The Structure of the Extreme Schwarzschild-de Sitter Space-time

Abstract

The extreme Schwarzschild-de Sitter space-time is a spherically symmetric solution of Einstein's equations with a cosmological constant Λ and mass parameter m > 0 which is characterized by the condition that 9Λm 2 = 1. The global structure of this space-time is here analyzed in detail. Conformal and embedding diagrams are constructed, and synchronous coordinates which are suitable for a discussion of the cosmic no-hair conjecture are presented.The permitted geodesic motions are also analyzed. By a careful investigation of the geodesics and the equations of geodesic deviation, it is shown that specific families of observers escape from falling into the singularity and approach nonsingular asymptotic regions which are represented by special "points" in the complete conformal diagram. The redshift of signals emitted by particles which fall into the singularity, as detected by those observers which escape, is also calculated.

Impulsive waves in the Nariai universe

“…Therefore, it is both locally and globally distinguished from the de Sitter space. Besides the historical attention it deserved thanks to its geometrical properties [16,19,20,21], more recently it has been the object of a renewed interest, since it emerges as the extremal limit of Schwarzschild-de Sitter black holes [22,23,24] (which is not equivalent to consider "extreme" black holes, studied, e.g., in [25]). Thus, it can be viewed as a "degenerate" black hole, in which the two horizons have the same (maximum) size and are in thermal equilibrium at the temperature T = √ Λ/2π.…”

“…For m = 0, instead, there is a pair of "monopole" particles (compare with [10,11]). Thus, the general solution (25) contains null particles at the poles of both twin 2-spheres which compose the wave front. However, Φ 22 is linear in H and the background is invariant under rotations.…”

“…Again, b 0 is the coefficient of an axially symmetric term. Except for the "pure" solutions (25) and (28), the spacetime (17) in general describes impulsive waves generated by an arbitrary superposition of multipole pointlike sources and an impulse of null dust in the Nariai universe.…”

Strong Cosmic Censorship for Surface‐Symmetric Cosmological Spacetimes with Collisionless Matter

“…An essential difficulty, however, arises from the so-called extremal case, depicted here (cf. [31]):…”

Gravitational Rutherford scattering and Keplerian orbits for electrically charged bodies in heterotic string theory

“…Furthermore, the inclusion of a cosmological constant leads to the Kottler solution [8], which spacetime is known as Schwarzschildde Sitter (SdS) if > 0, or the Schwarzschild-anti-de Sitter (SAdS) if < 0. So, trajectories for neutral particles in a purely SdS spacetime can be found in [9][10][11][12], while different aspects of the motion of neutral particles in the background of the purely SAdS spacetime have been presented in [13][14][15][16][17][18]. Uncharged particles in an RN black hole with = 0 were studied by Stuchlík and Hledík [19], whereas circular orbits were presented by Pugliese et al [20].…”