Gradient conformal stationarity and the CMC condition in LRS spacetimes

Abstract

We study the existence of gradient conformal Killing vectors (CKVs) in the class of locally rotationally symmetric (LRS) spacetimes which generalizes spherically symmetric spacetimes, and investigate some implications for the evolutionary character of marginally outer trapped surfaces. We first study existence of gradient CKVs via the obtention of a relationship between the Ricci curvature and the gradient of the divergence of the CKV. This provides an alternative set of equations, for which the integrability condition is obtained, to analyze the existence of gradient CKVs. A uniqueness result is obtained in the case of perfect fluids, where it is demonstrated that the Robertson-Walker solution is the unique perfect fluid solution with a nonvanishing pressure, admitting a timelike gradient CKV. The constant mean curvature condition for LRS spacetimes is also obtained, characterized by three distinct conditions which are specified by a set of three scalars. Linear combinations of these scalars, whose vanishing define the constant mean curvature condition, turn out to be related to the evolutions of null expansions of 2-spheres along their null normal directions. As such, some implications for the existence of black holes and the character of the associated horizons are obtained. It is further shown that dynamical black holes of increasing area, with a non-vanishing heat flux across the horizon, will be in equilibrium, with respect to the frame of the conformal observers.

25 pages; typos corrected; Abstract and references updated; some additional details, including calculations, provided for clarity; accepted for publication in CQG

References in corpus (12)

• Generalized Robertson-Walker space times, a survey
• A covariant approach for perturbations of rotationally symmetric spacetimes
• Perfect-fluid, generalised Robertson-Walker space-times, and Gray's decomposition
• Astrophysical Black Hole horizons in a cosmological context: Nature and possible consequences on Hawking Radiation
• MOTS in Schwarzschild: multiple self-intersections and extreme mass ratio mergers
• Stability of marginally outer trapped surfaces and symmetries
• Thermodynamics with conformal Killing vector in the charged Vaidya metric
• Symmetry and instability of marginally outer trapped surfaces
• Horizon area bound and MOTS stability in locally rotationally symmetric solutions
• On the existence of marginally trapped tubes in spacetimes with local rotational symmetry
• Existence of gradient CKV and gradient conformally stationary LRS spacetimes
• Rotating and twisting locally rotationally symmetric imperfect fluids