Quantum field theory, horizons and thermodynamics

It has been well known that in the point of view of a distant observer, all in-falling matter to a black hole (BH) will be eventually stalled and "frozen" just outside the event horizon of the BH, although an in-falling observer will see the matter falling straight through the event horizon. Thus in this "frozen star" scenario, as distant observers, we could never observe matter falling into a BH, neither could we see any "real" BH other than primordial ones, since all other BHs are believed to be formed by matter falling towards singularity. Here we first obtain the exact solution for a pressureless mass shell around a pre-existing BH. The metrics inside and interior to the shell are all different from the Schwarzschild metric of the enclosed mass. The metric interior to the shell can be transformed to the Schwarzschild metric for a slower clock which is dependent of the location and mass of the shell. Another result is that there does not exist a singularity nor event horizon in the shell. Therefore the "frozen star" scenario is incorrect. We also show that for all practical astrophysical settings the in-falling time recorded by an external observer is sufficiently short that future astrophysical instruments may be able to follow the whole process of matter falling into BHs. The distant observer could not distinguish between a "real" BH and a "frozen star", until two such objects merge together. It has been proposed that electromagnetic waves will be produced when two "frozen stars" merge together, but not true when two "real" bare BHs merge together. However gravitational waves will be produced in both cases. Thus our solution is testable by future high sensitivity astronomical observations.

Though it is still a big challenge to unify general relativity and quantum mechanics in modern physics, the theory of quantum field related with the gravitational effect has been well developed and some striking phenomena are predicted, such as Hawking radiation. However, the direct measurement of these quantum effects under general relativity is far beyond present experiment techniques. Fortunately, the emulation of general relativity phenomena in the laboratory has become accessible in recent years. However, up to now, these simulations are limited either in classical regime or in flat space whereas quantum simulation related with general relativity is rarely involved. Here we propose and experimentally demonstrate a quantum evolution of fermions in close proximity to an artificial black hole on a photonic chip. We successfully observe the acceleration behavior, quantum creation, and evolution of a fermion pair near the event horizon: a single-photon wave packet with positive energy escapes from the black hole while negative energy is captured. Our extensible platform not only provides a route to access quantum effects related with general relativity, but also has the potentiality to investigate quantum gravity in future.

Black holes are bodies that, according to the theory of General Relativity, attract all the matter that comes too close to their interior. Their existence today have been indicated by several observational data, even if indirect. The prediction of the existence of black holes long before the confirmation of observational data of any kind is an example of the very advanced stage in which theoretical physics has presently developed; and even if today there are some observations available, they are still too faible to provide an analysis of all the aspects predicted in theory for the phenomena. This is the reason why it would be interesting to simulate analogous objects, more accessible than real black holes, based on studies of condensed matter: the so-called acoustic black holes. In this work we develop the mathematical formalism for acoustic black holes, and by building the Painleve-Gullstrand metric we visualize the analogy between the acoustic metric of a fluid at supersonic speed and General Relativity. We can observe that results obtained by General Relativity, such as the existence of an event horizon, can be rescued with the use of this metric for the fluid. In particular, using Killing vectors we get to the concept of surface gravity, and from it we can calculate the temperature of an acoustic black hole, showing that thermodynamic effects such as the existence of Hawking radiation can also be studied with the use these analogue models.

This thesis consists of three separate studies of roles that black holes might play in our universe. In the first part we formulate a statistical method for inferring the cosmological parameters of our universe from LIGO/VIRGO measurements of the gravitational waves produced by coalescing black-hole/neutron-star binaries. This method is based on the cosmological distance-redshift relation, with "luminosity distances" determined directly, and redshifts indirectly, from the gravitational waveforms. Using the current estimates of binary coalescence rates and projected "advanced" LIGO noise spectra, we conclude that by our method the Hubble constant should be measurable to within an error of a few percent. The errors for the mean density of the universe and the cosmological constant will depend strongly on the size of the universe, varying from about 10% for a "small" universe up to and beyond 100% for a "large" universe. We further study the effects of random gravitational lensing and find that it may strongly impair the determination of the cosmological constant. In the second part of this thesis we disprove a conjecture that black holes cannot form in an early, inflationary era of our universe, because of a quantum-field-theory induced instability of the black-hole horizon. This instability was supposed to arise from the difference in temperatures of any black-hole horizon and the inflationary cosmological horizon; it was thought that this temperature difference would make every quantum state that is regular at the cosmological horizon be singular at the black-hole horizon. We disprove this conjecture by explicitly constructing a quantum vacuum state that is everywhere regular for a massless scalar field. We further show that this quantum state has all the nice thermal properties that one has come to expect of "good" vacuum states, both at the black-hole horizon and at the cosmological horizon. In the third part of the thesis we study the evolution and implications of a hypothetical primordial black hole that might have found its way into the center of the Sun or any other solar-type star. As a foundation for our analysis, we generalize the mixing-length theory of convection to an optically thick, spherically symmetric accretion flow (and find in passing that the radial stretching of the inflowing fluid elements leads to a modification of the standard Schwarzschild criterion for convection). When the accretion is that of solar matter onto the primordial hole, the rotation of the Sun causes centrifugal hangup of the inflow near the hole, resulting in an "accretion torus" which produces an enhanced outflow of heat. We find, however, that the turbulent viscosity, which accompanies the convective transport of this heat, extracts angular momentum from the inflowing gas, thereby buffering the torus into a lower luminosity than one might have expected. As a result, the solar surface will not be influenced noticeably by the torus's luminosity until at most three days before the Sun is finally devoured by the black hole. As a simple consequence, accretion onto a black hole inside the Sun cannot be an answer to the solar neutrino puzzle.

