Schwarzschild geometry counterpart in semiclassical gravity

We investigate the effects of vacuum polarization on vacuum static spherically-symmetric spacetimes. We start from the Polyakov approximation to the renormalized stress-energy tensor (RSET) of a minimally coupled massless scalar field. This RSET is not regular at $r=0$, so we define a regularized version of the Polyakov RSET. Using this Regularized RSET, and under the previous symmetry assumptions, we find all the solutions to the semiclassical field equations in vacuum. The resulting counterpart to the Schwarzschild classical geometry substitutes the presence of an event horizon by a wormhole throat that connects an external asymptotically flat region with an internal asymptotic region possessing a naked singularity: there are no semiclassical vacuum solutions with well-defined Cauchy surfaces. We also show that the Regularized Polyakov RSET allows for wormhole geometries of arbitrarily small throat radius. This analysis paves the way to future investigations of proper stellar configurations with an internal non-vacuum region.Comment: 22 pages, 4 figures, v2: references and minor changes added to match published versio

Comment on "Einstein-Gauss-Bonnet Gravity in Four-Dimensional Spacetime"

We argue that several statements in Phys. Rev. Lett. 124, 081301 (2020) are not correct.Comment: 2 pages, accepted as a Comment in Physical Review Letter

Inconsistencies in four-dimensional Einstein-Gauss-Bonnet gravity

We attempt to clarify several aspects concerning the recently presented four-dimensional Einstein-Gauss-Bonnet gravity. We argue that the limiting procedure outlined in [Phys. Rev. Lett. 124, 081301 (2020)] generally involves ill-defined terms in the four dimensional field equations. Potential ways to circumvent this issue are discussed, alongside some remarks regarding specific solutions of the theory. We prove that, although linear perturbations are well behaved around maximally symmetric backgrounds, the equations for second-order perturbations are ill-defined even around a Minkowskian background. Additionally, we perform a detailed analysis of the spherically symmetric solutions, and find that the central curvature singularity can be reached within a finite proper time.Comment: 8 pages, 2 figures, and a supplementary Mathematica notebook; version accepted for publication in Chinese Physics

Renormalized stress-energy tensor for scalar fields in Hartle-Hawking, Boulware and Unruh states in the Reissner-Nordstr\"om spacetime

In this paper, we consider a quantum scalar field propagating on the Reissner-Nordstr\"om black hole spacetime. We compute the renormalized stress-energy tensor for the field in the Hartle-Hawking, Boulware and Unruh states. When the field is in the Hartle-Hawking state, we renormalize using the recently developed ``extended coordinate'' prescription. This method, which relies on Euclidean techniques, is very fast and accurate. Once, we have renormalized in the Hartle-Hawking state, we compute the stress-energy tensor in the Boulware and Unruh states by leveraging the fact that the difference between stress-energy tensors in different quantum states is already finite. We consider a range of coupling constants and masses for the field and a range of electric charge values for the black hole, including near-extreme values. Lastly, we compare these results with the analytic approximations available in the literature.Comment: 18 pages, 4 figure

Ultracompact horizonless objects in order-reduced semiclassical gravity

The backreaction of quantum fields in their vacuum state results in equilibrium structures that surpass the Buchdahl compactness limit. Such backreaction is encapsulated in the vacuum expectation value of the renormalized stress-energy tensor (RSET). In previous works we presented analytic approximations to the RSET, obtained by dimensional reduction, available in spherical symmetry, and showed that the backreaction-generated solutions described ultracompact fluid spheres with a negative mass interior. Here, we derive a novel approximation to the RSET that does not rely on dimensional reduction, but rather on a perturbative reduction of the differential order. This approximation also leads to regular stars surpassing the Buchdahl limit. We conclude that this is a consequence of the negative energies associated with the Boulware vacuum which, for sufficiently compact fluid spheres, make the Misner-Sharp mass negative near the centre of spherical symmetry. Our analysis provides further cumulative evidence that quantum vacuum polarization is capable of producing new forms of stellar equilibrium with robust properties accross different analytical approximations to the RSET.Comment: 11 pages, 4 figure

