On Lovelock analogs of the Riemann tensor
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In this article, it was shown that any pure Lovelock vacuum in odd d = 2N + 1 dimensions is LovelOCK flat, i.e., any vacuum solution of the theory has vanishing Lovelocks-Riemann tensor.Abstract:
It is possible to define an analogue of the Riemann tensor for Nth order Lovelock gravity, its characterizing property being that the trace of its Bianchi derivative yields the corresponding analogue of the Einstein tensor. Interestingly there exist two parallel but distinct such analogues and the main purpose of this note is to reconcile both these formulations. In addition we will show that any pure Lovelock vacuum in odd d = 2N + 1 dimensions is Lovelock flat, i.e. any vacuum solution of the theory has vanishing Lovelock-Riemann tensor. Further, in presence of cosmological constant it is the Lovelock-Weyl tensor that vanishes.read more
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A way of decoupling gravitational sources in pure Lovelock gravity
TL;DR: In this paper, an algorithm for decoupling gravitational sources in Pure Lovelock gravity was proposed, which allows to obtain several new and known analytic solutions of physical interest in scenarios with extra dimensions and with presence of higher curvature terms.
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A distinguishing gravitational property for gravitational equation in higher dimensions
Naresh Dadhich,Naresh Dadhich +1 more
TL;DR: In this paper, it was shown that pure Lovelock gravity has only one Nth order term in the action and that the Ricci tensor is the only Riemann tensor that can be given in terms of the corresponding L 1 for all O(d = 2N+1) dimensions.
Journal ArticleDOI
A way of decoupling gravitational sources in pure Lovelock gravity
TL;DR: In this paper, an algorithm for decoupling gravitational sources in pure Lovelock gravity is presented. But the method is not suitable for scenarios with extra dimensions and with presence of higher curvature terms.
Journal ArticleDOI
A discerning gravitational property for gravitational equ ation in higher dimensions
TL;DR: In this paper, it was shown that pure Lovelock gravity is kinematic in 3D and that Riemann vanishes whenever Ricci does so, and this property can be generalized to all odd dimensions in a generalized theory.
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Buchdahl–Vaidya–Tikekar model for stellar interior in pure Lovelock gravity
TL;DR: Khugaev et al. as discussed by the authors showed that the pressure isotropy equation for Buchdahl-Vaidya-Tikekar metric ansatz has the same Gauss form in higher dimensions, and hence higher dimensional solutions could be obtained by redefining the space geometry characterizing Vaidya Tikekar parameter K. In this paper we extend this analysis to pure Lovelock gravity; i.e. a $$(2N+2)$$ -dimensional solution with a given
References
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The Lovelock gravity in the critical spacetime dimension
TL;DR: It is well known that the vacuum in the pure Lovelock gravity is always trivial in the odd critical (2 n + 1 ) dimension which means it is pure lovelock flat but it is not Riemann flat unless n = 1 as mentioned in this paper.
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Characterization of the Lovelock gravity by Bianchi derivative
TL;DR: In this article, it was shown that the second-order quasilinear differential operator as a second-rank divergence-free tensor in the equation of motion for gravitation could always be derived from the trace of the Bianchi derivative of the fourth-rank tensor, which is a homogeneous polynomial in curvatures.
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On the Bianchi identities
TL;DR: In this article, it was shown that a diffeomorphism of hypersurfaces preserving normal curvature is a congruence under certain conditions and an Riemann curvature tensor preserving sectional curvatures is an isometry.
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Thermodynamical universality of the Lovelock black holes
TL;DR: The necessary and sufficient condition for the thermodynamical universality of the static spherically symmetric Lovelock black hole is that it is the Nth order pure LovelOCK Λ-vacuum solution as discussed by the authors.
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The Riemann-Lovelock Curvature Tensor
TL;DR: In this paper, it was shown that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k ⩽ D < 4k.