arXiv subjects

Kamal Hajian

Publications and source records attributed to Kamal Hajian.

15 recordsLinked to original sources

arXiv2026

An Exact Single-Rotating Near-Horizon Geometry in Einstein-Gauss-Bonnet Gravity

We construct a five-dimensional singly rotating near-horizon solution in Einstein-Gauss-Bonnet gravity. We show that the Gauss-Bonnet term removes the local curvature singularity, yielding finite curvature invariants throughout the spacetime, provided the rotation parameter remains below a certain value set by the Gauss-Bonnet coupling. To our knowledge, this is the first analytic example of a singly rotating five-dimensional solution in this framework with finite curvature invariants over a nontrivial region of parameter space. We analyze the geometry across this space, identifying regular noncompact, singular, and marginal regimes. Finally, we study the thermodynamic properties, finding that while higher-derivative corrections regularize the local curvature behavior, they also introduce unique challenges to the standard thermodynamic description of Killing horizons.

gr-qc↗

arXiv2026

Information, entropy and the paradox of choice: A model for understanding human choice behavior

Choice overload occurs when individuals feel overwhelmed by excessive alternatives during decision making. Although larger choice sets are often assumed to be more satisfying, behavioral evidence reveals an inverted U-shaped relationship between satisfaction and choice set size. However, quantitative frameworks linking information processing to choice satisfaction remain underdeveloped. Here, we develop a simple framework based on relative entropy and effective information to explain this behavior. We propose that satisfaction depends on the probability of finding an ideal option within a choice set and is determined by the informational structure of preferential choice probabilities relative to a baseline state of indifference. Small to moderately sized sets allow efficient comparison and identification of preferred options, thereby maximizing both effective information and satisfaction. As the number of alternatives increases, cognitive limitations increase uncertainty, leading to reduced effective information and satisfaction. This mechanism naturally produces the experimentally observed inverted U-shaped dependence of satisfaction on choice set size. Behavioral experiments across varying choice set sizes closely matched model predictions, suggesting that effective information provides a robust metric for choice satisfaction. These findings offer a principled theoretical account of the paradox of choice and carry broader implications for consumer psychology and human choice behavior.

physics.soc-ph↗

arXiv2026

Dynamical Completion of Coupling-Charge Thermodynamics

The scalar-gauge pair formulation promotes gravitational coupling constants to conserved charges, clarifying their role in extended black hole thermodynamics. However, its original incarnation restricts these auxiliary scalar fields to rigid, non-dynamical configurations. In this paper, we introduce a local, dynamical completion of this framework. By constructing the kinetic sector from a defect, which is the difference between the top-form field strength and the associated gravitational Lagrangian density, we allow the scalar to propagate as a genuine massive degree of freedom. Crucially, this local sector acts as a charge-preserving massive scalar backreaction, ensuring the thermodynamic coupling remains a conserved integration constant rather than a locally varying field. When evaluated on constant-coupling configurations, the auxiliary stress-energy contributions vanish entirely, perfectly preserving the original black hole solutions, the first law, and the Smarr relation. We illustrate this construction using the cosmological constant and the Gauss-Bonnet coupling.

gr-qc↗

arXiv2026

A Universal Smarr Formula via Coupling Constants

In gravitational theories containing matter fields and higher-derivative corrections, the standard Smarr formula often fails unless all dimensionful couplings are incorporated consistently. Traditionally, parameters such as the cosmological constant or the coefficients of higher-derivative terms are regarded as immutable features of the theory and therefore excluded from the thermodynamic phase space. In our recent work, we developed a fully general framework that promotes every such coupling to a dynamical, freely varying parameter of black hole solutions. This is accomplished by introducing, for each coupling, an auxiliary scalar and gauge field, through which the coupling appears as a conserved charge associated with the global sector of an emergent gauge symmetry. The corresponding conjugate variables naturally arise as electric potentials evaluated at the black hole horizon. As a result, the first law and the Smarr relation acquire additional, systematically determined contributions, yielding a consistent and universal extension of black hole thermodynamics. We illustrate the validity of this construction by revisiting several black hole examples in the literature where the Smarr formula remains inconsistent even after treating the cosmological constant as a thermodynamic variable. Our analysis shows that only by including all dimensionful couplings in this generalized manner can one obtain an internally consistent Smarr relation, thereby providing the foundation for a truly universal formulation of black hole thermodynamics.

gr-qc↗

arXiv2025

Hodge Dual Gauge Symmetry in Minimal Einstein-Aether Theory

Einstein-aether gravity is a theory that breaks the local Lorentz symmetry by introducing a preferred direction via a vector field, which is considered to play the role of an aether. The theory is identified by four coupling constants between the aether and gravity. Minimal Einstein-aether is the special case in which only one of the couplings is non-zero. We show that the aether vector field in its minimal version is Hodge dual to a gauge field. The gauge symmetry in the dual description has been known for decades and has been used to implement a cosmological constant into the Lagrangian. As a result, solutions to the well-established gauge theory can be transferred into the minimal Einstein-aether theory straightforwardly. On the other hand, some of the proposed solutions to the minimal Einstein-aether theory could be discarded as pure gauges of the vanishing aether. We prove as a theorem that this holds true for all divergence-less aether fields.

