We discuss exact scalar field solutions describing gravitating compact objects in the Eddington-inspired Born–Infeld (EiBI) gravity, a member of the class of (metric-affine formulated) Ricci-based gravity (RBG) theories. We include a detailed account of the RBGs/GR correspondence exploited to analytically solve the field equations. The single parameter [Formula: see text] of the EiBI model defines two branches for the solution. The [Formula: see text] branch may be described as a “shell with no interior”, and constitutes an ill-defined, geodesically incomplete spacetime. The more interesting [Formula: see text] branch admits the interpretation of a “wormhole membrane”, an exotic horizonless compact object with the ability to transfer particles and light from any point on its surface (located slightly below the would-be Schwarzschild radius) to its antipodal point, in a vanishing fraction of proper time. This is a single example illustrating how the structural modifications introduced by the metric-affine formulation may lead to significant departures from General relativity (GR) even at astrophysically relevant scales, giving rise to physically plausible objects radically different from those we are used to think of in the metric approach, and that could act as a black hole mimickers whose shadows might present distinguishable signals.

中文翻译：

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EiBI 重力中的紧凑标量场解决方案

我们讨论了在 Eddington 启发的 Born-Infeld (EiBI) 引力中描述引力致密物体的精确标量场解决方案，该引力是（度量仿射公式化的）基于 Ricci 的引力 (RBG) 理论类的成员。我们详细介绍了用于解析求解场方程的 RBG/GR 对应关系。EiBI 模型的单个参数 [公式：见文本] 定义了解决方案的两个分支。[公式：见正文]分支可以被描述为“没有内部的壳”，并构成了一个定义不明确、测地线不完整的时空。更有趣的【公式：见正文】分支承认了“虫洞膜”的解释，一种奇异的无视界致密天体，能够将粒子和光从其表面上的任何点（位于可能的施瓦西半径略下方）转移到其对映点，在适当的时间内消失。这是一个单独的例子，说明了度量仿射公式引入的结构修改如何导致即使在天体物理学相关的尺度上也可能导致与广义相对论 (GR) 的显着偏离，从而产生与我们过去想象的完全不同的物理上似是而非的物体在度量方法中，这可以充当黑洞模仿者，其阴影可能会呈现可区分的信号。