The Penrose inequality for nonmaximal perturbations of the Schwarzschild initial data

Abstract

We show that the Penrose inequality is satisfied for a class of conformally flat axially symmetric nonmaximal perturbations of the Schwarzschild data. A role of horizon is played by a marginally outer trapped surface which does not have to be minimal.

Asymptotically hyperbolic Einstein constraint equations with apparent horizon boundary and the Penrose inequality for perturbations of Schwarzschild-AdS *

“…The second main result is a verification of the Penrose inequality for perturbations of Schwarzschild-AdS initial data. A similar study has been carried out by the second author and Tafel in [25,26] for asymptotically flat and axisymmetric initial data, where the Penrose inequality with angular momentum was confirmed up to second order of expansion with respect to a scale determined by the conformal extrinsic curvature. Moreover, the Penrose inequality for perturbations of Schwarzschild-AdS has been established in the time-symmetric case by Ambrozio [3].…”

Recent Developments in the Penrose Conjecture

“…The inequality is saturated for the Schwarzchild metric when p = p = J = 0. This result was later extended using similar methods to non-maximal perturbations of Schwarzchild initial data [22], and in this case the initial data satisfy the same Penrose inequality up to second order in ǫ. This seems like quite a restrictive result, but it is promising as it probably analogous to similar results which were established in the direction of the positive mass theorem before the full result was finally proved by Schoen and Yau (the theorem having first been proved for axially symmetric initial data and for second order perturbations away from flat initial data) [23].…”

Attractive gravity probe surfaces in higher dimensions

“…There are versions of the Riemannian Penrose inequality including the effect of the electric charge [36][37][38] and the angular momenta [39][40][41][42][43][44]. Studies of AGPSs with such contributions are In the neighborhood of x = x 1 , w is estimated as…”