Inversion of statistics and thermalization in the Unruh effect

We derive a master equation for the reduced density matrix of a uniformly accelerating quantum detector in arbitrary dimensions, generically coupled to a field initially in its vacuum state, and analyze its late time regime. We find that such density matrix asymptotically reaches a Gibbs state. The particularities of its evolution towards this state are encoded in the response function, which depends on the dimension, the properties of the fields, and the specific coupling to them. We also compare this situation with the thermalization of a static detector immersed in a thermal field state, pinpointing the differences between both scenarios. In particular, we analyze the role of the response function and its effect on the evolution of the detector towards equilibrium. Furthermore, we explore the consequences of the well-known statistics inversion of the response function of an Unruh-DeWitt detector linearly coupled to a free scalar field in odd spacetime dimensions. This allows us to precise in which sense accelerated detectors in Minkowski vacuum behave as static detectors in a thermal bath and in which sense they do not.Comment: 9 pages, no figure

Asymptotically flat vacuum solutions in order-reduced semiclassical gravity

We investigate the effects of quantum backreaction on the Schwarzschild geometry in the semiclassical approximation. The renormalized stress-energy tensor (RSET) of a scalar field is modelled via an order reduction of the analytical approximation derived by Anderson, Hiscock and Samuel (AHS). As the resulting AHS semiclassical Einstein equations are of fourth-derivative order in the metric, we follow a reduction of order prescription to shrink the space of solutions. Motivated by this prescription, we develop a method that allows to obtain a novel analytic approximation for the RSET that exhibits all the desired properties for a well-posed RSET: conservation, regularity, and correct estimation of vacuum-state contributions. We derive a set of semiclassical equations sourced by the order-reduced AHS-RSET in the Boulware state. We classify the self-consistent solutions to this set of field equations, discuss their main features and address how well they resemble the solutions of the higher-order semiclassical theory. Finally, we establish a comparison with previous results in the literature obtained through the Polyakov approximation for minimally coupled scalar fields.Comment: 20 pages, 4 figure

Vacuum Semiclassical Gravity Does Not Leave Space for Safe Singularities

General relativity predicts its own demise at singularities but also appears to conveniently shield itself from the catastrophic consequences of such singularities, making them safe. For instance, if strong cosmic censorship were ultimately satisfied, spacetime singularities, although present, would not pose any practical problems to predictability. Here, we argue that under semiclassical effects, the situation should be rather different: the potential singularities which could appear in the theory will generically affect predictability, and so one will be forced to analyse whether there is a way to regularise them. For these possible regularisations, the presence and behaviour of matter during gravitational collapse and stabilisation into new structures will play a key role. First, we show that the static semiclassical counterparts to the Schwarzschild and Reissner–Nordström geometries have singularities which are no longer hidden behind horizons. Then, we argue that in dynamical scenarios of formation and evaporation of black holes, we are left with only three possible outcomes which could avoid singularities and eventual predictability issues. We briefly analyse the viability of each one of them within semiclassical gravity and discuss the expected characteristic timescales of their evolution

