Abstract
We explain in detail how to calculate the gravitational mass and angular momentum multipoles of the most general non-extremal four-dimensional black hole with four magnetic and four electric charges. We also calculate these multipoles for generic supersymmetric four-dimensional microstate geometries and multi-center solutions. Both for Kerr black holes and BPS black holes many of these multipoles vanish. However, if one embeds these black holes in String Theory and slightly deforms them, one can calculate an infinite set of ratios of vanishing multipoles which remain finite as the deformation is taken away, and whose values are independent of the direction of deformation. For supersymmetric black holes, we can also compute these ratios by taking the scaling limit of multi-center solutions, and for certain black holes the ratios computed using the two methods agree spectacularly. For the Kerr black hole, these ratios pose strong constraints on the parameterization of possible deviations away from the Kerr geometry that should be tested by future gravitational wave interferometers.
Highlights
Introduction and summaryThere are many arguments that black holes can only restore the information that has fallen into them to our universe if there exists a structure at the scale of the horizon from where this information can be imprinted onto Hawking radiation [1,2,3]
The future observations of gravitational waves emitted during Extreme Mass-Ratio Inspiral (EMRI) events [15,16,17,18,19] are expected to reveal whether the mass multipoles and angular momentum multipoles are the same as those predicted by Classical General Relativity, or are perhaps modified
We outline a new window into black hole physics by calculating multipole ratios for supersymmetric and non-supersymmetric black holes, as well as for supersymmetric multi-center solutions
Summary
Introduction and summaryThere are many arguments that black holes can only restore the information that has fallen into them to our universe if there exists a structure at the scale of the horizon from where this information can be imprinted onto Hawking radiation [1,2,3]. Since the horizon is a null surface, a horizon-scale structure must have very unusual properties that prevent its collapse into a black hole Such a non-collapsing horizon-replacing structure can be constructed in String Theory, and consists of complicated topologically non-trivial bubbles wrapped by fluxes [4,5,6,7,8,9,10]. Besides the presence of a structure that allows information to escape, the region of the black hole horizon is the place where the full non-linear glory of general relativity manifests itself Both the current observations of gravitational waves emitted by black holes mergers [13], and future satellite-based experiments [14], are geared towards exploring how much the physics of this region deviates from what general relativity predicts. We can distinguish two possible causes for such modifications: a) horizon-scale structure that allows information to escape; b) modifications of General Relativity that become important at the horizon scale
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