Is the Carter-Israel conjecture correct?

arXiv:0908.3238v1 [astro-ph.HE] 22 Aug 2009 IS THE CARTER-ISRAEL CONJECTURE CORRECT? COSIMO BAMBI Institute for the Physics and Mathematics of the Universe, The University of Tokyo, Kashiwa, Chiba 277-8568, Japan KATHERINE FREESE The Michigan Center for Theoretical Physics, Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA ROHTA TAKAHASHI Cosmic Radiation Laboratory, Institute of Physical and Chemical Research, Wako, Saitama 351-0198, Japan According to the Carter-Israel conjecture, the end-state of the gravitational collapse of matter is a Kerr-Newman black hole. Nevertheless, neither the theory nor observations can confirm that. In this talk, we discuss the possibility that the collapsing matter can create a super- spinning compact object with no event horizon, and we show how near future observations at sub-millimeter wavelength of SgrA* can test this scenario for the black hole candidate in the Galactic Center. 1 Introduction The question about the nature of the end-state of the gravitational collapse of matter is a long- standing issue which is still unsolved. At the theoretical level, the question might be addressed by general relativity (GR), our current theory of gravity. Here we know some singularity theorems which show that collapsing matter leads to the formation of singularities. Basically there are two possibilities: if the singularity is hidden behind an event horizon, the final product is a black hole (BH), if it is not, we get a naked singularity (NS). However, the true question is if “real matter” can form a NS. That is unknown, even because it is not so easy to say what “real matter” must be. In addition to this, it is not obvious that GR can address the issue: the theory has been tested only in the weak field limit and we do not know if it works in the case of strong gravity. As for observations, today we have clear evidences supporting the existence of super-massive bodies at the center of many galaxies and compact stellar-mass bodies in the Galaxy. These objects are very likely the final product of the gravitational collapse of matter and are believed to be BHs, but actually there are no evidences that they have an event horizon and we do not know if the spacetime around them is like the one predicted by GR. Even if GR allows for the creation of NSs, their existence seems to be problematic: in a spacetime containing a NS, it is typically possible to go back in time and therefore to violate causality. So, it is common opinion that NSs cannot be created by any physical process (Cosmic Censorship conjecture) 1. When we consider the case of collapsing matter, this idea leads to the Carter-Israel conjecture: the final product of the gravitational collapse of matter is a Kerr- Newman BH. The latter is an object characterized by just three parameter; that is, the mass M, the electric charge Q, and the spin J (or the Kerr parameter a = J/M). These three parameters are not completely free, but must satisfy the relation M2 > Q2 + a2, which is just the condition for the existence of the horizon. In what follows, we can restrict our discussion to the case Q = 0, because the electric charge is usually negligible for large astrophysical bodies. 2 Motivations for new physics It is well known that simple considerations suggest that the Planck scale, EP l ∼1019 GeV, is the natural UV cut-offof classical GR. In this case, the theory would be unable to describe phenomena in which the characteristic energy exceeds EP l. If we apply this idea to the case of a Kerr spacetime with M < |a|, where observer-independent quantities like the scalar curvature diverge at the singularity, it is at least questionable to expect that the GR prediction of the violation of causality is reliable: the latter requires that a particle coming from infinity “enters” into the singularity2! On the other hand, new physics may replace the singularity with something else and Nature may conserve causality not because it is impossible to create a NS, but because there is no singularity in the full theory. Adopting this point of view, there are no fundamental reasons that forbid the creation of a super-compact object with M < |a| in the Universe. 3 Direct image of the accretion flow of SgrA* In this talk, we discuss the possibility of testing the Carter-Israel conjecture by observing the direct image of the accretion flow onto the BH candidate in the Galactic Center. This is a short summary of the material presented in Bambi and Freese 3 and Takahashi et al. 4. 3.1 Present observations Because of the strong gravitational field, the light passing near compact objects does not go along straight lines, but bends. The result is that the apparent size of a compact object seen by a distant observer is always larger than the real size of the object. In Doeleman et al. 5, the authors reported the observation at the wavelength of 1.3 mm of the radio source SgrA*, which is coincident with the position of the BH candidate in th

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