Interesting questions that arise in connection with the physics of black holes include the existence or non-existence of mathematical singularities in the physical universe, the rate at which an incoming particle can be observed to cross a black hole’s event horizon, the quantum mechanics of small particles inside a gravitational potential well, the rate of absorption of an incoming particle into the core of a black hole, the mechanism by which very high-energy particles can be emitted from a black hole’s potential well, and the nature of the interface between quantum mechanics and general relativity. The purpose of this Note is to suggest plausible answers to some of these questions. The discussion focuses on basic physics rather than mathematics, and quantum mechanics and general relativity are regarded as equally fundamental.

The black hole information puzzle can be resolved if two conditions are met. The first is that the information about what falls inside a black hole remains encoded in degrees of freedom that persist after the black hole completely evaporates. These degrees of freedom should be capable of purifying the information. The second is if these purifying degrees of freedom do not significantly contribute to the system's energy, as the macroscopic mass of the initial black hole has been radiated away as Hawking radiation to infinity. The presence of microscopic degrees of freedom at the Planck scale provides a natural mechanism for achieving these two conditions without running into the problem of the large pair-creation probabilities of standard remnant scenarios. In the context of Hawking radiation, the first condition implies that correlations between the in and out Hawking partner particles need to be transferred to correlations between the microscopic degrees of freedom and the out partners in the radiation. This transfer occurs dynamically when the in partners reach the singularity inside the black hole, entering the UV regime of quantum gravity where the interaction with the microscopic degrees of freedom becomes strong. The second condition suggests that the conventional notion of the vacuum's uniqueness in quantum field theory should fail when considering the full quantum gravity degrees of freedom. In this paper, we demonstrate both key aspects of this mechanism using a solvable toy model of a quantum black hole inspired by loop quantum gravity.

We establish the link between the thermodynamics and the quantum theory of black hole horizons through the construction of the thermodynamic partition function, partly based on some physically plausible arguments, by beginning from the description of quantum states of the horizon, considering loop quantum gravity (LQG) as the underlying theory. Although the effective “thermalized” form of the partition function has been previously used in the literature to study the effect of thermal fluctuations of the black hole horizon, nonetheless the direct link to any existing quantum theory (which is here taken to be LQG), especially a derivation of the partition function from the quantum states of the horizon, appears to be hitherto absent. This work is an attempt to bridge this small, but essential, gap that appears to be present between the existing literature of quantum theory and thermodynamics of black holes. Furthermore, it may be emphasized that this work isonlyconcerned with themetric independentapproaches to black hole thermodynamics.

Considered Schwarzschild black hole solution within General Relativity. The area of black hole event horizon attracts stable and vivid interest. The literature brief review points in Introduction out, that the coordinate singularity on horizon might have physical meaning. In the following two sections this point strengthens. But this contradicts the dogmatic physical worldview, so in Discussion section I disarmed possible critics. I'm signing my faith in Conclusion, that this paper have found the naked (them we can observe) singularities. Even if is showed, that physically reasonable solutions can have the nakedness of singularities, they are far from the actual experimental detection. Contrary to that, recognizing the physical-ness of coordinate singularities makes them automatically experimentally verified. Because the event horizon is in definition of experimentally verified black holes (e.g., 2007 MASTER Team discovered the Black Hole Ergosphere, surrounding event horizon). Context: Natural Sciences: Physics: General Relativity theory: Black holes: event horizon. Aims: To publish original, innovative and novel research article resulting in contradicting results in the field of science. To publish theoretical paper that reports the contradictory finding (coordinate singularity is actually real) in scientific field. To present counter-examples (singular force F and curvature scalar ψ) to usually accepted conjecture, which is “coordinate singularity is unphysical”. Settings and Design: The singularity is defined in Introduction. There is set the function S(r), describing singularities. This is followed by derivation of gravitational attraction F. It turns to be singular with the S(r). Then directly from Curvature Tensor is derived singular scalar tensor ψ, where you can see the S(r). Discussion answers possible critics preceded by Results. Methods and Material: Hardware: a PC; Software: a Web Browser, Maple V Release 5 with GRTensorII Version 1.70; Vector and Tensor analysis. Results: Although the surface gravity g has suffered from Scientific Community the procedure of Renormalization, nevertheless this operation left the gravitational attraction (force F) and scalar ψ to include singular function S(r). Conclusions: Already 11 years I firmly believe. That I found naked (one we can observe) singularity of Curvature, predicted by General Relativity. I called it “Sulo singularity”. It's my personal joy and triumph, which I would like to share through JCRSCI.

