Ricci Collineations of Static Space Times with Maximal Symmetric Transverse Spaces

Abstract

Static space times with maximal symmetric transverse spaces are classified according to their Ricci collineations. These are investigated for non-degenerate Ricci tensor (det.(R α ) = 0). It turns out that the only collineations admitted by these spaces can be ten, seven, six or four. Some new metrics admitting proper Ricci collineations are also investigated.

Einstein's equations as a thermodynamic identity: The cases of stationary axisymmetric horizons and evolving spherically symmetric horizons

“…Since the extra, higher derivative terms in Lanczos-Lovelock gravity can be thought of as quantum corrections to GR, this non-trivial result suggests the possibility that the thermodynamic interpretation of the field equations remains valid even if one includes possible quantum corrections to Einstein-Hilbert action functional motivated by quantum gravity models. Further, it is possible to show that the Einstein equations evaluated on the apparent horizon is a thermodynamic identity [13] even in the case of Friedmann universe. Some other recent work attempts to provide the structural reasons for the existence of these results [10,11].…”

The relation between F(R) gravity and Einstein-conformally invariant Maxwell source

“…with F ′ (R) ≡ dF (R)/dR and T matt µν the standard matter stress-energy tensor derived from the matter Lagrangian L matt in the action (2). One can consider geometrical terms in the left hand side of the field equation, and therefore Eq.…”

“…The so-called modified gravities constructed by adding correction terms to the usual Einstein-Hilbert action (e.g: [2,3,4]), is only one endeavor among others to go beyond Einstein general relativity and have opened a new window to study the origin of the current accelerated expansion of the Universe [5,6,7]. For example in Lovelock gravity, there have been some attempts for understanding the role of the higher curvature terms from various points of view [4].…”

“…For example in Lovelock gravity, there have been some attempts for understanding the role of the higher curvature terms from various points of view [4]. As an another example, a special case of considering the effect of higher curvature corrections, we will deal with in this paper the so-called F (R) gravity [2] (and for a review, see, [8]), whose action is an arbitrary function of curvature scalar R. When F (R) = R, the Einstein's general relativity is recovered. Some of the main reasons to consider F (R) gravity * hendi@mail.yu.ac.ir are as follows: First of all, there is simplicity: F (R) actions are sufficiently general to encapsulate some of the basic characteristics of higher-order gravity, but at the same time they are simple enough to be easy to handle.…”

Ricci Symmetries of Static Space-Times with Maximal Symmetric Transverse Spaces

“…The constraint equations (18 -25) In this case, it follows from equation (21) that A i (t, r) = 0. Replacing A i (t, r) = 0 into constraint equations (18)(19)(20)(21)(22)(23)(24)(25), indicate that the equations (18)(19)(20)(21) are satisfied identically while the others get replace into the constraints on P (t, r) and Q(t, r). Integrating equations (24) yields…”