Abstract
In this paper we wish to find the corresponding Gibbons-Hawking-York term for the most general quadratic in curvature gravity by using Coframe slicing within the Arnowitt-Deser-Misner (ADM) decomposition of spacetime in four dimensions. In order to make sure that the higher derivative gravity is ghost and tachyon free at a perturbative level, one requires infinite covariant derivatives, which yields a generalised covariant infinite derivative theory of gravity. We will be exploring the boundary term for such a covariant infinite derivative theory of gravity.
Highlights
Einstein’s General theory of Relativity (GR) has seen tremendous success in matching its predictions with observations in the weak field regime in the infrared (IR) [1], including the recent confirmation of the detection of Gravitational Waves [2]
Where K = hijKij, with Kij given by eq (4.25), and Ψ = hijΨij, where Ψij is given in eq (5.10), are spatial tensors evaluated on the hypersurface Σt and L is the Lagrangian density
Our work has focused on seeking the boundary term or GHY contribution for a covariant infinite derivative theory of gravity, which is quadratic in curvature
Summary
Einstein’s General theory of Relativity (GR) has seen tremendous success in matching its predictions with observations in the weak field regime in the infrared (IR) [1], including the recent confirmation of the detection of Gravitational Waves [2]. By definition, such a modification will not incur any new poles in the propagator and ensures that the modified propagator has a correct IR limit, where one recovers the predictions of pure Einstein-Hilbert action at large distances from the source and large time scales This is encouraging as there exists a non-singular blackhole solution, at least at the level of linearized equations of motion for such covariant infinite derivative theory of gravity in a static [6, 15, 17], and in a time dependent background [18,19,20].
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