General Relativity & Quantum Cosmology

According to the Belinski-Khalatnikov-Lifshitz conjecture, the Bianchi IX spacetime describes the evolution of each spatial point close to a generic spacelike singularity. However, near the singularity, quantum effects are expected to be relevant. Therefore, in this work a quantum analysis of the model is performed, mainly focusing on its chaotic nature. Considering some minimal approximations, it is possible to encode all the information of the quantum degrees of freedom in certain canonical variables, expanding thus the classical phase space. In this way, we can apply the usual methods of dynamical systems for studying chaos. In particular, two techniques are considered. On the one hand, an analytical study is carried out, which provides an isomorphism between the quantum dynamics of Bianchi IX and the geodesic flow on a Riemannian manifold. On the other hand, by means of numerical simulations, the fractal dimension of the boundary between points with different outcome in the space of initial data is studied. The main conclusion is that, although the quantum system is chaotic, the quantum effects considerably reduce this behavior as compared to its classical counterpart.

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Zoom link https://pitp.zoom.us/j/91559466008?pwd=UzQvTGRkR3VQWm9MWDlaaVAyNi9EQT09

In the quest to understand the fundamental structure of spacetime (and subsystems) in quantum gravity, it may be worth exploring the ultimate consequences of non-perturbative canonical quantization, carefully taking into account the constraints and gauge invariance of general relativity. As the reduced phase space (or even the pre-phase space) of gravity lacks a natural linear structure, a generalization of the standard method of quantization (based on global conjugate coordinates) is required. One such generalization is Isham's method based on transitive groups of symplectomorphisms, which we test in some simple examples. In particular, considering a particle that lives on a sphere, in the presence of a magnetic monopole flux, we algebraically recover Dirac's charge quantization condition from a "Casimir matching principle", which we propose as an important tool in selecting natural representations. Finally, we develop the non-perturbative reduced phase space quantization of causal diamonds in (2+1)-dimensional gravity. By solving the constraints in a constant-mean-curvature time gauge and removing all the spatial gauge redundancy, we find that the phase space is the cotangent bundle of $Diff^+(S^1)/PSL(2, \mathbb{R})$. Applying Isham's quantization we find that the Hilbert space of the associated quantum theory carries a (projective) irreducible unitary representation of the $BMS_3$ group. From the Casimir matching principle, we show that the states are realized as wavefunctions on the configuration space with internal indices in unitary irreps of $SL(2, \mathbb{R})$. A surprising result is that the twist of the diamond boundary loop is quantized in terms of the ratio of the Planck length to the boundary length.

Papers on quantization of causal diamonds:
https://arxiv.org/abs/2308.11741
https://arxiv.org/abs/2310.03100

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Zoom link https://pitp.zoom.us/j/98636934234?pwd=THBCcFpYWHYzWmY0YjViY3Q1a3VYdz09

Recently, models with different properties have been proposed for polymerized dust collapse and regular black holes. To fully understand their properties and differences, we provide a systematic procedure to construct effective polymerized spherically symmetric models encoding holonomy corrections as $1+1$d field theory from effective regular cosmological dynamics or stationary effective metrics. We apply this formalism and consider models that have the following advantages: The effective dynamics can be derived from a class of extended mimetic gravity Lagrangians in 4 dimensions. The models admit a consistent Lemaitre-Tolman-Bondi (LTB) condition, by which the dynamics is completely decoupled along the radial direction in LTB coordinates, trivializing the junction condition in dust collapse. The class of effective dynamics admits a polymerized Birkhoff-like theorem, which leads to a stationary effective metric in the polymerized vacuum. The effective dynamics can reproduce known regular black hole solutions, including Bardeen and Hayward, by a suitable choice of holonomy corrections. As a concrete example, we construct an effective model compatible with the improved dynamics of loop quantum cosmology in the decoupled LTB sector. We compare it with several effective polymerized models recently introduced in the context of loop quantum gravity and gain some new insights into the presence of shocks.

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Zoom link https://pitp.zoom.us/j/99966795418?pwd=Ty9mRXNML3NsUXdvcU1WUTdCaWpVZz09

Extreme mass-ratio binary black hole systems, known as EMRIs, are expected to radiate low-frequency gravitational waves detectable by planned space-based Laser Interferometer Space Antenna (LISA). We hope to use these systems to probe black hole spacetimes in exquisite detail and make precision measurements of supermassive black hole properties. Accurate models using general relativistic perturbation theory will allow us to unlock the potential of these unique systems. Such models must include post-geodesic corrections, which account for forces driving the smaller black hole away from a geodesic trajectory. When a spinning body orbits a black hole, its spin couples to the curvature of the background spacetime, introducing post-geodesic correction called the spin-curvature force. In this talk, I will present our calculation of EMRI waveforms that include both spin-curvature forces and the leading backreaction due to gravitational radiation. We use a near-identity transformation to eliminate dependence on the orbital phases, allowing for very fast computation of completely generic worldlines of spinning bodies; such efficiency is crucial for LISA data analysis. Finally, I will discuss what aspects still need to be included in future calculations so that we can use EMRIs for a new era of precision gravitational-wave astronomy, addressing outstanding puzzles in astrophysics, cosmology and fundamental theoretical physics.

