TITLE: Ghosts in theories of gravity and holographic theories
QUESTION [3 upvotes]: I want to understand when a theory leads to ghosts in gravity. Is there any relation between ghosts and non-linear higher order theories? Ghost is a clasical or quantum field concept?

REPLY [3 votes]: Ghosts also arise in the context of the classic theory through Ostrogradsky theorem. You should take a look at this paper:

Woodard, Richard. “Ostrogradskys Theorem on Hamiltonian Instability.” Scholarpedia, vol. 10, no. 8, 2015, p. 32243., doi:10.4249/scholarpedia.32243.

It's available on arXiv.
The general ideia is that, given a non-degenerate Lagrangian of the form
$$\mathcal{L}=\mathcal{L}(x,\dot x, \ddot x, ...)\;,$$
the associated Hamiltonian is necessarily linear in almost all of the canonical momenta, and the Hamiltonian is unbounded bellow, rendering the system unstable. It implies that non-degenerate systems with higher than one time-derivative dependence suffer from ghost-like (unphysical) degrees of freedom.
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