ergibt, die nicht als Gravitationstheorie interpretiert werden kann), (2) daB fur 1 2 Z der makroskopische Hintergrund allein durch den Einstein-Tensor bestimmt wird (man erhiilt fur den Hintergrund formal dieselben Gleichqen wie in der nicht modifizierten Einsteinschen Theorie) und (3) daB nur Wellen, die den masselosen und den massiven Gravitonen mit dem Spin 2 entsprechen, den Hintergrund erzeugen. Diese beiden Teilchensorten bewegen sich in der geometrischen Niiherung unabhiingig voneinander und geniigen jeweils einem eigenen Erhaltungssatz fiir die Gesamtzahl der masselosen und der massiven Spin-2-Teilchen.Die in dieser Arbeit vorgelegten Reaultate beatiitigen teilweise nuch die in [ll, 15, 181 fur schwache Felder in der linearen Niiherung gewonnenen Ergebnisse.

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Method of the Self-Consistent Field in General Relativity and its Application to the Gravitational Geon

Cited by 207 publications

References 11 publications

Scalar gravitational waves in the effective theory of gravity

Scalar gravitational waves in the effective theory of gravity

Some High-Frequency Gravitational Waves Related to Exact Radiative Spacetimes

High‐frequency Waves in Gravitational Theories with Fourth‐order Derivative Equations

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