Description |
Since the pioneering mathematical work of Lovelock (1971) no exact interior solution for static spherically symmetric perfect fluid matter has been explicitly found in the case of the Einstein–Gauss–Bonnet theory. We investigate this
problem and report classes of new exact solutions for this configuration. One of
the main motivations for the study of alternate gravity theories is the inability
of the highly successful theory of general relativity, obtained from the Einstein–
Hilbert action principle, to explain phenomena such as the late time accelerated
expansion of the universe without resorting to the introduction of concepts such
as dark matter. The expanding universe phenomenon has been demonstrated by
observational evidence such as in WMAP. Lovelock gravity neatly avoids calling
on such matter and instead involves a modification of geometry which generalises
that of general relativity. Unlike other competing theories, such as f(r) theory,
the Lovelock polynomials used in the action generate second order equations of
motions for all orders of the polynomial. To second order the Lovelock polyno-
mial is referred to as the Einstein–Gauss–Bonnet (EGB) quadratic polynomial
and is constructed from quadratic forms of the Ricci tensor, Ricci scalar and
Riemann tensor. This EGB term only contributes to the dynamics for metrics
with dimension more than 4. Therefore we are interested in studying the dimen-
sional order 5 as a first tangible case in order to examine the behaviour of the
EGB term and its effect on the physics when compared to the general relativity
case of dimension 4. The EGB field equations for n, n ≥ 5 have been obtained
however we confine this investigation to the 5 dimensional case only. We work
in a coordinate frame and write the associated EGB field equations for perfect
fluid matter. By introducing a coordinate transformation we rewrite the master
pressure isotropy condition in a form that allows us to locate exact solutions by
prescribing a form for one of the gravitational potentials. We impose the usual
tests of physical plausibility on the resulting solutions. In particular we exhibit a
model that is causal, satisfies the weak, strong and dominant energy conditions
and which represents a fluid with a vanishing pressure hypersurface identifying
the boundary of the fluid - the simplified Israel-Darmois junction conditions
have been used. The exact solution is matched to the exterior Boulware–Deser
(1985) exterior metric across the pressure–free boundary.
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