Astronomy and Astrophysics Seminars
Exact interior solutions for perfect fluids in Einstein–Gauss–Bonnet gravity
by Dr. Sudan Hansraj (Astrophysics and Cosmology Research Unit School of Mathematical Sciences University of KwaZulu Natal Durban South Africa)
Tuesday, January 6, 2015
from
to
(Asia/Kolkata)
at TIFR ( DAA SEMINAR A269 )
at TIFR ( DAA SEMINAR A269 )
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. |