coordinates, 
the metric tensor, and 
the curvature tensor. The following tensors are called Lovelock-tensors:
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In the following are coordinates, the metric tensor, and the curvature tensor. The following tensors are called Lovelock-tensors:
 | (1) |
These tensors are divergence-free, so that these tensors represents conserved quantities. With these tensors it is possible to set up relativistic field equations of gravitation:
 | (2) |
On the condition, that 
, we get a field equation, which is many-worlds-suitable:
 | (3) |
This many-worlds-suitability is possible under the condition, that the metric tensor can be divided at least into two subareas, so that 
and 
is, with 
. Whereby the indices are simple primed for the one subarea, and are double primed for the other subarea. With this we get from the field-equation (3):
 | (4) |
There are solutions for the field equation (3) which are singularity-free, and contains the Schwarzschild-metric as a borderline case. See for this: Einige Lösungen (Some solutions)