Some results on geometric inequalities in spherically symmetric spacetimes

Recent papers [1,2,3,4] on geometric inequalities present results not only on black holes but on normal bodies too. In spherical symmetry there is a highly accepted quasi-local notion of mass: the Misner-Sharp mass. Utilizing this notion it is possible to examine geometric inequalities on any SO(3) invariant surface on generic spherically symmetric spacetimes. My talk is to present results on trapped, marginally trapped and untrapped surfaces and based on the paper [5].

The talk was supported by OTKA grant K115434.

[1] Dain, S. and Jaramillo, J. L. and Reiris, M.,Area-charge inequality for black holes,
Classical and Quantum Gravity, vol. 29, 2012, 035013

[2] Khuri, M. A., Inequalities Between Size and Charge for Bodies and the Existence of Black Holes Due to Concentration of Charge,
Journal of Mathematical Physics, vol. 56, 2015, 11, 112503

[3] Reiris, Martin, On the shape of bodies in General Relativistic regimes,
Gen.Rel. Grav., vol. 46, 2014, 1777

[4] Anglada, Pablo and Dain, Sergio and Ortiz, Omar E., Inequality between size and charge in spherical symmetry,
Phys. Rev., vol. D93, 2016, 4, 044055

[5] Csukás, Károly Zoltán, Geometric inequalities in spherically symmetric space-times,
Gen. Rel. Grav., vol. 49, 2017, 7, 94