In this paper, we investigate the gravitational collapse of a Reissner–Nordström–AdS domain wall for both a nonextremal and overcharged collapse. During the collapse, we investigate the quasi-particle production that arises due to the time-dependent metric by coupling a complex scalar field to the background of the collapsing domain wall. The analysis is done by making use of the Ermakov equations which lead to an exact solution for the auxiliary function found in the Milne–Pinney equation. In the nonextremal case, we find that assuming the domain wall is positively charged, where the negatively charged particle production is suppressed compared to the positively charged particles due to the Coulomb attraction and repulsion of the particles with the domain wall itself. The induced quasi-particles approach thermality as time goes to infinity in the IR region of the spectrum, however the UV region of the spectrum remains nonthermal for all time. In the overcharged case, the domain wall oscillates about a radius outside of the naked singularity, abiding by the cosmic censorship conjecture, due to the competition between the Coulomb repulsion and the gravitational attraction. Due to the periodic behavior of the collapsing domain wall, the quasi-particle production acquires a generalized Berry Phase, which is a real and measurable phase. The generalized Berry phase leads to a suppression of the UV region of the spectrum.

We investigate the gravitational collapse of both a massive (Schwarzschild–AdS) and a massive-charged (Reissner–Nordström–AdS) 4-dimensional domain wall in AdS space. Here, we consider both the classical and quantum collapse, in the absence of quasi-particle production and backreaction. For the massive case, we show that, as far as the asymptotic observer is concerned, the collapse takes an infinite amount of time to occur in both the classical and quantum cases. Hence, quantizing the domain wall does not lead to the formation of the black hole in a finite amount of time. For the infalling observer, we find that the domain wall collapses to both the event horizon and the classical singularity in a finite amount of proper time. In the region of the classical singularity, however, the wave function exhibits both nonlocal and nonsingular effects. For the massive-charged case, we show that, as far as the asymptotic observer is concerned, the details of the collapse depend on the amount of charge present; that is, the extremal, nonextremal and overcharged cases. In the overcharged case, the collapse never fully occurs since the solution is an oscillatory solution which prevents the formation of a naked singularity. For the extremal and nonextremal cases, it takes an infinite amount of time for the outer horizon to form. For the infalling observer in the nonextremal case, we find that the domain wall collapses to both the event horizon and the classical singularity in a finite amount of proper time. In the region of the classical singularity, the wave function also exhibits both nonlocal and nonsingular effects. Furthermore, in the large energy density limit, the wave function vanishes as the domain wall approaches classical singularity implying that the quantization does not rid the black hole of its singular nature.

We investigate both the classical and quantum gravitational collapse of a charged, non-rotating $n$-dimensional BTZ black hole in AdS space. This is done by first deriving the conserved mass of a "spherically" symmetric domain wall, which is then taken as the classical Hamiltonian of the domain wall. In the classical picture, we show that, as far as the asymptotic observer is concerned, the details of the collapse depend on the amount of charge present in the domain wall. In the both the extremal and non-extremal cases, the collapse takes an infinite amount of observer time to complete. However, in the over-charged case, the collapse never actually occurs, instead one finds an oscillatory solution which prevents the formation of a naked singularity. As far as the infalling observer is concerned, the collapse is completed within a finite amount of proper time. Thus, the gravitational collapse follows that of the typical formation of a black hole via gravitational collapse. Quantum mechanically, in the absence of induced quasi-particle production and fluctuations of the metric geometry, we take primary interest in the behavior of the collapse near the horizon and near the classical singularity from the point of view of both asymptotic and infalling observers. For the asymptotic observer, we find that quantum effects near the horizon do not change the classical conclusions. For the infalling observer, the most interesting quantum mechanical effect are when the collapsing shell approaches the classical singularity. Here, we find, that the quantum effects in this region display non-local effects, which depend on the energy density of the domain wall.