Hydrostatic equilibrium in the semiclassical approximation

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.La teoría cuántica de campos en espacio-tiempos curvos (QFTCS) es una de las piedras angulares de la física teórica moderna. Esta teoría combina los reinos gravitatorio y cuántico de un modo único, por medio de considerar la influencia de los campos cuánticos sobre un espacio-tiempo clásico, y viceversa. Mientras que la QFTCS originó el estudio de los fenómenos de creación de partículas en cosmología y de emisión de radiación Hawking en agujeros negros, las implicaciones de esta teoría en la física de estrellas relativistas compactas han permanecido, en gran parte, sin ser abordadas. Esta tesis es una exploración. Dentro del marco de la QFTCS, buscamos nuevas figuras de equilibrio estelar sustentadas por las fuerzas repulsivas características de la energía del vacío. Con el fin de abordar un problema tan amplio, adoptamos un acercamiento progresivo, resolviendo el problema de la backreaction semiclásica en situaciones de creciente complejidad, pero siempre bajo los supuestos de estaticidad y simetría esférica. Modelizamos el tensor de energía-impulso renormalizado (RSET) asociado a la materia cuántica por medio de diversas aproximaciones analíticas con el fin de, en primer lugar, analizar su impacto sobre los agujeros negros de Schwarzschild y Reissner-Nordström. Acto seguido, nos centramos en estrellas ultracompactas cuya densidad clásica es constante. Estas búsquedas nos conducen al descubrimiento de un nuevo objeto compacto exótico: la estrella relativista semiclásica. Dichos objetos están compuestos por una mezcla de materia clásica y cuántica, posibles gracias a un sorprendente equilibrio de fuerzas entre ambos agentes. Las estrellas semiclásicas pueden llegar a ser tan compactas como los agujeros negros, pero destacan frente a otras propuestas similares porque i) es un modelo potencialmente comprobable mediante observaciones de ondas gravitatorias, y ii) no involucran ninguna física más allá de la QFTCS, que se trata de un marco sólido y bien establecido. Los análisis presentados en esta tesis se adentran en terra incognita, y desvelan un campo de estudio sorprendentemente rico: el equilibrio hidrostático en gravedad semiclásica. El contenido de esta tesis está basado en los siguientes artículos del candidato (y sus colaboradores) [1–7]. El contenido de cada uno de los capítulos es el siguiente: • El capítulo 1 es un resumen del contexto en el que se enmarcan nuestras investigaciones. Proporcionamos una visión general del campo de la gravedad semiclásica, con especial énfasis en las aproximaciones a los tensores de energía-impulso renormalizados. Introducimos el RSET de Polyakov Regularizado (RP-RSET), del cual hacemos uso en los capítulos 2 a 5, y revisamos las principales propiedades físicas de las estrellas relativistas semiclásicas. • En los capítulos 2 y 3 obtenemos las contrapartidas semiclásicas de los espacio-tiempos de Schwarzschild y Reissner-Nordström, es decir, las geometrías asintóticamente planas y estáticas del vacío (o electrovacío) que incorporan la backreaction del RP-RSET (regularizado con un cutoff ). El resultado más reseñable es la ausencia completa de horizontes de sucesos, que se transforman en singularidades de curvatura a consecuencia de la backreaction. La contrapartida semiclásica del agujero negro extremal exhibe un horizonte singular, “cuasi-extremal”. Concluimos que en gravedad semiclásica los horizontes deben ser evaporativos y dinámicos. En caso contrario, es necesario introducir un fluido de materia clásico para obtener espacio-tiempos regulares. • El capítulo 4 es el más largo de esta tesis ya que contiene una clasificación exhaustiva del espacio de soluciones de estrellas clásicas y semiclásicas de densidad constante. Proporcionamos un catálogo de todas las soluciones estelares semiclásicas, con especial énfasis en una familia de objetos que logran superar el límite de Buchdahl a la vez que están arbitrariamente cerca de convertirse en regulares. Esta propiedad sugiere explorar otros esquemas de regularización para el RP-RSET que consigan lograr una regularidad estricta. • El capítulo 5 contiene el resultado central de esta tesis. Encontramos, por medio de las mínimas suposiciones, familias de esquemas de regularización para el RP-RSET que son consistentes con la existencia de espacio-tiempos estelares de compacidad arbitraria. Las soluciones resultantes exhiben una serie de propiedades universales: un interior de masa negativa con presiones clásicas que crecen hacia el interior, así como la ausencia de singularidades de curvatura y horizontes de sucesos. Concluimos con una disertación acerca de las implicaciones de este descubrimiento. • Por último, el capítulo 6 constituye una primera incursión en una de las futuras líneas de investigación surgidas a raíz de esta tesis. Retomamos la contrapartida semiclásica de la geometría de Schwarzschild pero esta vez por medio de una aproximación al RSET alternativa, basada en una reducción de orden perturbativa. Al comparar estos resultados con los del capítulo 2 logramos extraer conclusiones físicas robustas de los análisis semiclásicos. Finalmente, esbozamos algunos resultados preliminares que surgen al aplicar este método a estrellas de densidad constante. Así, probamos la existencia de estrellas relativistas semiclásicas con características afines a las del capítulo 5. • Concluimos con algunos comentarios finales y perspectivas de futuro en el capítulo 7. He ideado esta tesis como un mapa de carreteras que muestra el camino principal que seguimos en nuestras investigaciones, pero también los diversos desvíos que se produjeron por el camino. Es una recopilación de reflexiones, ideas, intuiciones y una especie de recipiente a través del cual he intentado plasmar mi forma de experimentar la investigación en física teórica. Espero que la lectura de esta tesis sea de tu agrado, pero sobre todo deseo que sea útil para alguien, en algún lugar (de algún modo). No dudes en ponerse en contacto conmigo por cualquier motivo relacionado con este texto. Te lo agradezco de corazón.Tesis Univ. Granada

