Higher Order Gravity Theories and Their Black Hole Solutions

By C. Charmousis. 2008

142 citations recorded by the source corpus.

In this chapter, we will discuss a particular higher order gravity theory, Lovelock theory, that generalises in higher dimensions than 4, general relativity. After briefly motivating modifications of gravity, we will introduce the theory in question and we will argue that it is a unique, mathematically sensible, and physically interesting extension of general relativity. We will see, by using the formalism of differential forms, the relation of Lovelock gravity to differential geometry and topology of even-dimensional manifolds. We will then discuss a generic staticity theorem, quite similar to Birkhoff’s theorem in general relativity, which will give us the charged static black hole solutions. We will examine their asymptotic behaviour, analyse their horizon structure and briefly their thermodynamics. For the thermodynamics we will give a geometric justification of why the usual entropy–area relation is broken. We will then examine the distributional matching conditions for Lovelock theory. We will see how induced four-dimensional Einstein–Hilbert terms result on the brane geometry from the higher order Lovelock terms. With the junction conditions at hand, we will go back to the black hole solutions and give applications for braneworlds: perturbations of codimension 1 braneworlds and the exact solution for braneworld cosmology as well as the determination of maximally symmetric codimension 2 braneworlds. In both cases, the staticity theorem evoked beforehand will give us the general solution for braneworld cosmology in codimension 1 and maximal symmetry warped branes of codimension 2. We will then end with a discussion of the simplest Kaluza–Klein reduction of Lovelock theory to a four-dimensional vector–scalar–tensor theory which has the unique property of retaining second-order field equations. We will comment briefly the non-linear generalisation of Maxwell’s theory and scalar–tensor theory. We will conclude by listing some open problems and common difficulties.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c85c6d91156c7b94645087578f268977436839d2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Strong coupling in Horava gravity (2009, background): “This means that linearised theory breaks down in this limit, just as it does for the Chern-Simons limit of Gauss-Bonnet gravity [10] (for a review on these gravity theories see [11, 12]).”
Black Holes in Higher Dimensions (2008, background): “Important related subjects that we do not discuss include: black holes in brane-world scenarios (reviewed in [186]); black holes in spacetimes with Kaluza–Klein asymptotics (reviewed in [129]), and in general black holes with different asymptotics than flat or AdS; black holes in higherderivative th”
The Lovelock Black Holes (2008, background): “onds to the case η I η II = +1. The freedom in choosing the parameters M, σ, η independently in each region allows for a wide class of solutions. The whole catalog was recently studied in [60]. 24See [161] for a recent review. See also [162] where boundary terms in odd-dimensions are discussed. 24 F”
Modified Gravity and Cosmology (2011, background): “64There is a typo in the corresponding expression for MUV pl in [270].”
Smarr formula and an extended first law for Lovelock gravity (2010, background): “In particular, exact, static black hole solutions were found beginning with the work of the authors of [7–9] (see also the recent reviews [10, 11]).”