Massive Shell Models in the Gravitational Theories with Higher Derivatives

Abstract

The model of a. thin massive shell is investigated in the framework of gravitational theories with fourth-order derivatives. The corresponding jump conditions are derived, and their possible consequences for structure and motion of the matter sources are shortly discussed. The results are compared with the conditions obtained in General Relativity Theory. Schalenmodelle in Cfravitationstheorien mit htiheren AbleitungenI n h a l t s u b e r s i c h t . Es werden masse-behaftete diinne Schalenmodelle im Rahmen von Gravitationstheorien vierter Ordnung untersucht. Die entsprechenden Sprungbedingungen werden abgeleitet und die Bewegung der Materiequellen kurz diskutiert. Die Resultate werden mit den in der Allgemeinen Relativitiitstheorie erhaltenen verglichen.

Screening and Absorption of Gravitation in Pre-Relativistic and Relativistic Theories

“…The discussion of these equations performed in [18] shows that both cases are characterized in that they possess, besides massless gravitons, only one kind of gravitons with non-vanishing restmass. (These results were corroborated by subsequent considerations [8,10].) In the linear approximation for static fields with the Hilbert coordinate condition…”

“…Moreover, the transition to gravitational theories that are formulated in Riemann-Cartan space is mainly motivated by the fact that then the spin-density of matter (or spin current) can couple to the postRiemannian structure. 10 Therefore, the full content of this theory becomes only obvious when one considers the coupling of gravitation to spinorial matter.…”

“…Especially, it was shown [121,124] that, for physical reasons, the Einstein-Hilbert part of the Lagrangian must be necessarily included (for this point, see also [58]) and that one has to impose supplementary conditions on the matter source term. These considerations were continued in [18,19] (see also [8,9,10]). The consequences for singularities of massive bodies and cosmological collapse were also analyzed in [117,54].…”

Some static spherically symmetric interior solutions of f (R) gravity

“…The Israel junction conditions for f (R) theory can be found in the literature [37][38][39]. Choosing the coordinates so that the metric is in the form:…”

Higher-order brane gravity models

“…Similar approach was used for less-general f (R) theories of gravity on the brane by Borzeszkowski and Frolov [13]; Parry at al. [14], Deruelle et al [15], and for f (X,Y, Z) = aX 2 + bY + cZ (a, b, c = const.)…”