Hydrostatic equilibrium in the semiclassical approximation

Resumo

Quantum field theory in curved spacetimes (QFTCS) stands as one of the cornerstones of modern theoretical physics. This theory blends together the gravitational and quantum realms in a unique way: It considers the influence of quantum fields on a classical spacetime, and vice versa. While QFTCS gave birth to the phenomena of cosmological particle creation and Hawking radiation emission in black holes, its impact on the physics of compact relativistic stars has remained, for the most part, undiscussed. This thesis is an exploratory analysis. Within the framework of QFTCS, we search for new figures of stellar equilibrium supported by the repulsive forces that characterize vacuum energies. To tackle such an ambitious problem, we follow a constructive approach, solving the semiclassical backreaction problem in scenarios of increasing complexity, but always under the assumptions of staticity and spherical symmetry. The renormalized stress-energy tensor (RSET) of quantum matter is modeled through various analytical approximations in order to evaluate its impact on the Schwarzschild and Reissner-Nordström black holes first, to later address (ultra- )compact stars of uniform classical density. Our explorations lead to the discovery of a novel exotic compact object: the semiclassical relativistic star. These objects are composed of a mixture of classical and quantum matter, sustained thanks to a surprising balance of forces between these two agents. Semiclassical stars can become as compact as black holes but stand out among other proposals since they are i) potentially testable through gravitational-wave observations, and ii) do not rely on any physics beyond QFTCS, which is a solid, well-established framework. The analyses presented in this thesis venture into terra incognita, and unveil a surprisingly rich field of study: hydrostatic equilibrium in semiclassical gravity. The content of this thesis is based on the following publications by the candidate (and collaborators) [1–7]. The content of each Chapter is the following: • Chapter 1 is a summary of the context in which these investigations are embedded. We provide an overview of the field of semiclassical gravity, with particular emphasis on approximating renormalized stress-energy tensors. We introduce the Regularized Polyakov RSET (RP-RSET), to be used in Chapters 2 to 5, and review the main physical properties of semiclassical relativistic stars. • In Chapters 2 and 3 we obtain the semiclassical counterparts to the Schwarzschild and Reissner-Nordström spacetimes, that is, the asymptotically flat, static vacuum (or electrovacuum) geometries incorporating the backreaction of the RP-RSET (regularized with a cutoff). The most remarkable result is the complete absence of event horizons, transformed into curvature singularities by backreaction effects. The semiclassical counterpart to the extremal black hole exhibits a singular, “quasi-extremal” horizon. Consequently, in semiclassical gravity horizons must be evaporative and dynamical. Otherwise, some classical matter fluid must be introduced to obtain regular spacetimes. • Chapter 4 is the longest Chapter of this thesis as it exhaustively classifies the space of solutions of classical and semiclassical stars of uniform density. We provide a catalogue of all semiclassical stellar solutions, with particular emphasis on a family of objects that can surpass Buchdahl limit while being arbitrarily close to becoming regular. This property suggests exploring other regularization schemes for the RP-RSET that might accomplish strict regularity. • Chapter 5 contains the central result of the thesis. We find, through minimal assumptions, families of regularization schemes for the RP-RSET that are consistent with stellar spacetimes of arbitrary compactness. The resulting solutions exhibit a series of universal properties: a negative-mass interior with classical pressures that grow inwards, and the absence of curvature singularities and event horizons. We elaborate on the implications of this result. • Finally, Chapter 6 constitutes a first incursion into one of the future lines of inquiry suggested by this thesis. We rederive the semiclassical Schwarzschild counterpart but through an alternative RSET approximation based on a perturbative reduction of order. We compare these results with those in Chapter 2, allowing to extract robust physical conclusions from semiclassical analyses along the way. Finally, we sketch some preliminary results that apply this method to uniform density stars, showing that semiclassical relativistic stars with akin characteristics also exist under this prescription. • We conclude with some closing remarks and future prospects in Chapter 7. I like to think of this thesis as a road map showing the main pathway we followed, but also the various diversions that came along the way. It is a compilation of reflections, ideas, intuitions, and a sort of vessel through which I have attempted to embody my way of experiencing the process of research in theoretical physics. I hope you find joy in reading this thesis, but above all I wish it becomes useful for someone, somewhere (somehow). Do not hesitate contacting me for whatever reason regarding this text. I sincerely appreciate it.