Abstract
In this work two new families of non-singular or regular black hole solutions are displayed. These black holes behave as de Sitter space near its center and have a well defined AdS asymptotic region for negative cosmological constant. These solutions are constructed on a general ground through the introduction of a finite density of mass/energy. This removes the usual singularity of a black hole and also introduces a new internal geometry. The thermodynamic properties of these solutions are discussed as well.
Highlights
One of the most relevant predictions of General Relativity was the existence of black holes and nowadays there is substantial evidence that this is a usual phenomenon in nature
For the physics of a black hole, this implies that the gravitational collapse stops before a singularity can be formed
In practice Planck stars can be studied as a geometry which far away from the core recovers a standard black hole solution, says Schwarzschild for instance, but whose center, contains a dense core, can still be treated as a manifold
Summary
One of the most relevant predictions of General Relativity was the existence of black holes and nowadays there is substantial evidence that this is a usual phenomenon in nature. The core of the geometry must approach, in a first approximation, a de Sitter space as such the geodesics diverge mimicking the repulsing force mentioned above This kind of solutions are called non-singular or regular black holes and in the context of this work can be considered synonyms to Planck star. It is direct to check that the equations of motion can be rewritten as This seems to indicate, as expected, that any Lovelock gravity should have for ground states constant curvature manifolds. It is direct to demonstrate that, in general, the κi can be complex numbers, even though ∀αp ∈ R This does restrict the possible constant curvature solutions, and so the potential ground states of the theory, and severely constraints the space of solutions with a well defined asymptotic region for arbitrary {αp}.
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