Quantum field theory is currently the most accurate description of matter, but this framework is the result of a long evolution of the concept of particle in physics. In this article, we trace this development: starting from classical mechanics, where particles are treated as point-like objects; moving to quantum mechanics, where they are described as waves associated with probabilities; and finally arriving at quantum field theory, where particles appear as excitations of fundamental fields. We show that in curved or expanding spacetimes, the definition of a particle is no longer unique: different observers can adopt different vacuum states and consequently identify particles in different ways. We also discuss the role of the quantum vacuum and its connection to the cosmological constant problem, one of the major open questions in contemporary physics. By connecting quantum theory, general relativity, and cosmology, the article addresses both the progress achieved and the conceptual challenges that remain in describing the universe at its most extreme scales.

QUANTUM gravitational effects are usually ignored in calculations of the formation and evolution of black holes. The justification for this is that the radius of curvature of space-time outside the event horizon is very large compared to the Planck length (Għ/c3)1/2 ≈ 10−33 cm, the length scale on which quantum fluctuations of the metric are expected to be of order unity. This means that the energy density of particles created by the gravitational field is small compared to the space-time curvature. Even though quantum effects may be small locally, they may still, however, add up to produce a significant effect over the lifetime of the Universe ≈ 1017 s which is very long compared to the Planck time ≈ 10−43 s. The purpose of this letter is to show that this indeed may be the case: it seems that any black hole will create and emit particles such as neutrinos or photons at just the rate that one would expect if the black hole was a body with a temperature of (κ/2π) (ħ/2k) ≈ 10−6 (M/M)K where κ is the surface gravity of the black hole1. As a black hole emits this thermal radiation one would expect it to lose mass. This in turn would increase the surface gravity and so increase the rate of emission. The black hole would therefore have a finite life of the order of 1071 (M/M)−3 s. For a black hole of solar mass this is much longer than the age of the Universe. There might, however, be much smaller black holes which were formed by fluctuations in the early Universe2. Any such black hole of mass less than 1015 g would have evaporated by now. Near the end of its life the rate of emission would be very high and about 1030 erg would be released in the last 0.1 s. This is a fairly small explosion by astronomical standards but it is equivalent to about 1 million 1 Mton hydrogen bombs. It is often said that nothing can escape from a black hole. But in 1974, Stephen Hawking realized that, owing to quantum effects, black holes should emit particles with a thermal distribution of energies — as if the black hole had a temperature inversely proportional to its mass. In addition to putting black-hole thermodynamics on a firmer footing, this discovery led Hawking to postulate 'black hole explosions', as primordial black holes end their lives in an accelerating release of energy.

Bardeen-like regular black holes in [formula omitted] Einstein–Gauss–Bonnet gravity

Shadow of novel rotating black hole in GR coupled to nonlinear electrodynamics and constraints from EHT results