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Zoom link https://pitp.zoom.us/j/91917788358?pwd=MWp5OUhxbkRmZDFxWWE4cHR0VlBTUT09

Abstract TBA

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Zoom link https://pitp.zoom.us/j/92901106970?pwd=SEdZajRQYWlrQzJhRnM0WnRpeHVNdz09

In the last years, asymptotic symmetries have regained a lot of interest, and various extensions of the well known BMS group have been considered in the literature. Many charges associated to the diffeomorphisms of the sphere (superboosts and superrotations) have been proposed, but it has not been clear if these charges can be derived from a symplectic potential that is covariant and stationary, i.e satisfying the Wald-Zoupas usual requirements. In this talk I will consider a new asymptotic symmetry group, which is a one dimensional extension of the generalized-BMS group, and construct a stationary symplectic potential, covariant with respect to these symmetries, by adding corner terms to the usual Einstein-Hilbert symplectic potential. Then, we will recover the charges introduced by Compère, Fiorucci and Ruzziconi for superboosts and superrotations. In order to ensure covariance, we will need to introduce an edge mode which has already appeared in the literature, the supertranslation field. I will also explain that its introduction as a corner term can lead us to construct a local (asymptotic) notion of energy for the gravitational waves, providing a physical interpretation of the new charges.

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Zoom link https://pitp.zoom.us/j/97926664729?pwd=VzV2VmQ4eVlzcFdaZkNBNnpqRkMvUT09

A high specific abundance of millisecond radio pulsars has been observed in globular clusters (GCs), motivating theoretical studies of the formation and evolution of these sources through stellar evolution coupled to stellar dynamics. In this talk, I will first demonstrate how we model millisecond pulsars in GCs using realistic cluster simulations. I will show the importance of electron-capture supernovae for neutron star retention, and how millisecond pulsar formation is greatly enhanced through dynamical interaction processes. I will also present some latest results on isolated millisecond pulsars, which are especially intriguing given the fact that millisecond pulsars are descendants of binary star systems. I will demonstrate the potential formation channels of isolated millisecond pulsars, some of which may also link to the formation of magnetars and the newly discovered fast radio bursts in a GC.

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Zoom link https://pitp.zoom.us/j/97622593487?pwd=SHNoM1o3T1JjWVROTkJoZ0NWYmdyQT09

To develop a quantum gravity theory, it is fundamental to move away from the gauge-fixing approach and instead employ a gauge-free analysis. There is an increasing body of evidence suggesting that the symmetries employed for gauge-fixing might carry charge. Consequently, setting the associated fields to zero is a physical constraint on the system, which should be avoided. In this talk, we will examine a partial fixing of the Fefferman-Graham (FG) gauge, referred to as the Weyl-Fefferman-Graham (WFG) gauge, which restores boundary Weyl covariance. We will show that the diffeomorphism mapping WFG to FG can be charged and discuss how this relates to holography.

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Zoom link https://pitp.zoom.us/j/93359035909?pwd=aHo0TUFXekZaeCtrT2FzNDZKUW15Zz09

We investigate perturbations of the Schwarzschild geometry using a linearization of the Einstein vacuum equations within a Bondi-Sachs, or null cone, formalism. We develop a numerical method to calculate the quasinormal modes, and present results for the case ℓ= 2. The values obtained are different than those of a Schwarzschild black hole, and we interpret them as quasinormal modes of a Schwarzschild white hole.

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Zoom link https://pitp.zoom.us/j/93648313308?pwd=akZMZXFKejIwdFphOVU0ZjFpeW13dz09

We use a result of Hawking and Gilkey to define a Euclidean path integral of gravity and matter which has the special property of being independent of the choice of basis in the space of fields. This property allows the path integral to describe also physical regimes that do not admit position bases. These physical regimes are pre-geometric in the sense that they do not admit a mathematical representation of the physical degrees of freedom in terms of fields that live on a spacetime. In regimes in which a spacetime representation does emerge, the geometric properties of the emergent spacetime, such as its dimension and volume, depend on the balance of fermionic pressure and bosonic and gravitational pull. That balance depends, at any given energy scale, on the number of bosonic and fermionic species that contribute, which in turn depends on their masses. This yields an explicit mechanism by which the effective spacetime dimension can depend on the energy scale.

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Zoom link https://pitp.zoom.us/j/91471624951?pwd=RDBYTXc2MGs5bkFKUytYR0huOHYwdz09

If axion Dark Matter exists, then they can collapse to form self-gravitating exotic compact objects known as axion stars. As mergers of such compact objects can potentially yield detectable gravititational waves which are correlated with a burst of electromagnetic radiation, much effort have been expended to compute these signals. I will discuss both the technical and theoretical challenges of this endeavour, and demonstrate such decays. I will show that axion stars may not be stable to electromagnetic decay, raising the question on whether we should expect to see these objects in the first place.

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Zoom link https://pitp.zoom.us/j/98298572209?pwd=WVFZUFJqQzZQdU8vcjhQRVpzVHZDdz09