We investigate the gravitational collapse of a non-rotating n-dimensional BTZ black hole in AdS space in the context of both classical and quantum mechanics. This is done by first deriving the conserved mass of a “spherically” symmetric domain wall, which is taken as the classical Hamiltonian of the black hole. Upon deriving the conserved mass, we also point out that, for a “spherically” symmetric shell, there is an easy and straight-forward way of determining the conserved mass, which is related to the proper time derivative of the interior and exterior times. This method for determining the conserved mass is generic to any situation (i.e. any equation of state), since it only depends on the energy per unit area, σ, of the shell. Classically, we show that the time taken for gravitational collapse follows that of the typical formation of a black hole via gravitational collapse; that is, an asymptotic observer will see that the collapse takes an infinite amount of time to occur, while an infalling observer will see the collapse to both the horizon and the classical singularity occur in a finite amount of time. Quantum mechanically, we take primary interest in the behavior of the collapse near the horizon and near the classical singularity from the point of view of both asymptotic and infalling observers. In the absence of radiation and fluctuations of the metric, quantum effects near the horizon do not change the classical conclusions for an asymptotic observer. The most interesting quantum mechanical effect comes in when investigating near the classical singularity. Here, we find, that the quantum effects in this region are able to remove the classical singularity at the origin, since the wave function is non-singular, and it also displays non-local effects, which depend on the energy density of the domain wall.

In this paper, we consider the occupation number of induced quasi-particles which are produced during a time-dependent process using three different methods: Instantaneous diagonalization, the usual Bogolyubov transformation between two different vacua (more precisely the instantaneous vacuum and the so-called adiabatic vacuum), and the Unruh-DeWitt detector methods. Here we consider the Hamiltonian for a time-dependent Harmonic oscillator, where both the mass and frequency are taken to be time-dependent. From the Hamiltonian we derive the occupation number of the induced quasi-particles using the invariant operator method. In deriving the occupation number we also point out and make the connection between the Functional Schrodinger formalism, quantum kinetic equation, and Bogolyubov transformation between two different Fock space basis at equal times and explain the role in which the invariant operator method plays. As a concrete example, we consider particle production in the flat FRW chart of de Sitter spacetime. Here we show that the different methods lead to different results: The instantaneous diagonalization method leads to a power law distribution, while the usual Bogolyubov transformation and Unruh-DeWitt detector methods both lead to thermal distributions (however the dimensionality of the results are not consistent with the dimensionality of the problem; the usual Bogolyubov transformation method implies that the dimensionality is 3D while the Unruh-DeWitt detector method implies that the dimensionality is 7D/2). It is shown that the source of the descrepency between the instantaneous diagonalization and usual Bogolyubov methods is the fact that there is no notion of well-defined particles in the out vacuum due to a divergent term. In the usual Bogolyubov method, this divergent term cancels leading to the thermal distribution, while in the instantaneous diagonalization method there is no such cancelation leading to the power law distribution. However, to obtain the thermal distribution in the usual Bogolyubov method, one must use the large mass limit. On physical grounds, one should expect that only the modes which have been allowed to sample the horizon would be thermal, thus in the large mass limit these modes are well within the horizon and, even though they do grow, they remain well within the horizon due to the mass. Thus, one should not expect a thermal distribution since the modes will not have a chance to thermalize.

We reinvestigate the emission of Hawking radiation during gravitational collapse to a black hole. Both CGHS collapse of a shock wave in (1+1)-dimensional dilaton gravity and Schwarzschild collapse of a spherically symmetric thin shell in (3+1)-dimensional gravity are considered. Studying the dynamics of in-vacuum polarization, we find that a multi-parametric family of out-vacua exists. Initial conditions for the collapse lead dynamically to different vacua from this family as the final state. Therefore, the form of the out-vacuum encodes memory about the initial quantum state of the system. While most out-vacua feature a non-thermal Hawking flux and are expected to decay quickly, there also exists a thermal vacuum state. Collectively, these observations suggest an interesting possible resolution of the information loss paradox.

We investigate the effect of induced massive radiation given off during the time of collapse of a massive spherically symmetric domain wall in the context of the functional Schr\"odinger formalism. Here we find that the introduction of mass suppresses the occupation number in the infrared regime of the induced radiation during the collapse. The suppression factor is found to be given by $e^{-\beta m}$, which is in agreement with the expected Planckian distribution of induced radiation. Thus a massive collapsing domain wall will radiate mostly (if not exclusively) massless scalar fields, making it difficult for the domain wall to shed any global quantum numbers and evaporate before the horizon is formed.

