https://doi.org/10.1140/epjc/s10052-024-13660-2
Regular Article - Theoretical Physics
The Chini integrability condition in second order Lovelock gravity
1
Astrophysics Research Centre, School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X54001, 4000, Durban, South Africa
2
Department of Mathematics, Faculty of Applied Sciences, Durban University of Technology, P O Box 1334, 4000, Durban, South Africa
Received:
6
September
2024
Accepted:
27
November
2024
Published online:
29
December
2024
We analyse neutral and charged matter distributions in second order Lovelock gravity, also known as Einstein–Gauss–Bonnet gravity, in arbitrary dimensions for a static, spherically symmetric spacetime. We first transform the charged condition of pressure isotropy, an Abel differential equation of the second kind, into canonical form. We then determine a systematic approach to integrate the condition of pressure isotropy by showing that the canonical form is a Chini differential equation. The Chini invariant, which allows the master differential equation to be separable, is identified. This enables us to find three new general solutions, in implicit form, to the condition of pressure isotropy. We also show that previously obtained exact specific solutions arise as special cases in our general class of models. The Chini invariant does not arise in general relativity; it is a distinguishing feature of Einstein–Gauss–Bonnet gravity.
© The Author(s) 2024
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