The black hole information problem beyond quantum theory

<p><strong>The future of theoretical physics is unclear. Two large areas that fall under the umbrella of theoretical physics are cosmology and quantum gravity. Modern cosmology is relatively a much younger field than quantum gravity, and both of these fields require further developments of general relativity. In this thesis we do not hope to resolve the problems facing modern cosmology or theories of quantum gravity. Rather, we will conduct original research into aspects of general relativity that may be used in the future to aid the development and testing of theories of cosmology and quantum gravity.</strong></p><p>It is our view that the largest problem facing astrophysics and cosmology stem from the existence of the dark sector of the Universe. The implication here being that more than ninety percent of the energy density of the Universe is “missing in action” and seemingly consists of dark energy and dark matter. Furthermore, it is apparent that there exist conceptual flaws in our understanding of observational concepts such as expansion versus motion and observer biases. To this end, we investigate the standard spacetime metric used in cosmology, the Friedmann–Lemaˆıtre-Roberston–Walker (FLRW) metric in a peculiar coordinate system — the Painlev´e–Gullstrand coordinates. In this coordinate system (slicing), space is no longer expanding, rather, the galaxies are receding from each other. We hope this will aid in the understanding of expansion, motion, curvature, and observer bias with future work. We further investigate the possibility of black holes in cosmology being directly coupled to the accelerated expansion of the Universe — in other words, black holes as a source for dark energy. However, we show that this is highly implausible.</p><p>Relatively recently it has been postulated that the near black hole horizon limit may be a regime where quantum gravity effects become relevant i.e., quantum gravity may not be restricted to near the Planck scale. We investigate a curious model of black and white holes that shows how one may transition into the other over a finite period of time. This is research conducted in the near horizon limit of the Schwarzschild black hole. We introduce a time dependent function into the usual Schwarzschild black hole spacetime (leaving this new spacetime not a simple coordinate transformed version of the original). This function allows the black hole to transition into a white hole. Importantly, the action for this transition can be shown to be zero, meaning it can be added to the Feynman path integral at no cost.</p><p>Finally, we move to investigating the black hole memory effect. During the last decade, there has been an interesting connection made between the Bondi– Metzner–Sachs (BMS) group — an infinite dimensional group of symmetries found at null infinity — and the gravitational memory effect. In particular, it was shown that the passage of a gravitational wave that alters a Schwarzschild black hole is seen as a supertranslation of the spacetime at null infinity. We extend these calculations to the Kerr and Kerr–Newman black holes. Hence, showing that there may be a way to verify the abstract mathematical ideas predicated on the BMS group by detection of the memory effect in future observations.</p><p>It is our hope that when future gravitational wave detectors such as the laser-interferometer-space-antenna (LISA) are launched, research conducted in this thesis may shed light on how the memory may relate to black holes in their asymptotic & near horizon limits to aid our understanding of the nature of quantum gravity.</p>

In this thesis, the author studies the information loss problem using semi-classical black holes. If a black hole loses information after evaporation, it will imply the violation of unitarity and predictability. Therefore, to understand the nature of the Theory of Everything and to reconcile the quantum theory and gravitation, we need to understand the problem of the information loss. If we assume that there exists a unitary theory of quantum gravity as a working hypothesis, the area of a black hole is proportional to the statistical entropy of the black hole, and there is an observer who can see information from Hawking radiation, then it is inevitable to accept black hole complementarity. However, if there is an observer who can see both information of inside and outside, i.e., if the duplication experiment is possible, then black hole complementarity will be violated. A duplication experiment and other thought experiments can be investigated by semi-classical backgrounds. In this thesis, we focus on three subjects: gravitational objects of Einstein gravity with renormalized energy-momentum tensors, gravitational objects of modified theories of gravity, and initial conditions which can be prepared by quantum tunneling. To study such subjects, we use the following techniques: traditional analytic approaches, numerical approaches using the double-null formalism, and Euclidean analytic continuations. We study a possibility of a duplication experiment in a charged black hole and a regular black hole. Causal structures allow the possibility; but to regularize curvatures around the inner horizon, we require a sufficiently large number of massless fields which contribute to Hawking radiation. In fact, if we assume the large number, we can violate black hole complementarity even for neutral black holes. The required number of fields can be reduced to a reasonable amount; although we need a large number, if it is finite, the number may be allowed by a model of quantum gravity including string theory. This suggests that the area of the black hole may not imply the statistical entropy of the internal and physical degrees of freedom and there may be no observer who can read information via Hawking radiation. Also, we study a possibility of a formation of a bubble universe. The author used weaker assumptions than previous authors to obtain bubble universes. The Brans-Dicke theory can allow a false vacuum bubble as an instanton solution and such a theory may be allowed by quantum gravity including string theory. False vacuum bubbles will emit negative energy along the out-going direction and such negative energy can be used to obtain a bubble universe. Although we have to check whether these scenarios are possible in realistic quantum gravity, if it is possible, then it will strongly support a loss of information and a violation of unitarity at least in the ‘effective’ sense. These conclusions imply that, if there exists a unitary theory of quantum gravity or the Theory of Everything, we will observe a lose of information and a violation of unitarity in the ‘effective’ way.