Hydrostatic equilibrium in the semiclassical approximation

[EN] Quantum field theory in curved spacetimes (QFTCS) stands as one of the corner- stones 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 Schwarzs- child 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 semiclas- sical 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 be- ing 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.[ES] La teoría cuántica de campos en espacio-tiempos curvos (QFTCS) es una de las piedras angulares de la física teórica moderna. Esta teoría combina los reinos gravitatorio y cuántico de un modo único, por medio de considerar la influencia de los campos cuánticos sobre un espacio-tiempo clásico, y viceversa. Mientras que la QFTCS originó el estudio de los fenómenos de creación de partículas en cosmología y de emisión de radiación Hawking en agujeros negros, las implicaciones de esta teoría en la física de estrellas relativistas compactas han permanecido, en gran parte, sin ser abordadas. Esta tesis es una exploración. Dentro del marco de la QFTCS, buscamos nuevas figuras de equilibrio estelar sustentadas por las fuerzas repulsivas características de la energía del vacío. Con el fin de abordar un problema tan amplio, adoptamos un acercamiento progresivo, resolviendo el problema de la backreaction semiclásica en situaciones de creciente complejidad, pero siempre bajo los supuestos de estaticidad y simetría esférica. Modelizamos el tensor de energía-impulso renormalizado (RSET) asociado a la materia cuántica por medio de diversas aproximaciones analíticas con el fin de, en primer lugar, analizar su impacto sobre los agujeros negros de Schwarzschild y Reissner-Nordström. Acto seguido, nos centramos en estrellas ultracompactas cuya densidad clásica es constante. Estas búsquedas nos conducen al descubrimiento de un nuevo objeto compacto exótico: la estrella relativista semiclásica. Dichos objetos están compuestos por una mezcla de materia clásica y cuántica, posibles gracias a un sorprendente equilibrio de fuerzas entre ambos agentes. Las estrellas semiclásicas pueden llegar a ser tan compactas como los agujeros negros, pero destacan frente a otras propuestas similares porque i) es un modelo potencialmente comprobable mediante observaciones de ondas gravitatorias, y ii) no involucran ninguna física más allá de la QFTCS, que se trata de un marco sólido y bien establecido. Los análisis presentados en esta tesis se adentran en terra incognita, y desvelan un campo de estudio sorprendentemente rico: el equilibrio hidrostático en gravedad semiclásica. El contenido de esta tesis está basado en los siguientes artículos del candidato (y sus colaboradores) [1–7]. El contenido de cada uno de los capítulos es el siguiente: • El capítulo 1 es un resumen del contexto en el que se enmarcan nuestras in- vestigaciones. Proporcionamos una visión general del campo de la gravedad semiclásica, con especial énfasis en las aproximaciones a los tensores de energía-impulso renormalizados. Introducimos el RSET de Polyakov Regular- izado (RP-RSET), del cual hacemos uso en los capítulos 2 a 5, y revisamos las principales propiedades físicas de las estrellas relativistas semiclásicas. • En los capítulos 2 y 3 obtenemos las contrapartidas semiclásicas de los espacio-tiempos de Schwarzschild y Reissner-Nordström, es decir, las ge- ometrías asintóticamente planas y estáticas del vacío (o