We investigate gravitational collapse of a (3+1)-dimensional BTZ black string in AdS space in the context of both classical and quantum mechanics. This is done by first deriving the conserved mass per unit length of the cylindrically symmetric domain wall, which is taken as the classical Hamiltonian of the black string. In the quantum mechanical context, we take primary interest in the behavior of the collapse near the horizon and near the origin (classical singularity) from the point of view of an infalling observer. In the absence of radiation, quantum effects near the horizon do not change the classical conclusions for an infalling observer, meaning that the horizon is not an obstacle for him/her. The most interesting quantum mechanical effect comes in when investigating near the origin. First, quantum effects are able to remove the classical singularity at the origin, since the wave function is non-singular at the origin. Second, the Schrödinger equation describing the behavior near the origin displays non-local effects, which depend on the energy density of the domain wall. This is manifest in that derivatives of the wavefunction at one point are related to the value of the wavefunction at some other distant point.

It is currently believed that the Standard Model is an effective low energy theory which in principle may contain higher dimensional non-renormalizable operators. These operators may modify the standard model Higgs potential in many ways, one of which being the appearance of a second vacuum. For a wide range of parameters, this new vacuum becomes the true vacuum. It is then assumed that our universe is currently sitting in the false vacuum. Thus the usual second-order electroweak phase transition at early times will be followed by a second, first-order phase transition. In cosmology, a first-order phase transition is associated with the production of gravity waves. In this paper we present an analysis of the production of gravitational waves during such a second electroweak phase transition. We find that, for one certain range of parameters, the stochastic background of gravitational waves generated by bubble nucleation and collision have an amplitude which is estimated to be of order $\Omega_{GW}h^2\sim10^{-11}$ at $f=3\times 10^{-4}$Hz, which is within reach of the planned sensitivity of LISA. For another range of parameters, we find that the amplitude is estimated o be of order $\Omega_{GW}h^2\sim10^{-25}$ around $f=10^3$Hz, which is within reach of LIGO. Hence, it is possible to detect gravity waves from such a phase transition at two different detectors, with completely different amplitude and frequency ranges.

In this thesis we investigate quantum mechanical effects to various aspects of gravitational collapse. These quantum mechanical effects are implemented in the context of the Functional Schr\odinger formalism. The Functional Schr\odinger formalism allows us to investigate the time-dependent evolutions of the quantum mechanical effects, which is beyond the scope of the usual methods used to investigate the quantum mechanical corrections of gravitational collapse. Utilizing the time-dependent nature of the Functional Schr\odinger formalism, we study the quantization of a spherically symmetric domain wall from the view point of an asymptotic and infalling observer, in the absence of radiation. To build a more realistic picture, we then study the time-dependent nature of the induced radiation during the collapse using a semi-classical approach. Using the domain wall and the induced radiation, we then study the time-dependent evolution of the entropy of the domain wall. Finally we make some remarks about the possible inclusion of backreaction into the system.

We study the evolution of time-dependent fluctuations and particle production in an expanding dS and contracting AdS universe. Using the functional Schrödinger formalism we are able to probe the time-dependent regime which is out of the reach of the standard approximations like the Bogolyubov method. In both cases, the evolution of fluctuations is governed by the harmonic oscillator equation with time-dependent frequency. In the case of an expanding dS universe we explicitly show that the frequency of fluctuations produced at a certain moment diminish in time, while the distribution of the created particles quickly approaches the thermal radiation of the dS space. In the case of a contracting AdS universe we show that the frequency of fluctuations produced at a certain moment grow in time. Nominally, the temperature of radiation diverges as the Big Crunch is approaching, however, increasing oscillations of the spectrum make the temperature poorly defined, which is in agreement with the fact that AdS space does not have an event horizon which would cause thermal radiation. Unlimited growth of fluctuations indicates that an eventual tunneling into AdS vacuum would have catastrophic consequences for our universe.

We investigate the effect on the Hawking radiation given off during the time of collapse of a Reisner-Nordstr\"om domain wall. Using the functional Schr\"odinger formalism we are able to probe the time-dependent regime, which is out of the reach of the standard approximations like the Bogolyubov method. We calculate the occupation number of particles for a scalar field and complex scalar field. We demonstrate that the particles from the scalar field are unaffected by the charge of the Reisner-Nordstr\"om domain wall, as is expected since the scalar field doesn't carry any charge, which would couple to the charge of the Reisner-Nordstr\"om domain wall. Here the situation effectively reduces to the uncharged case, a spherically symmetric domain wall. To take the charge into account, we consider the complex scalar field which represents charged particles and anti-particles. Here investigate two different cases, first the non-extremal case and second the extremal case. In the non-extremal case we demonstrate that when the particle (anti-particle) carries charge opposite to that of the domain wall, the occupation number becomes suppressed during late times of the collapse. Therefore the dominate occupation number is when the particle (anti-particle) carries the same charge as the domain wall, as expected due to the Coulomb potential carried by the domain walls. In the extremal case we demonstrate that as time increases the temperature of the radiation decreases until when the domain wall reaches the horizon and the temperature then goes to zero. This is in agreement with the Hawking temperature for charged black holes.