In this paper we argue for a close connection between the non-existence of global symmetries in quantum gravity and a unitary resolution of the black hole information problem. In particular we show how the essential ingredients of recent calculations of the Page curve of an evaporating black hole can be used to generalize a recent argument against global symmetries beyond the AdS/CFT correspondence to more realistic theories of quantum gravity. We also give several low-dimensional examples of quantum gravity theories which do not have a unitary resolution of the black hole information problem in the usual sense, and which therefore can and do have global symmetries. Motivated by this discussion, we conjecture that in a certain sense Euclidean quantum gravity is equivalent to holography.

Causal radial geodesics with a positive interval in the Schwarzschild metric include a subset of trajectories completely confined behind a horizon, which compose a thermal statistical ensemble with the Hawking-Gibbons temperature. The Bekenstein-Hawking entropy is given by an action at corresponding geodesics of particles with a summed mass equal to that of the black hole in the limit of a large mass. The entropy of a charged black hole is calculated in this way by using the partition function evaluated at radial geodesics confined behind horizons. We establish two quantum phase states inside the black hole and a transition between them. For the Kerr-Newman black hole we specify an angular motion on geodesics to reduce the problem to the case of radial motion elaborated on in previous papers. An appropriate value of entropy for a charged and rotating black hole is obtained by calculating the partition function on thermal geodesics confined behind horizons. The quantum aggregation is classified in a similar way to the Reissner-Nordstr\o{}m black hole.

It is reasonably expected 1) that a theory of quantum gravity will unify the extremes of scale currently described by General Relativity and quantum mechanics, and 2) that black holes are the crucible from which a theory of quantum gravity will emerge. In perspective, we already have a mechanism that links the local, macroscopic frame with the remote, apparently microscopic frame. A simple mathematical principle acts as a limit on D(n), suggesting a “maximum physical reality”, and that effects which are clearly perspectival at D=3 become “more real” (effectively observer-independent) with each D(n) increment. The model suggests alternative interpretations of gravitation and the quantum, entanglement, space, the Standard Model of particles and interactions, black holes, the measurement problem and the information paradox.

During the past 30 years, research in general relativity has brought to light strong hints of a very deep and fundamental relationship between gravitation, thermodynamics and quantum theory. The most striking indication of such a relationship comes from black hole thermodynamics, where it appears that certain laws of black hole mechanics are, in fact, simply the ordinary laws of thermodynamics applied to a system containing a black hole. This paper will review the present status of black hole thermodynamics and will discuss some of the related unresolved issues concerning gravitation, thermodynamics and quantum theory.

Black holes, initially thought of as very interesting mathematical and geometric solutions of general relativity, over time, have come up with surprises and challenges for modern physics. In modern times, they have started to test our confidence in the fundamental understanding of nature. The most serious charge on the black holes is that they eat up information, never to release and subsequently erase it. This goes absolutely against the sacred principles of all other branches of fundamental sciences. This realization has shaken the very base of foundational concepts, both in quantum theory and gravity, which we always took for granted. Attempts to get rid of of this charge, have led us to crossroads with concepts, hold dearly in quantum theory. The sphere of black hole’s tussle with quantum theory has readily and steadily grown, from the advent of the Hawking radiation some four decades back, into domain of quantum information theory in modern times, most aptly, recently put in the form of the firewall puzzle. Do black holes really indicate something sinister about their existence or do they really point towards the troubles of ignoring the fundamental issues, our modern theories are seemingly plagued with? In this review, we focus on issues pertaining to black hole evaporation, the development of the information loss paradox, its recent formulation, the leading debates and promising directions in the community.

