Notes on nonsingular models of black holes

By Valeri P. Frolov. 2016

246 citations recorded by the source corpus.

We discuss static spherically symmetric metrics which represent non-singular black holes in four- and higher-dimensional spacetime. We impose a set of restrictions, such as a regularity of the metric at the center $r=0$ and Schwarzschild asymptotic behavior at large $r$. We assume that the metric besides mass $M$ contains an additional parameter $\ell$, which determines the scale where modification of the solution of the Einstein equations becomes significant. We require that the modified metric obeys the limiting curvature condition, that is its curvature is uniformly restricted by the value $\sim \ell^{-2}$. We also make a "more technical" assumption that the metric coefficients are rational functions of $r$. In particular, the invariant $(\nabla r)^2$ has the form $P_n(r)/\tilde{P}_n(r)$, where $P_n$ and $\tilde{P}_n$ are polynomials of the order of $n$. We discuss first the case of four dimensions. We show that when $n\le 2$ such a metric cannot describe a non-singular black hole. For $n=3$ we find a suitable metric, which besides $M$ and $\ell$ contains a dimensionless numerical parameter. When this parameter vanishes the obtained metric coincides with Hayward's one. The characteristic property of such spacetimes is $-\xi^2=(\nabla r)^2$, where $\xi^2$ is a time-like at infinity Killing vector. We describe a possible generalization of a non-singular black-hole metric to the case when this equality is violated. We also obtain a metric for a charged non-singular black hole obeying similar restrictions as the neutral one, and construct higher dimensional models of neutral and charged black holes.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/8518e743c51c489c82d635247a03ab596a34bfbf

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Citations in the corpus

Regular Black Holes: A Short Topic Review (2023, methodology): “2 The case with two shape functions For the RBHs with two shape functions [6, 23, 81, 82], we apply the similar procedure to the above, that is, we expand the both of shape functions (see Eq.”
Phenomenological aspects of black holes beyond general relativity (2018, background): “This has been partially considered in [16, 23], and is in fact one of the main ingredients leading to the inconsistency of these models [19].”
Black-bounce to traversable wormhole (2018, background): “This metric does not correspond to a traditional regular black hole such as the Bardeen, Bergmann–Roman, Frolov, or Hayward geometries [1–11].”
Constraints on black-hole charges with the 2017 EHT observations of M87* (2021, background): “For each of these solutions we vary the corresponding charge (in units of M ) in the allowed range, i.e., RN: 0 < q̄ ≤ 1; Bardeen: 0 < q̄m ≤ √ 16/27; Hayward: 0 < l̄ ≤ √ 16/27; Frolov: 0 < l̄ ≤ √ 16/27, 0 < q̄ ≤ 1; KS: 0 < l̄; EMd-1: 0 < q̄ < √ 2, but report the normalised value in the figure so tha”