We propose a two-parameter, static and spherically symmetric regular geometry, which, for specific parameter values represents a regular black hole. The matter required to support such spacetimes within the framework of general relativity (GR), is found to violate the energy conditions, though not in the entire domain of the radial coordinate. A particular choice of the parameters reduces the regular black hole to a singular, mutated Reissner–Nordström geometry. It also turns out that our regular black hole is geodesically complete. Fortunately, despite energy condition violation, we are able to construct a viable source, within the framework of GR coupled to matter, for our regular geometry. The source term involves a nonlinear magnetic monopole in a chosen version of nonlinear electrodynamics. We also suggest an alternative approach towards constructing a source, using the effective Einstein equations which arise in the context of braneworld gravity. Finally, we obtain the circular shadow profile of our regular black hole and provide a preliminary estimate of the metric parameters using recent observational results from the EHT collaboration.

我们提出了一种双参数、静态、球对称的规则几何结构，对于特定的参数值，它代表一个规则的黑洞。人们发现，在广义相对论（GR）框架内支持这种时空所需的物质违反了能量条件，尽管不是在整个径向坐标域中。参数的特定选择将规则黑洞简化为奇异的、变异的赖斯纳-诺德斯特伦几何结构。事实证明，我们的常规黑洞在测地线上是完整的。幸运的是，尽管违反了能量条件，我们仍然能够在广义相对论与物质耦合的框架内为我们的规则几何结构构建一个可行的来源。源项涉及所选版本的非线性电动力学中的非线性磁单极子。我们还提出了另一种构建源的方法，即使用在膜世界引力背景下出现的有效爱因斯坦方程。最后，我们获得了常规黑洞的圆形阴影轮廓，并使用 EHT 合作的最新观测结果提供了度量参数的初步估计。