Two techniques for computing black hole entropy in generally covariant gravity theories including arbitrary higher derivative interactions are studied. The techniques are Wald's Noether charge approach introduced recently, and a field redefinition method developed in this paper. Wald's results are extended by establishing that his local geometric expression for the black hole entropy gives the same result when evaluated on an arbitrary cross-section of a Killing horizon (rather than just the bifurcation surface). Further, we show that his expression for the entropy is not affected by ambiguities which arise in the Noether construction. Using the Noether charge expression, the entropy is evaluated explicitly for black holes in a wide class of generally covariant theories. Further, it is shown that the Killing horizon and surface gravity of a stationary black hole metric are invariant under field redefinitions of the metric of the form $\bar{g}_{ab}\equiv g_{ab} + \Delta_{ab}$, where $\Delta_{ab}$ is a tensor field constructed out of stationary fields. Using this result, a technique is developed for evaluating the black hole entropy in a given theory in terms of that of another theory related by field redefinitions. Remarkably, it is established that certain perturbative, first order, results obtained with this method are in fact {\it exact}. The possible significance of these results for the problem of finding the statistical origin of black hole entropy is discussed.}

Consistency between quantum mechanical and general relativistic views of the world is a longstanding problem, which becomes particularly prominent in black hole physics. We develop a coherent picture addressing this issue by studying the quantum mechanics of an evolving black hole. After interpreting the Bekenstein-Hawking entropy as the entropy representing the degrees of freedom that are coarse-grained to obtain a semiclassical description from the microscopic theory of quantum gravity, we discuss the properties these degrees of freedom exhibit when viewed from the semiclassical standpoint. We are led to the conclusion that they show features which we call extreme relativeness and spacetime-matter duality---a nontrivial reference frame dependence of their spacetime distribution and the dual roles they play as the "constituents" of spacetime and as thermal radiation. We describe black hole formation and evaporation processes in distant and infalling reference frames, showing that these two properties allow us to avoid the arguments for firewalls and to make the existence of the black hole interior consistent with unitary evolution in the sense of complementarity. Our analysis provides a concrete answer to how information can be preserved at the quantum level throughout the evolution of a black hole, and gives a basic picture of how general coordinate transformations may work at the level of full quantum gravity beyond the approximation of semiclassical theory.

Quantum mechanics is one of the most successful theoretical structures in all of science. Developed between 1925-26 to explain the optical spectrum of atoms, the theory over the succeeding 80 years has beenextended, first to quantum field theories, gauge field theories, and noweven string theory. It is used every day by thousands of physicists tocalculate physical phenomena to exquisite precision, with no ambiguity inthe results. To claim that this is a theory which is not understood bythose physicists is absurd. And yet, as eminent a physicist as RichardFeynman, who did as much as anyone else to extend quantum theory to field theories and was a master at producing those exquisite calculations, could say that anyone who claimed they understood quantum theory clearly did not understand quantumtheory.One hundred years ago Einstein postulated one of the most unsettlingfeatures of the theory, the wave-particle duality, with his particulateexplanation for light of the photoelectric effect, and an explanation whichwas in direct conflict with Maxwell's brilliant development of a wave, orfield, theory of light. Einstein believed that the particulate nature would ultimately be explainable by some sort of non-linear theory of electromagnetism, and was outraged by the acceptance of the community of the probabilistic quantum theory. His programme was of course dealt a (near?) fatal blow by Bell's discovery that the three desiderata - a theory which agrees with experiment, a theorywhich is local in its effects, and a theory in which nature, at its heart, isnot probabilistic - are incompatible.That discomfort felt by Einstein and by Feynman is felt by numerous otherpeople as well. This discomfort is heightened by the fact that the theoryof gravity, another of Einstein's great achievements, has resisted allefforts at reconciliation with quantum mechanics. This book explores thatdiscomfort, and tries to pin down what the locus of that discomfort is.For many, the locus is in the probabilistic nature at the heart of thetheory. Nature should surely, at some fundamental level, know what it isdoing. The photon, despite our inability to measure it, should know whereit is and how fast it is going. The papers by t'Hooft, Hiley, and Smolin fall intothis camp. Some suspect that the macroscopic world of our immediate senseexperiences, and the microscopic world of quantum phenomena, are genuinelydifferent, that the fundamental conceptual nature of physics changes fromone to the other, with some unknown boundary between them. Penrose, in hispreface alludes to his speculations on this, as does Leggett to his ownspeculations in his paper. And a number of articles (e.g., by Hartle, Rovelli, and others) opine that if only everyone looked at quantum mechanics in the right way (their way), it would lose its mystery, and be as natural as Newton's world view. (I myself tend to this position, which is however somewhat tempered by the realization that the clarity and naturalness of my viewpoint is not shared by the others who believe equally firmly in their own natural, clear, but radicallydifferent, viewpoint). A number of articles simply examine thecounterintuitive nature of quantum theory in general, using it to makesense of time travel (Greenberger and Svozil) and demonstrating the unusualfeatures of induction about the past from present observations withinquantum theory (Aharonov and Dolev).The book is not free from rather overblown titles (e.g., 'Liberation andPurification from Classical Prejudice', or 'A Quantum Theory of the HumanPerson') but those articles nevertheless contain at least amusing speculations.In quantum gravity, the incompatibilities between the two masterstrokes of thetwentieth century are highlighted. There is a strong suspicion amongstmany in this field that progress in understanding quantum gravity demands a deeper understanding of the great mystery of quantum theory which this book explores. This book is a useful and, at times, fascinating introduction to the flounderings which are taking place in trying to understand not only the solution but even what the problem is. Finally, however, the question of the title of this book remains unanswered.

