Gravitational observatories

Abstract

We consider four-dimensional general relativity with vanishing cosmological constant defined on a manifold with a boundary. In Lorentzian signature, the timelike boundary is of the form σ × ℝ, with σ a spatial two-manifold that we take to be either flat or S2. In Euclidean signature we take the boundary to be S2 × S1. We consider conformal boundary conditions, whereby the conformal class of the induced metric and trace K of the extrinsic curvature are fixed at the timelike boundary. The problem of linearised gravity is analysed using the Kodama-Ishibashi formalism. It is shown that for a round metric on S2 with constant K, there are modes that grow exponentially in time. We discuss a method to control the growing modes by varying K. The growing modes are absent for a conformally flat induced metric on the timelike boundary. We provide evidence that the Dirichlet problem for a spherical boundary does not suffer from non-uniqueness issues at the linearised level. We consider the extension of black hole thermodynamics to the case of conformal boundary conditions, and show that the form of the Bekenstein-Hawking entropy is retained.

Cosmological observatories

“…, retrieving the result in flat space obtained in [25]. This is expected as this limit corresponds to a boundary size that is parameterically small compared to the cosmological horizon.…”

“…• In the worldline limit of the cosmic patch, we retrieve a set of modes that approximate the quasinormal modes of the static patch [51], whilst also uncovering a family of modes in the scalar sector with a negative imaginary part. The latter modes have a Minkowskian analogue uncovered in [25]. • In the stretched horizon limit, our modes degenerate into a variety of modes.…”

“…Further taking the large Kℓ limit of the above expression yields N d.o.f. ≈ 8π 3 GNK 2 , a behaviour identified in [25] for black holes in Minkowski space subject to conformal boundary conditions.…”

“…Following [25], we would like to study the thermodynamic behaviour of solutions subject to conformal boundary conditions, but now in the presence of Λ > 0.…”

Static sphere observers and geodesics in Schwarzschild-de Sitter spacetime

“…Recent studies of quantum gravity in de Sitter [1][2][3][4][5][6][7][8][9][10][11][12] suggest that, inspired by recent progress in our understanding of quantum gravity in Anti-de Sitter space [13][14][15][16], non-perturbative contributions in the (Euclidean) path integral could play an important role [7,[17][18][19][20]. The simplest, most elementary, solutions of relevance in this context are black holes in de Sitter space, whose contribution to the Euclidean path integral can be (partially) understood using the formalism of constrained instantons [9,21].…”