A number of works have tried to explain this conundrum with different ideas, which follow one of three possibilities. When Genzel et al. (1996) first discovered missing RGB stars, they proposed that this might be due to stellar collisions depleting giant stars in the innermost parts through the high stellar densities that are reached near the SMBH. Later, Davies et al. (1998), Alexander (1999), Bailey & Davies (1999), and Dale et al. (2009) addressed this idea in detail and came to the conclusion that it can only explain the absence of the brightest and most extended giant stars. A different suggested possibility to explain the missing stars is that our GC does not only have one, but a binary of two massive black holes. This hypothesised binary could indeed carve a core into the stellar distribution through three-body interactions, as shown by a number of authors (Baumgardt et al. 2006; Portegies Zwart et al. 2006; Matsubayashi et al. 2007; Löckmann & Baumgardt 2008; Gualandris & Merritt 2012). Nonetheless, the mass of the secondary needs to be of the order of 
\hbox{${\sim}10^5~M_{\odot}$}
~105M⊙

 to explain the observed core. Such a massive secondary black hole would require the Milky Way to have experienced a major merger relatively recently, which is excluded by observations (see Hansen & Milosavljević 2003; Yu & Tremaine 2003; Chen & Liu 2013). Moreover, the existence of such a massive secondary black hole is largely ruled out from a number of other considerations, for instance, constraints on the proper motion of Sgr A* from radio interferometry (see Gualandris & Merritt 2009). A number of inspiraling smaller-mass black holes can also create a shallow stellar density profile in the centre, which would relax the major merger requirement, as has been shown by Mastrobuono-Battisti et al. (2014). It has also been put forward that a star cluster falling towards the GC could increase the density profile outside of 10′′ , so that within this distance the profile would be like a core (Kim & Morris 2003; Ernst et al. 2009; Antonini et al. 2012; Antonini 2014). However, mass segregation would rebuild a steeper profile in as fast as a quarter of the relaxation time (as shown by Preto & Amaro-Seoane 2010; Amaro-Seoane & Preto 2011). This requirement would hence need a steady inflow of clusters to maintain a weak cusp profile in the centre. Finally, Merritt (2010) and Antonini (2014) found that if the nuclear cluster in the GC formed with an extended enough initial core profile, the current stellar distribution would still not be dynamically relaxed. While this solution is possible, it requires fine-tuning in the initial conditions to produce the density distribution seen in the GC. Amaro-Seoane & Chen (2014) proposed that the discs of young stars observed at the GC (Paumard et al. 2006) are connected to the missing bright giants: the precursor gaseous discmust have gone through a fragmentation phase that produced dense enough clumps to ensure an efficient removal of the outer layers of the giants through collisions, rendering them invisible to observations. Their degenerate cores would nonetheless populate the same area of phase space where the missing bright giants should be. Kieffer & Bogdanović (2016) recently showed that in order to be viable, this scenario requires the total mass of the fragmenting disc to have been several orders of magnitude higher than that of the early-type stars in the stellar discs in the GC.
Citation: Hansen & Milosavljević 2003
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