gr-qc↗

arXiv2024

Coupling Constants as Conserved Charges in Black Hole Thermodynamics

In a generic theory of gravity coupled to matter fields, the Smarr formula for black holes does not work properly if the contributions of the coupling constants defining the theory are not incorporated. However, these couplings, such as the cosmological constant or the dimensionful parameters that appear in the Lagrangian, are fixed parameters defining the theory, and they cannot be varied. Here, we present a robust method, applicable to any covariant Lagrangian, that upgrades the role of the couplings from being constants in the theory to being free parameters of the solutions. To this end, for each one of the couplings in a theory, a pair of auxiliary scalar and gauge fields is introduced. The couplings are shown to be conserved charges of the global part of the implemented gauge symmetry. Besides, their conjugate chemical potentials are defined as the electric potential of the corresponding gauge fields on the black hole horizon. Using this method, we systematically extend the first law and the Smarr formula by coupling conserved charges and their conjugate potentials. The thermodynamics of a black hole solution in a quadratic gravity theory is given as an example.

gr-qc↗

arXiv2024

Single-rotating Five-dimensional Near-horizon Extremal Geometry in General Relativity

The geometries with SL$(2,\mathbb{R})$ and some axial U$(1)$ isometries are called ``near-horizon extremal geometries" and are found usually, but not necessarily, in the near-horizon limit of the extremal black holes. We present a new member of this family of solutions in five-dimensional Einstein-Hilbert gravity that has only one nonzero angular momentum. In contrast with the single-rotating Myers-Perry extremal black hole and its near-horizon geometry in five dimensions, this solution may have a nonvanishing and finite entropy. Although there is a uniqueness theorem that prohibits the existence of such single-rotating near-horizon geometries in five-dimensional general relativity, this solution has a curvature singularity at one of the poles, which breaks the smoothness conditions in the theorem.

gr-qc↗

arXiv2024

On the Origin of Black Hole Paradoxes

Black hole firewall paradox is an inconsistency between four postulates in black hole physics: (1) the unitary evolution in quantum systems, (2) application of the semi-classical field theory in low curvature backgrounds, (3) statistical mechanical origin of the black hole entropy, and (4) the equivalence principle in the version of no drama for free-falling observers in the vicinity of the horizon. Based on the existence of the Hawking radiation for the static observers standing outside a Schwarzschild black hole, we show a direct contradiction between the postulates (2) and (4). If there is not a way out of this new problem, it implies the necessity of relaxing one of these two assumptions for resolving the black hole firewall paradox.

hep-th↗

arXiv2022

Light speed memory as a local observable for soft hairs

Einstein observers in flat space-time are inertial observers which use light to synchronize their clocks. For such observers, speed of light is a constant by construction. However, one can use super-translations to change coordinates from Einstein to BMS coordinates. From the point of view of BMS observers, speed of light is not a constant all over the space-time and in all directions. So in general, clocks which are synchronized for Einstein observers are not synchronized for BMS observers, and vice versa. Based on this fact, we propose a local observable for detecting the soft hairs, which is the variations in speed of light for such observers. We also investigate the relation of this observable to gravitational memory, which is a permanent change of position of test particles at infinity, after a gravitational wave passes completely from them. It is shown that the BMS time coordinate is the physical time after a gravitational wave, and it is the legitimate time to be used to calculate the light speed. Based on this argument, the analysis predicts a permanent change in the speed of light rays which propagate in asymptotics after a gravitational wave. Moreover, it is explained how this change is related to the gravitational memory by comparing their significance in observations.

gr-qc↗

arXiv2021

First law of black hole thermodynamics and Smarr formula with a cosmological constant

The first law of black hole thermodynamics in the presence of a cosmological constant $Λ$ can be generalized by introducing a term containing the variation $δΛ$. Similar to other terms in the first law, which are variations of some conserved charges like mass, entropy, angular momentum, electric charge etc., it has been shown [Classical Quantum Gravity 35, 125012 (2018)] that the new term has the same structure: $Λ$ is a conserved charge associated with a gauge symmetry; and its role in the first law is quite similar to an ``electric charge" rather than to the pressure. Besides, its conjugate chemical potential resembles an ``electric potential" on the horizon, in contrast with the volume enclosed by horizon. In this work, first we propose and prove the generalized Smarr relation in this new paradigm. Then, we reproduce systematically the ``effective volume" of a black hole which has been introduced before in the literature as the conjugate of pressure. Our construction removes the ambiguity in the definition of volume. Finally, we apply and investigate this formulation of ``$Λ$ as a charge" on a number of solutions to different models of gravity for different spacetime dimensions. Especially, we investigate the applicability and validity of the analysis for black branes, whose enclosed volume is not well defined in principle.