Essentially, in this paper we propose a new description of the quantum dynamics by two relativistic propagation wave packets, in the two conjugated spaces, of the coordinates and of the momentum. Compared to the Schrödinger-Dirac equation, which describes a free particle by a wave function continuously expanding in time, considered as the amplitude of a probabilistic distribution of this particle, the new equations describe a free particle as an invariant distribution of matter propagating in the two spaces, as it should be. Matter quantization arises from the equality of the integral of the matter density with the mass describing the dynamics of this density in the phases of the wave packets. In this description, the classical Lagrange and Hamilton equations are obtained as the group velocities of the two wave packets in the coordinate and momentum spaces. When to the relativistic Lagrangian we add terms with a vector potential conjugated to coordinates, as in the Aharonov-Bohm effect, and a scalar potential conjugated to time, we obtain the Lorentz force and the Maxwell equations as characteristics of the quantum dynamics. In this framework, the conventional Schrödinger-Dirac equations of a quantum particle in an electromagnetic field obtain additional terms explicitly depending on velocity, as is expected in the framework of relativistic theory. Such a particle wave function takes the form of a rapidly varying wave, with the frequency corresponding to the rest energy, modulated by the electric potential  where this particle is confined, the vector potential   of the electromagnetic radiation, and the gravitational potential. In the gravitational field of a black hole, the velocity of a quantum particle is directed to the Schwarzschild boundary from the outside and from the inside, without passing this boundary. When the very strong gravitational field of a large agglomeration of matter has spherical symmetry with a radius smaller than the Schwarzschild radius, the quantum particles in the central region are crushed up to quasi-uniform distributions of matter, exploding with velocities much larger than the light velocity, towards the Schwarzschild boundary, but decelerating in the gravitational field and reaching this boundary only in an infinite time. The matter of a black hole has the tendency to concentrate around the Schwarzschild boundary, with a radius proportional to its mass. In this framework, we believe that our universe is a huge black hole, with the explosion of its central matter as the Big Bang-inflation process, and an increasing radius on account of an absorption of matter from the Total Universe, where our universe has been formed. In a gravitational wave, the time-space interval in the first-order approximation is the product of a gravitational invariant including the amplitude tensor, and a coordinate invariant including the polarization vector. The gravitational invariant describes a rotation of the metric tensor around the direction of the propagation of this wave, with spin 2, as a gravitational quantum called graviton. The coordinate invariant describes a matter rotation with the spins ½ for Fermions, and 1 for Bosons. From the new dynamic equations, for a free particle in the coordinate and momentum spaces, we reobtain the two basic equations of the quantum field theory, but with a change of sign, and an additional term depending on momentum, to the rest mass as the eigenvalue of these equations. However, when these eigenvalues are eliminated, the wave function takes the form of a wave packet of spinors of the same form as in the conventional quantum field theory, with a normalization volume as the integral of the ratio of the energy to the rest energy, over the momentum domain which gives finite dimensions to the quantum particle, as a finite distribution of matter in the coordinate space.

Improvements in detection technology has enabled researchers to discover interstellar phenomena at an exponential rate; the most enticing of such marvels are black holes. Development of black hole thermodynamics have yielded promising interdisciplinary results. This paper will explore the fundamental concepts pertaining to black holes, and a brief outline of the scientific contributions made by notable theorists in their respective fields. These concepts will be followed by an in-depth discussion concerning the fundamental attributes and characteristics of black holes. One concept that will be thoroughly discussed is black hole radiation, a theory developed heavily by physicist Stephen Hawking, which was predicated on research concerning the anatomy and effects of rotating black holes in the universe. Derivations of formulae relevant to Hawking radiation, black hole entropy, and classical black hole dynamics will be done, as these are imperative to the elucidation of such sophisticated concepts. Furthermore, these formulae will be applied to pre-existing interstellar phenomena in order to understand the significance of the theoretical findings. Ultimately, mathematical models will be put to the test using real black holes. A model will also be generated in a Python environment to visually exemplify Hawking radiation for a Schwarzschild black hole. Developing a cohesive understanding of the thermodynamic concepts related to black holes will prove fruitful in the application of scientific knowledge to an ever-changing world enticed by interstellar phenomena.

The "no hair" theorem, a key result in General Relativity, states that an\nisolated black hole is defined by only three parameters: mass, angular\nmomentum, and electric charge; this asymptotic state is reached on a\nlight-crossing time scale. We find that the "no hair" theorem is not formally\napplicable for black holes formed from collapse of a rotating neutron star.\nRotating neutron stars can self-produce particles via vacuum breakdown forming\na highly conducting plasma magnetosphere such that magnetic field lines are\neffectively "frozen-in" the star both before and during collapse. In the limit\nof no resistivity, this introduces a topological constraint which prohibits the\nmagnetic field from sliding off the newly-formed event horizon. As a result,\nduring collapse of a neutron star into a black hole, the latter conserves the\nnumber of magnetic flux tubes $N_B = e \\Phi_\\infty /(\\pi c \\hbar)$, where\n$\\Phi_\\infty \\approx 2 \\pi^2 B_{NS} R_{NS}^3 /(P_{\\rm NS} c)$ is the initial\nmagnetic flux through the hemispheres of the progenitor and out to infinity. We\ntest this theoretical result via three-dimensional general relativistic plasma\nsimulations of rotating black holes that start with a neutron star dipole\nmagnetic field with no currents initially present outside the event horizon.\nThe black hole's magnetosphere subsequently relaxes to the split monopole\nmagnetic field geometry with self-generated currents outside the event horizon.\nThe dissipation of the resulting equatorial current sheet leads to a slow loss\nof the anchored flux tubes, a process that balds the black hole on long\nresistive time scales rather than the short light-crossing time scales expected\nfrom the vacuum "no-hair" theorem.\n