General Relativity and Quantum Cosmology (gr-qc)

Abstract: In this series of papers, we present a set of methods to revive quantum geometrodynamics, which has been buried due to its numerous mathematical and conceptual challenges. In this paper, we introduce the regularization scheme on which we base the subsequent quantization and continuum limit of the theory. Specifically, we constrain the phase space of classical geometrodynamics to piecewise constant fields, resulting in a theory with finitely many degrees of freedom of the spatial metric field. As this representation effectively corresponds to a lattice theory, we can utilize well--known techniques to depict the constraints and their algebra on the lattice. We compute lattice corrections to the constraint algebra and show that they vanish in the continuum limit. This model can now be quantized using the usual methods of finite--dimensional quantum mechanics, as we demonstrate in the following paper. The application of the continuum limit is the subject of a future publication.

Abstract: In recent times, astounding observations of both over- and under-luminous type Ia supernovae have emerged. These peculiar observations hint not only at surpassing the Chandrasekhar limit but may also suggest potential modifications in the physical attributes of their progenitors, such as their cooling rate. This, in turn, can influence their temporal assessments and provide a compelling explanation for these intriguing observations. In this spirit, we investigate here the cooling process of white dwarfs in $f(R,T)$ gravity with the simplest model $f(R,T) = R + \lambda T$, where $\lambda$ is the model parameter. Our modelling suggests that the cooling timescale of white dwarfs exhibits an inverse relationship with the model parameter $\lambda$, which implies that for identical initial conditions, white dwarfs in $f(R,T)$ gravity cool faster. This further unveils that in the realm of $f(R,T)$ gravity, the energy release rate for white dwarfs increases as $\lambda$ increases. Furthermore, we also report that the luminosity of the white dwarfs also depends on $\lambda$ and an upswing in $\lambda$ leads to an amplification in the luminosity, and consequently a larger white dwarf in general relativity can exhibit comparable luminosity to a smaller white dwarf in $f(R,T)$ gravity.

Abstract: Dark matter is undoubtedly one of the fundamental, albeit unknown, components of the standard cosmological model. The failure to detect WIMPs, the most promising candidate particle for cold dark matter, actually opens the way for the exploration of viable alternatives, of which ultralight bosonic particles with masses $\sim 10^{-21}$ eV represent one of the most encouraging. N-body simulations have shown that such particles form solitonic cores in the innermost parts of virialized galactic halos that are supported by internal quantum pressure on characteristic $\sim$kpc de Broglie scales. In the Galaxy, this halo region can be probed by means of S-stars orbiting the supermassive black hole Sagittarius A* to unveil the presence of such a solitonic core and, ultimately, to bound the boson mass $m_\psi$. Employing a Monte Carlo Markov Chain algorithm, we compare the predicted orbital motion of S2 with publicly available data and set an upper bound $m_\psi \lesssim 3.2\times 10^{-19}$ eV on the boson mass, at 95% confidence level. When combined with other galactic and cosmological probes, our constraints help to reduce the allowed range of the bosonic mass to $(2.0 \lesssim m_\psi \lesssim 32.2)\times 10^{-20}$ eV, at the 95% confidence level, which opens the way to precision measurements of the mass of the ultralight bosonic dark matter.

Abstract: We present analytic stationary and axially-symmetric black hole solutions to the semiclassical Einstein equations that are sourced by the trace anomaly. We also find that the same spacetime geometry satisfies the field equations of a subset of Horndeski theories featuring a conformally coupled scalar field. We explore various properties of these solutions, and determine the domain of existence of black holes. These black holes display distinctive features, such as a non-spherically symmetric event horizon and violations of the Kerr bound.