86 research outputs found
Horizon quantum mechanics of collapsing shells
No full textAbstract We study the probability that a horizon appears when concentric shells of matter collide, by computing the horizon wave-function of the system. We mostly consider the collision of two ultra-relativistic shells, both shrinking and expanding, at the moment their radii are equal, and find a probability that the system is a black hole which is in qualitative agreement with what one would expect according to the hoop conjecture and the uncertainty principle of quantum physics, and parallels the results obtained for simpler sources. One new feature however emerges, in that this probability shows a modulation with the momenta of the shells and the radius at which the shells collide, as a manifestation of quantum mechanical interference. Finally, we also consider the case of one light shell collapsing into a larger central mass
Star equilibrium: from BNG to TOV
No full textWe study the role of the equilibrium equation in
bootstrapped Newtonian gravity (BNG) by including terms
inspired by the post-Newtonian expansion of the Tolman–
Oppenheimer–Volkov (TOV) equation. We then compare
(approximate) BNG solutions for homogenous stars with
their Newtonian and General Relativistic exact solutions.
Regardless of the additional terms from the conservation
equation, BNG stars do not exhibit a Buchdahl limit. How-
ever, specific extra terms added to this equation can cause the
pressure to become negative inside stars with compactness
smaller than the critical values for BNG black hole formation
Polytropic stars in bootstrapped Newtonian gravity
No full textWe study self-gravitating stars in the bootstrapped Newtonian picture for polytropic equations of state. We consider stars that span a wide range of compactness values. Both matter density and pressure are sources of the gravitational potential. Numerical solutions show that the density profiles can be well approximated by Gaussian functions. Later we assume Gaussian density profiles to investigate the interplay between the compactness of the source, the width of the Gaussian density profile and the polytropic index. We also dedicate a section to comparing the pressure and density profiles of the bootstrapped Newtonian stars to the corresponding general relativistic solutions. We also point out that no Buchdahl limit is found, which means that the pressure can in principle support a star of arbitrarily large compactness. In fact, we find solutions representing polytropic stars with compactness above the Buchdhal limit
Quantum hoop conjecture: Black hole formation by particle collisions
No full textAbstractWe address the issue of (quantum) black hole formation by particle collision in quantum physics. We start by constructing the horizon wave-function for quantum mechanical states representing two highly boosted non-interacting particles that collide in flat one-dimensional space. From this wave-function, we then derive a probability that the system becomes a black hole as a function of the initial momenta and spatial separation between the particles. This probability allows us to extend the hoop conjecture to quantum mechanics and estimate corrections to its classical counterpart
Horizon wave-function and the quantum cosmic censorship
No full textAbstractWe investigate the Cosmic Censorship Conjecture by means of the horizon wave-function (HWF) formalism. We consider a charged massive particle whose quantum mechanical state is represented by a spherically symmetric Gaussian wave-function, and restrict our attention to the superextremal case (with charge-to-mass ratio α>1), which is the prototype of a naked singularity in the classical theory. We find that one can still obtain a normalisable HWF for α2<2, and this configuration has a non-vanishing probability of being a black hole, thus extending the classically allowed region for a charged black hole. However, the HWF is not normalisable for α2>2, and the uncertainty in the location of the horizon blows up at α2=2, signalling that such an object is no more well-defined. This perhaps implies that a quantum Cosmic Censorship might be conjectured by stating that no black holes with charge-to-mass ratio greater than a critical value (of the order of 2) can exist
Approximating compact objects in bootstrapped Newtonian gravity: use of the canonical potential
No full textWe consider compact objects in a classical and non-relativistic generalisation of Newtonian gravity, dubbed bootstrapped Newtonian theory, which includes higher-order derivative interaction terms of the kind generically present in the strong-field regime of gravity. By means of a field redefinition, the original bootstrapped Newtonian action is written in a canonical Newtonian form with non-linear source terms. Exact analytic solutions remain unattainable, but we show that perturbative solutions of the canonical theory can be efficiently used to derive approximate descriptions of compact objects. In particular, using the canonical potential, we can more directly and generally show that the Arnowitt–Deser–Misner mass differs from the (Newtonian) proper mass due to the non-linear couplings in the theory. A few examples of sources with different density profiles are explicitly reanalysed in this framework
Quantum production of black holes at colliders
No full textWe investigate black hole production in p p col- lisions at the Large Hadron Collider by employing the hori- zon quantum mechanics for models of gravity with extra spatial dimensions. This approach can be applied to pro- cesses around the fundamental gravitational scale and nat- urally yields a suppression below the fundamental gravita- tional scale and for increasing number of extra dimensions. The results of numerical simulations performed with the black hole event generator BLACKMAX are here reported in order to illustrate the main differences in the numbers of expected black hole events and mass distributions
Bootstrapped Newtonian stars and black holes
No full textWe study equilibrium configurations of a homogenous ball of matter in a bootstrapped description of gravity which includes a gravitational self-interaction term beyond the Newtonian coupling. Both matter density and pressure are accounted for as sources of the gravitational potential for test particles. Unlike the general relativistic case, no Buch- dahl limit is found and the pressure can in principle support a star of arbitrarily large compactness. By defining the hori- zon as the location where the escape velocity of test particles equals the speed of light, like in Newtonian gravity, we find a minimum value of the compactness for which this occurs. The solutions for the gravitational potential here found could effectively describe the interior of macroscopic black holes in the quantum theory, as well as predict consequent devia- tions from general relativity in the strong field regime of very compact objects
Binary mergers in bootstrapped Newtonian gravity: mass gap and black hole area law
No full textWe study binary mergers in bootstrapped Newtonian gravity, where higher-order
couplings are added to the non-relativistic Lagrangian for the Newtonian
potential. In this theory, the Arnowitt-Deser-Misner (ADM) mass differs from
both the proper mass of Newtonian gravity and the proper mass of general
relativity, which affects the interpretation of astrophysical and cosmological
events. The aforementioned difference particularly provides important
phenomenological constraints for the mass of the emitted matter and the
compactness of the final object after the merger. The interpretation of the
GW150914 signal in this theory also shows that LIGO's findings do not violate
the mass gap, contrary to usual claims. We indeed find that typical stellar
black hole masses can fit LIGO's data for a considerable range of compactness
values. We calculate the black hole entropy in this context, which leads to a
generalised black hole area law. Non-linear effects are found to effectively
change only the gravitational strength via the renormalization of Newton's
constant in this case.Comment: 14 pages, 1 figure, to appear in Phys.Lett.
Bootstrapping Newtonian gravity
No full textA nonlinear equation obtained by adding gravitational self-interaction terms to the Poisson equation for Newtonian gravity is here employed in order to analyze a static spherically symmetric homogeneous compact source of given proper mass and radius and the outer vacuum. The main feature of this picture is that, although the freedom of shifting the potential by an arbitrary constant is of course lost, the solutions remain qualitatively very close to the Newtonian behavior. We also notice that the negative gravitational potential energy is smaller than the proper mass for sources with small compactness, but for sources that should form black holes according to general relativity, the gravitational potential energy becomes of the same order of magnitude of the proper mass, or even larger. Moreover, the pressure overcomes the energy density for large values of the compactness, but it remains finite for finite compactness; hence there exists no Buchdahl limit. This classical description is meant to serve as the starting point for investigating quantum features of (near) black hole configurations within the corpuscular picture of gravity in future developments
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