gr-qc↗

arXiv2018

Cosmological constant is a conserved charge

Cosmological constant can always be considered as the on-shell value of a top form in gravitational theories. The top form is field strength of a gauge field, and the theory enjoys a gauge symmetry. We show that cosmological constant is the charge of global part of the gauge symmetry, and is conserved irrespective of the dynamics of the metric and other fields. In addition, we introduce its conjugate chemical potential, and prove the generalized first law of thermodynamics which includes variation of cosmological constant as a conserved charge. We discuss how our new term in the first law is related to the volume-pressure term. In parallel with the seminal Wald entropy, this analysis suggests that pressure can also be considered as a conserved charge.

gr-qc↗

arXiv2016

Black Hole Entropy from Entropy of Hawking Radiation

We provide a simple way for calculating the entropy of a Schwarzschild black hole from the entropy of its Hawking radiation. To this end, we show that if a thermodynamic system loses its energy only through the black body radiation, its loss of entropy is always 3/4 of the entropy of the emitted radiation. This proposition enables us to relate the entropy of an evaporating black hole to the entropy of its Hawking radiation. Explicitly, by calculating the entropy of the Hawking radiation emitted in the full period of evaporation of the black hole, we find the Bekenstein-Hawking entropy of the initial black hole.

gr-qc↗

arXiv2016

Conserved Charges and First Law of Thermodynamics for Kerr-de Sitter Black Holes

Recently, a general method for calculating conserved charges for (black hole) solutions to generally covariant gravitational theories, in any dimensions and with arbitrary asymptotic behaviors has been introduced. Equipped with this method, which can be dubbed as "solution phase space method," we calculate mass and angular momentum for the Kerr-dS black holes. Furthermore, for any choice of horizons, associated entropy and the first law of thermodynamics are derived. Interestingly, according to insensitivity of the analysis to the chosen cosmological constant, the analysis unifies the thermodynamics of rotating stationary black holes in 4 (and other) dimensions with either AdS, flat or dS asymptotics. We extend the analysis to include electric charge, i.e. to the Kerr-Newman-dS black holes.

gr-qc↗

arXiv2016

Quantum Jump from Singularity to Outside of Black Hole

Considering the role of black hole singularity in quantum evolution, a resolution to the firewall paradox is presented. It is emphasized that if an observer has the singularity as a part of his spacetime, then the semi-classical evolution would be non-unitary as viewed by him. Specifically, a free-falling observer inside the black hole would have a Hilbert space with non-unitary evolution; a quantum jump for particles encountering the singularity to outside of the horizon as late Hawking radiations. The non-unitariness in the jump resembles the one in collapse of wave function, but preserves entanglements. Accordingly, we elaborate the first postulate of black hole complementarity: freely falling observers who pass through the event horizon would have non-unitary evolution, while it does not have physically measurable effects for them. Besides, no information would be lost in the singularity. Taking the modified picture into account, the firewall paradox can be resolved, respecting No Drama. A by-product of our modification is that roughly half of the entropy of the black hole is released close to the end of evaporation in the shape of very hot Hawking radiation.

gr-qc↗

arXiv2015

On Thermodynamics and Phase Space of Near Horizon Extremal Geometries

Near Horizon Extremal Geometries (NHEG), are geometries which may appear in the near horizon region of the extremal black holes. These geometries have $SL(2,\mathbb{R})\!\times\!U(1)^n$ isometry, and constitute a family of solutions to the theory under consideration. In the first part of this report, their thermodynamic properties are reviewed, and their three universal laws are derived. In addition, at the end of the first part, the role of these laws in black hole thermodynamics is presented. In the second part of this thesis, we review building their classical phase space in the Einstein-Hilbert theory. The elements in the NHEG phase space manifold are built by appropriately chosen coordinate transformations of the original metric. These coordinate transformations are generated by some vector fields, dubbed "symplectic symmetry generators." To fully specify the phase space, we also need to identify the symplectic structure. In order to fix the symplectic structure, we use the formulation of Covariant Phase Space method. The symplectic structure has two parts, the Lee-Wald term and a boundary contribution. The latter is fixed requiring on-shell vanishing of the symplectic current, which guarantees the conservation and integrability of the symplectic structure, and leads to the new concept of "symplectic symmetry." Given the symplectic structure, we construct the corresponding conserved charges, the "symplectic symmetry generators." We also specify the explicit expression of the charges as a functional over the phase space. These symmetry generators constitute the "NHEG algebra," which is an infinite dimensional algebra (may be viewed as a generalized Virasoro), and admits a central extension which is equal to the black hole entropy.

gr-qc↗