By combining the Bekenstein–Hawking entropy formula with the black hole parameters calculated from the fractal quantum gravity (FQG) theory, we can derive that the entropy of black holes equals the number of spacetime quantum of actions (STQAs) included in the black hole. Based on this discovery, the black hole information paradox can be resolved. If we consider the whole universe as a black hole, the entropy of the universe can be calculated as an equivalent number of STQAs included in the universe. This equivalent number is increasing as the universe expands, which means that the entropy of the universe is increasing as the universe expands, so we can explain why the second law of thermodynamics exists. Since infinity doesn’t exist in the FQG theory framework, the singularity in the center of the black hole and at the big bang of the universe can be resolved by introducing a minimum volume. Thus, the initial angular momentum at the Big Bang, the formation of the subatomic particles, dark matter particles and black holes in the earlier stages after the Big Bang can be calculated. These dark matter particles and black holes can work as the seed of the galaxies, which can explain the recent discoveries by the James Webb Space Telescope, such as the asymmetry of the rotation of the galaxies, the over-mature galaxies at the early age of the universe, as well as the old puzzle of the asymmetry between matter and anti-matters. We also calculated the curvature of the universe as positive and with an extremely small value, which means that it is a flat universe in agreement with the actual observation. The FQG equation predicts that the number of STQAs in a stable subatomic particle should be a prime number. Based on this prediction, we can calculate the free parameters in the Standard Model of Particle Physics. We have expanded the fractal geometry theory in order to describe the fractal distribution patterns of the elementary particles in spacetime and energy. When the fractal dimension is an integer number and equals the topological dimensions, we obtain a three-dimensional space, three-dimensional time and three-dimensional energy for the current universe. These results could shed more light on a fuller understanding of the nature of time and energy.

Black holes represent one of the most enigmatic predictions of general relativity, yet their existence introduces profound tensions between classical and quantum physics. While traditional models suggest that black holes are eternal, Stephen Hawking’s demonstration of quantum particle emission at the event horizon implies that no black hole can survive indefinitely. This phenomenon, now known as Hawking radiation, reframes black holes as thermodynamic systems with a finite lifetime and entropy that evolves over time. In this paper, I examine the theoretical foundations of Hawking radiation within the semi-classical framework, where quantum field effects emerge against a curved spacetime background. Derivations of the Hawking temperature, entropy, and evaporation timescales are presented and applied across stellar-mass, supermassive, and primordial black holes. The calculations demonstrate that while evaporation proceeds almost imperceptibly for astrophysical black holes, primordial black holes may exhibit measurable decay signatures in the current epoch. These results underscore the principle that even the most massive gravitational entities are subject to quantum instability and ultimate decay. By analyzing the thermodynamic and quantum mechanical consequences of Hawking radiation, this work situates the information paradox as a central challenge for reconciling relativity with quantum theory, even for the universe.

This paper applies Chronos Theory—a framework modeling time as a quantized, structured energetic field—to the physics of black holes. By introducing a universal logarithmic shell structure with fixed parameters, we predict discrete clustering in normalized quasinormal mode (QNM) frequencies, Hawking radiation spectra, and information release intervals. Using existing LIGO/Virgo QNM datasets, numerical relativity results, and theoretical models for Hawking evaporation, we show preliminary evidence for shell alignment in Schwarzschild QNMs and propose a falsifiable simulation protocol for Hawking mode quantization and burst timing. The work provides a cross-domain predictive link between classical black hole oscillations, quantum evaporation, and the information paradox, unifying them under a single temporal field constraint testable with current and near-future simulations.

