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Register a new userCosmological Black Hole Observations and Kants Transcendental Aesthetic
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Juna A. Kollmeier
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Kant put forward the notion of the Transcendental Aesthetic (TA) in his manuscript ${it A; Critique; of; Pure; Reason}$. In this note I review the TA in light of the detection of gravitational wave radiation. While the notion of the TA has been refuted in many different ways since its introduction, I argue that this simple proof by contradiction is of interest pedagogically and philosophically. I hope this elucidation may be useful in introductory science courses and in science communication more generally.
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A number of philosophers and scientists have discussed the possibility of inseparability between the subject (i.e., the observer) and the object (i.e., the observed universe). In particular, it has recently been proposed that this inseparability may be obtained through the discrete physical universe being filled with the observers continuous consciousness through quantum evolution with time going backwards. The proposal of a universe view with interwoven matter and mind through cyclical time bears a resemblance to Immanuel Kants discussion of the Copernican Revolution in philosophy, where the priority shifted from the object to the subject.
We determine the causal structure of the McVittie spacetime for a cosmological model with an asymmetric bounce. The analysis includes the computation of trapping horizons, regular, trapped, and anti-trapped regions, and the integration of the trajectories of radial null geodesics before, during, and after the bounce. We find a trapped region since the beginning of the contracting phase up to shortly before the bounce, thus showing the existence of a black hole. When the universe reaches a certain minimum scale in the contracting phase, the trapping horizons disappear and the central singularity becomes naked. These results suggest that neither a contracting nor an expanding universe can accommodate a black hole at all times.
By 1917, V.M. Slipher had singlehandedly established a tendency for spiral nebulae to be redshifted (21 out of 25 cases). From a modern perspective, it could seem surprising that the expansion of the universe was not announced at this point. Examination of Sliphers papers shows that he reached a more subtle conclusion: the identification of cosmological peculiar velocities, including the bulk motion of the Milky Way, leading to a beautiful argument in favour of nebulae as distant stellar systems. Nevertheless, Sliphers data actually contain evidence at >8sigma for a positive mean velocity, even after subtracting the dipole owing to the motion of the observer. In 1929, Hubble estimated distances for a sample of no greater depth, using redshifts due almost entirely to Slipher. Hubbles distances were flawed in two distinct ways: in addition to an incorrect absolute calibration, the largest distances were systematically under-estimated. Nevertheless, he claimed the detection of a linear distance-redshift relation. Statistically, the evidence for such a correlation is less strong than the simple evidence for a positive mean velocity in Hubbles sample. Comparison with modern data shows that a sample of more than twice Hubbles depth would generally be required in order to reveal clearly the global linear expansion in the face of the noise from peculiar velocities. When the theoretical context of the time is examined, the role of the de Sitter model and its prediction of a linear distance-redshift relation looms large. A number of searches for this relation were performed prior to Hubble over the period 1924-1928, with a similar degree of success. All were based on the velocities measured by Slipher, whose work from a Century ago stands out both for the precision of his measurements and for the subtle clarity of the arguments he employed to draw correct conclusions from them.
Primordial black holes (PBHs) are those which may have formed in the early Universe and affected the subsequent evolution of the Universe through their Hawking radiation and gravitational field. To constrain the early Universe from the observational constraint on the abundance of PBHs, it is essential to determine the formation threshold for primordial cosmological fluctuations, which are naturally described by cosmological long-wavelength solutions. I will briefly review our recent analytical and numerical results on the PBH formation.
Dynamical solutions for an evolving multiple network of black holes near a cosmological bounce dominated by a scalar field are investigated. In particular, we consider the class of black hole lattice models in a hyperspherical cosmology, and we focus on the special case of eight regularly-spaced black holes with equal masses when the model parameter $kappa > 1$. We first derive exact time evolving solutions of instantaneously-static models, by utilizing perturbative solutions of the constraint equations that can then be used to develop exact 4D dynamical solutions of the Einstein field equations. We use the notion of a geometric horizon, which can be characterized by curvature invariants, to determine the black hole horizon. We explicitly compute the invariants for the exact dynamical models obtained. As an application, we discuss whether black holes can persist in such a universe that collapses and then subsequently bounces into a new expansionary phase. We find evidence that in the physical models under investigation (and particularly for $kappa > 1$) the individual black holes do not merge before nor at the bounce, so that consequently black holes can indeed persist through the bounce.
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