Abstract
We present the features of a model which generalizes Schwarzschild’s homogeneous star by adding a transition zone for the density near the surface. By numerically integrating the modified TOV equations for the f(mathcal {R})=mathcal {R}+lambda mathcal {R}^2 Palatini theory, it is shown that the ensuing configurations are everywhere finite. Depending on the values of the relevant parameters, objects more, less or as compact as those obtained in GR with the same density profile have been shown to exist. In particular, in some region of the parameter space the compactness is close to that set by the Buchdahl limit.
Highlights
The idea that the endpoint of stellar evolution of sufficiently massive and compact stars is a black hole can be tested by exploring the consequences of the existence of very compact objects, which would offer a window to extreme relativistic effects, and point out to new physics
1 + exp r −q where ρ0, q and are parameters. Such a form improves the case ρ = constant by replacing the abrupt fall to zero of the latter at the surface of the star with a transition zone, which can be considered as a first approach to an atmosphere
We have shown that Schwarzschild’s homogeneous star can be ameliorated by the addition of a transition zone near the
Summary
The idea that the endpoint of stellar evolution of sufficiently massive and compact stars is a black hole can be tested by exploring the consequences of the existence of very compact objects, which would offer a window to extreme relativistic effects, and point out to new physics (for a review see [1]). In the static and spherically symmetric case they obey 2M < R < 3M [9] They have a photosphere, and a second - stable - light ring [10,11], that give rise to a trapping zone for particles with zero mass. Such a zone may have important consequences for gravitational perturbations [12],1 since some of their modes can decay very slowly [14], and source nonlinear effects which may destabilize the system [15]
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