29 research outputs found
Hamiltonian formulation of f(Riemann) theories of gravity
We present a canonical formulation of gravity theories whose Lagrangian is an
arbitrary function of the Riemann tensor. Our approach allows a unified
treatment of various subcases and an easy identification of the degrees of
freedom of the theory.Comment: 12 pages, REVTeX
Non-relativistic stellar structure in higher-curvature gravity: systematic construction of solutions to the modified Lane-Emden equations
We study the structure of static spherical stars made up of a
non-relativistic polytropic fluid in linearized higher-curvature theories of
gravity (HCG). We first formulate the modified Lane-Emden (LE) equation for the
stellar profile function in a gauge-invariant manner, finding it boils down to
a sixth order differential equation in the generic case of HCG, while it
reduces to a fourth order equation in two special cases, reflecting the number
of additional massive gravitons arising in each theory. Moreover, the existence
of massive gravitons renders the nature of the boundary-value problem unlike
the standard LE: some of the boundary conditions can no longer be formulated in
terms of physical conditions at the stellar center alone, but some demands at
the stellar surface necessarily come into play. We present a practical scheme
for constructing solutions to such a problem and demonstrate how it works in
the cases of the polytropic index n = 0 and 1, where analytical solutions to
the modified LE equations exist. As physical outcomes, we clarify how the
stellar radius, mass, and Yukawa charges depend on the theory parameters and
how these observables are mutually related. Reasonable upper bounds on the
Weyl-squared correction are obtained.Comment: 27 pages, 17 figure