We study the possibility to explain the mystery of the dark matter (DM) through the transition from General Relativity to embedding gravity. This modification of gravity, which was proposed by Regge and Teitelboim, is based on a simple string-inspired geometrical principle: our spacetime is considered here as a four-dimensional surface in a flat bulk. We show that among the solutions of embedding gravity, there is a class of solutions equivalent to solutions of GR with an additional contribution of non-relativistic embedding matter, which can serve as cold DM. We prove the stability of such type of solutions and obtain an explicit form of the equations of motion of embedding matter in the non-relativistic limit. According to them, embedding matter turns out to have a certain self-interaction, which could be useful in the context of solving the core-cusp problem that appears in the ΛCDM model.

中文翻译：

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来自非相对论嵌入引力的暗物质

我们研究了通过从广义相对论到嵌入引力的转变来解释暗物质 (DM) 之谜的可能性。Regge 和 Teitelboim 提出的这种重力修正是基于一个简单的弦启发几何原理：我们的时空在这里被视为扁平体中的四维表面。我们表明，在嵌入重力的解中，有一类解等价于 GR 的解，并附加了非相对论嵌入物质的贡献，可以作为冷 DM。我们证明了此类解的稳定性，并获得了非相对论极限下嵌入物质运动方程的显式形式。根据他们的说法，嵌入物质最终具有一定的自我相互作用，Λ清洁发展机制模型。