electrovacío) que incorporan la backreaction del RP-RSET (regularizado con un cutoff ). El resultado más reseñable es la ausencia completa de horizontes de sucesos, que se transforman en singularidades de curvatura a consecuencia de la back- reaction. La contrapartida semiclásica del agujero negro extremal exhibe un horizonte singular, “cuasi-extremal”. Concluimos que en gravedad semiclásica los horizontes deben ser evaporativos y dinámicos. En caso contrario, es nece- sario introducir un fluido de materia clásico para obtener espacio-tiempos regulares. • El capítulo 4 es el más largo de esta tesis ya que contiene una clasificación exhaustiva del espacio de soluciones de estrellas clásicas y semiclásicas de densidad constante. Proporcionamos un catálogo de todas las soluciones estelares semiclásicas, con especial énfasis en una familia de objetos que logran superar el límite de Buchdahl a la vez que están arbitrariamente cerca de convertirse en regulares. Esta propiedad sugiere explorar otros esquemas de regularización para el RP-RSET que consigan lograr una regularidad estricta. • El capítulo 5 contiene el resultado central de esta tesis. Encontramos, por medio de las mínimas suposiciones, familias de esquemas de regularización para el RP-RSET que son consistentes con la existencia de espacio-tiempos estelares de compacidad arbitraria. Las soluciones resultantes exhiben una serie de propiedades universales: un interior de masa negativa con presiones clásicas que crecen hacia el interior, así como la ausencia de singularidades de curvatura y horizontes de sucesos. Concluimos con una disertación acerca de las implicaciones de este descubrimiento. • Por último, el capítulo 6 constituye una primera incursión en una de las futuras líneas de investigación surgidas a raíz de esta tesis. Retomamos la contrapartida semiclásica de la geometría de Schwarzschild pero esta vez por medio de una aproximación al RSET alternativa, basada en una reducción de orden perturbativa. Al comparar estos resultados con los del capítulo 2 logramos extraer conclusiones físicas robustas de los análisis semiclásicos. Finalmente, esbozamos algunos resultados preliminares que surgen al aplicar este método a estrellas de densidad constante. Así, probamos la existencia de estrellas relativistas semiclásicas con características afines a las del capítulo 5. • Concluimos con algunos comentarios finales y perspectivas de futuro en el capítulo 7. He ideado esta tesis como un mapa de carreteras que muestra el camino principal que seguimos en nuestras investigaciones, pero también los diversos desvíos que se produjeron por el camino. Es una recopilación de reflexiones, ideas, intuiciones y una suerte de vial a través del cual he intentado plasmar mi forma de experimentar la investigación en física teórica. Espero que la lectura de esta tesis sea de tu agrado, pero sobre todo deseo que sea útil para alguien, en algún lugar (de algún modo). No dudes en ponerte en contacto conmigo por cualquier motivo relacionado con este texto. Te lo agradezco de corazón.Este trabajo ha sido posible gracias a la financiación procedente del Gobierno de España a través de los proyectos PID2020-118159GB-C43, PID2020-118159GB-C44 (con contribución del FEDER), y por la Junta de Andalucía mediante el proyecto FQM219. Agradezco el apoyo económico de la beca CEX2021-001131-S financiada por MCIN/AEI/ 10.13039/501100011033Peer reviewe