https://doi.org/10.1140/epjc/s10052-016-4394-0
Regular Article - Theoretical Physics
Solving higher curvature gravity theories
1
IUCAA, Post Bag 4, Ganeshkhind, Pune University Campus, Pune, 411 007, India
2
Theoretical Physics Department, Indian Association for the Cultivation of Science, Kolkata, 700032, India
* e-mail: sumantac.physics@gmail.com
Received:
31
August
2016
Accepted:
20
September
2016
Published online:
8
October
2016
Solving field equations in the context of higher curvature gravity theories is a formidable task. However, in many situations, e.g., in the context of f(R) theories, the higher curvature gravity action can be written as an Einstein–Hilbert action plus a scalar field action. We show that not only the action but the field equations derived from the action are also equivalent, provided the spacetime is regular. We also demonstrate that such an equivalence continues to hold even when the gravitational field equations are projected on a lower-dimensional hypersurface. We have further addressed explicit examples in which the solutions for Einstein–Hilbert and a scalar field system lead to solutions of the equivalent higher curvature theory. The same, but on the lower-dimensional hypersurface, has been illustrated in the reverse order as well. We conclude with a brief discussion on this technique of solving higher curvature field equations.
© The Author(s), 2016
