On the static Lovelock black holes

Self Cite

It is well known that Einstein gravity is kinematic (meaning that there is no non-trivial vacuum solution; i.e. the Riemann tensor vanishes whenever the Ricci tensor does so) in 3 dimension because the Riemann tensor is entirely given in terms of the Ricci tensor. Could this property be universalized for all odd dimensions in a generalized theory? The answer is yes, and this property uniquely singles out pure Lovelock (it has only one N th order term in the action) gravity for which the N th order Lovelock-Riemann tensor is indeed given in terms of the corresponding Ricci tensor for all odd, d = 2N + 1, dimensions. This feature of gravity is realized only in higher dimensions and it uniquely picks out pure Lovelock gravity from all other generalizations of Einstein gravity. It serves as a good distinguishing and guiding criterion for the gravitational equation in higher dimensions.

Section: Gravitational Equation In Higher Dimensionsmentioning

confidence: 99%

A distinguishing gravitational property for gravitational equation in higher dimensions

Dadhich

2016

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“…In Einstein gravity potential goes as 1/r d−3 that takes the familiar 1/r form only in four dimensions and none else. In contrast, for pure Lovelock it goes as 1/r α with α = (d − 2m − 1)/m [15], and hence there exists dimension spectrum d = 3m + 1 for 1/r potential. It should be emphasized that we are interested in exact solutions of gravitational field equations, not just Newtonian limit and hence must be contrasted with earlier approaches in [30,31].…”

Section: Introductionmentioning

confidence: 96%

“…Finally pure Lovelock theories, i.e., a single term in the Lovelock polynomial, exhibit very interesting features. These include -(a) there is a close connection between pure Lovelock and dimensionally continued black holes [15,16], (b) gravity is kinematic in all critical d = 2m +1 dimensions, i.e., vacuum is pure Lovelock flat [17], (c) bound orbits exist for a given m in all 2m +1 < d < 4m +1 dimensions, in contrast, for Einstein gravity they do so only in four dimensions [18] and finally (d) equipartition of gravitational and non-gravitational energy defines location of black hole horizon [19].…”

Section: Introductionmentioning

confidence: 99%

1/r potential in higher dimensions

Chakraborty

Dadhich

2018

Self Cite

In Einstein gravity, gravitational potential goes as 1/r d−3 in d non-compactified spacetime dimensions, which assumes the familiar 1/r form in four dimensions. On the other hand, it goes as 1/r α , with α = (d −2m −1)/m, in pure Lovelock gravity involving only one mth order term of the Lovelock polynomial in the gravitational action. The latter offers a novel possibility of having 1/r potential for the noncompactified dimension spectrum given by d = 3m+1. Thus it turns out that in the two prototype gravitational settings of isolated objects, like black holes and the universe as a whole -cosmological models, the Einstein gravity in four and mth order pure Lovelock gravity in 3m + 1 dimensions behave in a similar fashion as far as gravitational interactions are considered. However propagation of gravitational waves (or the number of degrees of freedom) does indeed serve as a discriminator because it has two polarizations only in four dimensions.

“…EGB is the N = 2 case of the Lovelock polynomial. Vacuum solutions have been determined for Lovelock gravity in general [20][21][22] as well as for dimensionally continued [5,[23][24][25], and also for pure Lovelock black holes [26,27]. Sharma [28] showed that the limiting case of the polytropic fluid may be regarded as isothermal and is important in the study of clusters of stars.…”

Section: Introductionmentioning

confidence: 99%

Generalized spheroidal spacetimes in 5-D Einstein–Maxwell–Gauss–Bonnet gravity

Hansraj

2017

The field equations for static EGBM gravity are obtained and transformed to an equivalent form through a coordinate redefinition. A form for one of the metric potentials that generalizes the spheroidal ansatz of Vaidya-Tikekar superdense stars and additionally prescribing the electric field intensity yields viable solutions. Some special cases of the general solution are considered and analogous classes in the Einstein framework are studied. In particular the FinchSkea ansatz is examined in detail and found to satisfy the elementary physical requirements. These include positivity of pressure and density, the existence of a pressure free hypersurface marking the boundary, continuity with the exterior metric, a subluminal sound speed as well as the energy conditions. Moreover, the solution possesses no coordinate singularities. It is found that the impact of the Gauss-Bonnet term is to correct undesirable features in the pressure profile and sound speed index when compared to the equivalent Einstein gravity model. Furthermore graphical analyses suggest that higher densities are achievable for the same radial values when compared to the 5-dimensional Einstein case. The case of a constant gravitational potential, isothermal distribution as well as an incompressible fluid are studied. All exact solutions derived exhibit an equation of state explicitly.