We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical subsystems. This allows using the formal classical logic and classical probability theory in quantum mechanics. Our approach nevertheless allows completely reproducing the standard mathematical formalism of quantum mechanics and identifying its applicability limits. We especially attend to the quantum state reduction problem.

With the help of 'Heart of the God model of the universe' (1),'Siva's classical Equation for space time' (2) and 'Siva's Theory of quantum Gravity' (3) a new particle 'K-Suryon' has been predicted. It is the elementary particle with mass 1.15 x 10 -64 kg and radius 8.15 x 10 -134 mts. It is described as the basic building block of 'space- time' & mass. Mass of real particle 'K-Suryon' is 4.6x10 -64 Kgs. It has to be incorporated in standard model. This discovery will explain how the Quantum Gravity is synchronizing with General Relativity. It will open new ways of research in 'dark matter' and 'black hole' physics. It reveals the concept of mass creation more profoundly than 'Higgs mechanism'.

Black holes represent fundamental laboratories for testing quantum gravity theories, where extreme curvature and thermal physics provide unique opportunities to probe Planck-scale modifications to space time. We investigate quantum gravity corrections to black hole thermodynamics through the Generalized Uncertainty Principle (GUP), focusing on modifications to Hawking radiation and accretion disk physics. Our comprehensive analysis reveals that GUP effects systematically alter the temperature-mass relationship for black holes, leading to observable signatures in both the thermal emission spectrum and accretion disk properties. Through detailed calculations incorporating relativistic effects and advanced statistical mechanics, we demonstrate that quantum gravity modifications introduce spectral distortions in the X-ray regime that are potentially detectable with current and future high-energy missions. The modified thermodynamics also affects accretion efficiency, disk temperature profiles, and iron line emission, producing characteristic signatures in the observed continuum spectra. Our analysis of recent data from NuSTAR, XRISM, and other X-ray observatories places new constraints on the GUP parameter β≤1500 for stellar-mass black holes, representing the most stringent limits from black hole observations to date. These results demonstrate the potential for black hole observations to probe fundamental quantum gravity effects and provide complementary constraints to those derived from neutron star studies. The framework developed here establishes black hole systems as viable laboratories for testing quantum gravity theories through multi-messenger astronomy.

It is now known that when a massive star collapses under the force of its own gravity, the final fate of such a continual gravitational collapse will be either a black hole or a naked singularity under a wide variety of physically reasonable circumstances within the framework of general theory of relativity. The research of recent years has provided considerable clarity and insight on stellar collapse, black holes and the nature and structure of spacetime singularities. We discuss several of these developments here. There are also important fundamental questions that remain unanswered on the final fate of collapse of a massive matter cloud in gravitation theory, especially on naked singularities which are hypothetical astrophysical objects and on the nature of cosmic censorship hypothesis. These issues have key implications for our understanding on black hole physics today, its astrophysical applications, and for certain basic questions in cosmology and possible quantum theories of gravity. We consider these issues here and summarize recent results and current progress in these directions. The emerging astrophysical and observational perspectives and implications are discussed, with particular reference to the properties of accretion disks around black holes and naked singularities, which may provide characteristic signatures and could help distinguish these objects.

One of the main challenges in theoretical physics over the last five decades has been to reconcile quantum mechanics with general relativity into a theory of quantum gravity. However, such a theory has been proved to be hard to attain due to i) conceptual difficulties present in both the component theories (General Relativity (GR) and Quantum Theory); ii) lack of experimental evidence, since the regimes at which quantum gravity is expected to be applicable are far beyond the range of conceivable experiments. Despite these difficulties, various approaches for a theory of Quantum Gravity have been developed. In this thesis we focus on two such approaches: Loop Quantum Gravity and the Topos theoretic approach. The choice fell on these approaches because, although they both reject the Copenhagen interpretation of quantum theory, their underpinning philosophical approach to formulating a quantum theory of gravity are radically different. In particular LQG is a rather conservative scheme, inheriting all the formalism of both GR and Quantum Theory, as it tries to bring to its logical extreme consequences the possibility of combining the two. On the other hand, the Topos approach involves the idea that a radical change of perspective is needed in order to solve the problem of quantum gravity, especially in regard to the fundamental concepts of `space' and `time'. Given the partial successes of both approaches, the hope is that it might be possible to find a common ground in which each approach can enrich the other.