IDEAL characterization of higher dimensional spherically symmetric black holes

Abstract

In general relativity, an IDEAL (Intrinsic, Deductive, Explicit, ALgorithmic) characterization of a reference spacetime metric g0 consists of a set of tensorial equations T [g] = 0, constructed covariantly out of the metric g, its Riemann curvature and their derivatives, that are satisfied if and only if g is locally isometric to the reference spacetime metric g0. We give the first IDEAL characterization of generalized Schwarzschild-Tangherlini spacetimes, which consist of Λ-vacuum extensions of higher dimensional spherically symmetric black holes, as well as their versions where spheres are replaced by flat or hyperbolic spaces. The standard Schwarzschild black hole has been previously characterized in the work of Ferrando and Sáez, but using methods highly specific to 4 dimensions. Specialized to 4 dimensions, our result provides an independent, alternative characterization. We also give a proof of a version of Birkhoff's theorem that is applicable also on neighborhoods of horizon and horizon bifurcation points, which is necessary for our arguments.

Relativistic kinematic approach to the classical ideal gas

“…It is worth remarking that under the barotropic constraint (28), from (22) and (26) we obtain ρ ′ (p) = f = 1 γ ( ρ p + 1). This equation can be integrated and leads to a solution of the form (19), accordingly with the statement of proposition above.…”

Compatibility Complex for Black Hole Spacetimes

“…Namely, a so-called IDEAL characterization [12,[14][15][16] of a given spacetime consists of a list of tensors {T i [g]} covariantly built from the metric, Riemann tensor and covariant derivatives such that the conditions T i [g] = 0 are sufficient to guarantee that (M, g ab ) is locally isometric to the given reference spacetime. As was pointed out in the recent works [10,24], where IDEAL characterizations were given for cosmological FLRW and Schwarzschild-Tangherlini black hole spacetimes, one can use the tensors {T i [g]} to construct linear gauge invariants on the characterized spacetime. In particular, the identity [36] guarantees that the linear operatorṪ g i [h] is a gauge invariant whenever T i [g] = 0 (or even more generally when T i [g] is a combination of Kronecker-deltas with constant coefficients).…”

Compatibility complex for black hole spacetimes

“…Namely, a so-called IDEAL characterization [9,11,13,12] of a given spacetime consists of a list of tensors {T i [g]} covariantly built from the metric, Riemann tensor and covariant derivatives such that the conditions T i [g] = 0 are sufficient to guarantee that (M, g ab ) is locally isometric to the given reference spacetime. As was pointed out in the recent works [8,21], where IDEAL characterizations were given for cosmological FLRW and Schwarzschild-Tangherlini black hole spacetimes, one can use the tensors {T i [g]} to construct linear gauge invariants on the characterized spacetime. In particular, the identity…”