  We are concerned with global finite-energy solutions of the three-dimensional
compressible Euler-Poisson equations with gravitational potential and general
pressure law, especially including the constitutive equation of white dwarf
stars. We construct global finite-energy solutions of the Cauchy problem for
the Euler-Poisson equations with large initial data of spherical symmetry as
the inviscid limit of the solutions of the corresponding Cauchy problem for the
Navier-Stokes-Poisson equations. The strong convergence of the vanishing
viscosity solutions is achieved through entropy analysis, uniform estimates in
$L^p$, and a more general compensated compactness framework via several new
ingredients. A key estimate is first established for the integrability of the
density over unbounded domains independent of the viscosity coefficient. Then a
special entropy pair is carefully designed by solving a Goursat problem for the
entropy equation such that a higher integrability of the velocity is
established, which is a crucial step. Moreover, the weak entropy kernel for the
general pressure law and its fractional derivatives of the required order near
vacuum ($\rho=0$) and far-field ($\rho=\infty$) are carefully analyzed. Owing
to the generality of the pressure law, only the $W^{-1,p}_{{\rm
loc}}$-compactness of weak entropy dissipation measures with $p\in [1,2)$ can
be obtained; this is rescued by the equi-integrability of weak entropy pairs
which can be established by the estimates obtained above so that the div-curl
lemma still applies. Finally, based on the above analysis of weak entropy
pairs, the $L^p$ compensated compactness framework for the compressible Euler
equations with general pressure law is established. This new compensated
compactness framework and the techniques developed in this paper should be
useful for solving further nonlinear problems with similar features.