We study the time evolution of the entropy of a collapsing charged spherical domain wall, from the point of view of an asymptotic observer, by investigating the entropy of the entire system (i.e. charged domain wall and radiation) and induced radiation alone during the collapse. By taking the difference, we find the entropy of the collapsing charged domain wall, since this is the object which will form a black hole. We find that for large values of time (times larger than $tf_-/R_+\approx8$), the entropy of the collapsing domain wall is a constant, which is of the same order as the Bekenstein-Hawking entropy.

We investigate an important question of Hawking-like radiation as seen by an infalling observer during gravitational collapse. Using the functional Schrodinger formalism we are able to probe the time dependent regime which is out of the reach of the standard approximations like the Bogolyubov method. We calculate the occupation number of particles whose frequencies are measured in the proper time of an infalling observer in two crucially different space-time foliations: Schwarzschild and Eddington-Finkelstein. We demonstrate that the distribution in Schwarzschild reference frame is not quite thermal, though it becomes thermal once the horizon is crossed. We approximately fit the temperature and find that the local temperature increases as the horizon is approached, and diverges exactly at the horizon. In Eddington-Finkelstein reference frame the temperature at the horizon is finite, since the observer in that frame is not accelerated. These results are in agreement with what is generically expected in the absence of backreaction. We also discuss some subtleties related to the physical interpretation of the infinite local temperature in Schwarzschild reference frame.

The Gauss-Codazzi method is used to discuss the gravitational collapse of a charged Reisner-Nordstroumlm domain wall. We solve the classical equations of motion of a thin charged shell moving under the influence of its own gravitational field and show that a form of cosmic censorship applies. If the charge of the collapsing shell is greater than its mass, then the collapse does not form a black hole. Instead, after reaching some minimal radius, the shell bounces back. The Schroumldinger canonical formalism is used to quantize the motion of the charged shell. The limits near the horizon and near the singularity are explored. Near the horizon, the Schroumldinger equation describing evolution of the collapsing shell takes the form of the massive wave equation with a position dependent mass. The outgoing and incoming modes of the solution are related by the Bogolubov transformation which precisely gives the Hawking temperature. Near the classical singularity, the Schroumldinger equation becomes nonlocal, but the wave function describing the system is nonsingular. This indicates that while quantum effects may be able to remove the classical singularity, it may also introduce some new effects.

We study the time evolution of the entropy of a collapsing spherical domain wall, from the point of view of an asymptotic observer, by investigating the entropy of the entire system (i.e. domain wall and radiation) and induced radiation alone during the collapse. By taking the difference, we find the entropy of the collapsing domain wall, since this is the object which will form a black hole. We find that for large values of time (times larger than t/Rs ≈ 8), the entropy of the collapsing domain wall is a constant, which is of the same order as the Bekenstein-Hawking entropy.

Higher dimensional non-renormalizable operators may modify the Standard Model Higgs potential in many interesting ways. Here, we consider the appearance of a second vacuum which may play an important role in cosmology. For the certain range of parameters, the usual second order electroweak phase transition is followed by a first order phase transition that may drive the late time accelerated expansion of the universe. Such a potential contains kink-like solutions which in turn can play a crucial role in reconstructing the global shape of the potential in colliders, as we explicitly demonstrate.

We investigate gravitational collapse in the context of quantum mechanics. We take primary interest in the behavior of the collapse near the horizon and near the origin ( classical singularity) from the point of view of an infalling observer. In the absence of radiation, quantum effects near the horizon do not change the classical conclusions for an infalling observer, meaning the horizon is not an obstacle for him. However, quantum effects are able to remove the classical singularity at the origin, since the wave function is non-singular at the origin. Also, near the classical singularity, some non-local effects become important. In the Schrodinger equation describing behavior near the origin, derivatives of the wave function at one point are related to the value of the wave function at some other distant point.