This manuscript argues that the “black hole information paradox” is not a genuine paradox but arises from extending the unitary postulate of quantum mechanics beyond its valid domain Paper 16:Thermodynamic Ontology… . The authors contend that unitarity applies to closed, zero-entropy systems, whereas black holes are maximally entropic, open systems that exchange energy with their environment. When entropy and enthalpy are explicitly accounted for, the paradox dissolves. Key contributions include: Thermodynamic ontology: A Gibbs free energy density framework is introduced, where collapse occurs when entropy inflow, weighted by temperature, exceeds stabiliser enthalpy. This entropy–enthalpy ledger formalises why black holes cannot be treated as pure states Paper 16:Thermodynamic Ontology… . Comparative analysis: Schrödinger’s cat is revisited, showing coherence leaks inevitably toward mixed states, while dark matter provides a counterexample approaching the pure-state limit due to its minimal entropy exchange Paper 16:Thermodynamic Ontology… . Black holes as entropy furnaces: Hawking radiation is recast as entropy-driven coherence loss, with entropy conserved across the system–environment ledger rather than “lost.” Axiomatic structure: The paper sets out five guiding axioms (No Free Superposition, Collapse Footprints, Entropy-Time Synchrony, Interactability Threshold, Beacon Audit Inequality), embedding black hole physics into a broader thermodynamic ontology Paper 16:Thermodyn

This study critically reevaluates the Harlow-Hayden (HH) solution to the black hole information paradox and its articulation in the firewall paradox. The exploration recognizes the HH solution as a revolutionary approach in black hole physics, steering away from traditional constraints to depict the event horizon as a computational rather than a physical barrier. The paper first maps the initial physical dilemma that instigated the HH journey, introducing Alice, an observer facing intricate computational challenges as she approaches the black hole. I then depict the evolution of the narrative, describing how Alice was facilitated with a quantum computer to surmount the computational challenges and further detailing the augmented complexities arising from the integration of the physical dynamics of the black hole. Yet, HH's research applies the AdS/CFT correspondence to explore the dynamic unitary transformation in solving the firewall paradox through decoding Hawking radiation. However, it identifies a contradiction; the eternal perspective of black holes from the AdS/CFT theory challenges the firewall paradox's foundation. Finally, I narrate a paradigm shift as HH reframes Alice's task within the realms of error-correcting codes, illustrating a remarkable transition from a physical problem in black hole physics to a computational predicament in computer science. The study revisits pivotal moments in understanding black hole physics ten years later through this reexamination.

Entanglement islands have played a key role in the recent derivation of the Page curve and other progress on the black hole information problem. Arising from the inclusion of connected wormhole saddles in a gravitational replica trick, islands signal that degrees of freedom in the black hole interior are not microscopically independent of the exterior Hawking radiation. Islands were originally discovered in the context of AdS/CFT coupled to an external, nongravitating reservoir, where the coupling gives graviton excitations an anomalous boundary scaling dimension (or “mass”). It has been claimed in the literature that this mass is crucial for the existence of islands and even the Page curve itself. In this paper, however, we explain how entanglement islands can also appear in setups with massless gravitons and no external reservoir, giving a number of examples including the entanglement wedges of boundary CFT regions, of radiation at null infinity in asymptotically flat spacetimes, and of radiation inside a semiclassical but gravitating spacetime. In each case, the Page curve is physically observable and can be determined with sufficiently careful experiments on many copies of the black hole. We give general arguments for the existence of gauge-invariant operators in gravity which are compactly supported to all orders in perturbation theory (whenever no isometries of the background spacetime exist) and refine a recently-proposed explicit construction of such operators. When a

In this thesis, I study Interface Conformal Field Theories (ICFT) and their holographic dual, which is composed of two asymptotically Anti-de-Sitter (AdS) spaces glued through a thin gravitating membrane. I restrict the study to simple minimal models, which allow for analytic control while providing universally applicable results. The analysis is set in 2D ICFT/3D gravity, but I expect much of the results to be generalizable to higher dimensions. I first consider this system at equilibrium and at finite temperature. By solving the equations of motion in the bulk, I find the allowable solution landscape. Classifying the rich set of solutions among 3 thermodynamical phases, I draw the phase diagram outlining the nature of the various phase transitions. I then examine a simple out-of-equilibrium situation arising from connecting at an interface two spatially infinite CFTs at different temperatures. Then a "Non-Equilibrium Steady State" (NESS) describes the growing region where the interaction has settled into a stationary phase. I determine the holographic dual of this region, composed of two spinning planar black holes glued at the membrane. I find an expression for the deformed out-of-equilibrium event horizon. This geometry suggests that the field theory interface acts as a perfect scrambler, a property that until now seemed unique to black hole horizons. Finally, I study the entanglement structure of the aforementioned geometries by means of the Ryu-Takayanagi prescription.

