Generic 2D Horndeski theories arise from dimensional reduction of d≥4 gravities, yielding a Birkhoff theorem for quasi-topological gravities where static spherically symmetric solutions satisfy g_tt g_rr = -1 and are determined algebraically.
A set of invariant quality factors measuring the deviation from the Kerr metric
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abstract
A number of scalar invariant characterizations of the Kerr solution are presented. These characterizations come in the form of {\em quality factors} defined in stationary space-times. A quality factor is a scalar quantity varying in the interval $[0,1]$ with the value 1 being attained if and only if the space-time is locally isometric to the Kerr solution. No knowledge of the Kerr solution is required to compute these quality factors. A number of different possibilities arise depending on whether the space-time is Ricci-flat and asymptotically flat, just Ricci-flat, or Ricci non-flat. In each situation a number of quality factors are constructed and analysed. The relevance of these quality factors is clear in any situation where one seeks a rigorous formulation of the statement that a space-time is "close" to the Kerr solution, such as: its non-linear stability problem, the asymptotic settlement of a radiating isolated system undergoing gravitational collapse, or in the formulation of some uniqueness results.
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All $2D$ generalised dilaton theories from $d\geq 4$ gravities
Generic 2D Horndeski theories arise from dimensional reduction of d≥4 gravities, yielding a Birkhoff theorem for quasi-topological gravities where static spherically symmetric solutions satisfy g_tt g_rr = -1 and are determined algebraically.