Anisotropic stars as ultracompact objects in general relativity

Anisotropic stresses are ubiquitous in nature, but their modeling in general relativity is poorly understood and frame dependent. We introduce the first study on the dynamical properties of anisotropic self-gravitating fluids in a covariant framework. Our description is particularly useful in the context of tests of the black hole paradigm, wherein ultracompact objects are used as black hole mimickers but otherwise lack a proper theoretical framework. We show the following: (i) anisotropic stars can be as compact and as massive as black holes, even for very small anisotropy parameters; (ii) the nonlinear dynamics of the $1+1$ system is in good agreement with linearized calculations, and shows that configurations below the maximum mass are nonlinearly stable; (iii) strongly anisotropic stars have vanishing tidal Love numbers in the black-hole limit; and (iv) their formation will usually be accompanied by gravitational-wave echoes at late times.

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