We chart the breakdown of semiclassical gravity by analyzing the Virasoro conformal blocks to high numerical precision, focusing on the heavy-light limit correspond-ing to a light probe propagating in a BTZ black hole background. In the Lorentzian regime, we find empirically that the initial exponential time-dependence of the blocks transitions to a universal $ t-\frac{3}{2} $ power-law decay. For the vacuum block the transition occurs at $ t\approx \frac{\uppi c}{6{h}_L} $ , confirming analytic predictions. In the Euclidean regime, due to Stokes phenomena the naive semiclassical approximation fails completely in a finite region enclosing the ‘forbidden singularities’. We emphasize that limitations on the reconstruction of a local bulk should ultimately stem from distinctions between semiclassical and exact correlators.

In this paper, we obtain some general results on information retrieval from the black hole interior, based on the recent progress on quantum extremal surface formula and entanglement island. We study an AdS black hole coupled to a bath with generic dynamics, and ask whether it is possible to retrieve information about a small perturbation in the interior from the bath system. We show that the one-norm distance between two reduced states in a bath region A is equal to the same quantity in the bulk quantum field theory for region AI where I is the entanglement island of A. This is a straightforward generalization of bulk-boundary correspondence in AdS/CFT. However, we show that a contradiction arises if we apply this result to a special situation when the bath dynamics includes a unitary operation that carries a particular measurement to a region A and send the result to another region W. Physically, the contradiction arises between transferability of classical information during the measurement, and non-transferability of quantum information which determines the entanglement island.We propose that the resolution of the contradiction is to realize that the state reconstruction formula does not apply to the special situation involving interior-information-retrieving measurements. This implies that the assumption of smooth replica AdS geometry with boundary condition set by the flat space bath has to break down when the particular measurement operator is applied to the bath. Usin

We give a pedagogical review of how concepts from quantum information theory build up the gravitational side of the anti-de Sitter/conformal field theory correspondence. The review is self-contained in that it only presupposes knowledge of quantum mechanics and general relativity; other tools-including holographic duality itself-are introduced in the text. We have aimed to give researchers interested in entering this field a working knowledge sufficient for initiating original projects. The review begins with the laws of black hole thermodynamics, which form the basis of this subject, then introduces the Ryu-Takayanagi proposal, the Jafferis-Lewkowycz-Maldacena-Suh (JLMS) relation, and subregion duality. We discuss tensor networks as a visualization tool and analyze various network architectures in detail. Next, several modern concepts and techniques are discussed: Rényi entropies and the replica trick, differential entropy and kinematic space, modular Berry phases, modular minimal entropy, entanglement wedge cross-sections, bit threads, and others. We discuss the extent to which bulk geometries are fixed by boundary entanglement entropies, and analyze the relations such as the monogamy of mutual information, which boundary entanglement entropies must obey if a state has a semiclassical bulk dual. We close with a discussion of black holes, including holographic complexity, firewalls and the black hole information paradox, islands, and replica wormholes.

In this paper, we demonstrate that wormholes must be entangled regardless of asymptotic boundary conditions. By assuming black hole complementarity, we argue that traversable wormholes instantiate entanglement-assisted quantum channels and that this entanglement must be present between the stretched horizons as an initial condition prior to traversability. In conclusion, this result demonstrates the forward direction of the ER/EPR conjectures.