While the superposition of quantum evolutions is known to produce interference effects, the interference between evolutions with regular and chaotic classical limits remains largely unexplored. Here, we use a Mach-Zehnder interferometer to investigate the superposition of two quantum evolutions, implemented via post-selection, and to compare it with the corresponding classical mixture. The quantum kicked top provides a natural platform for this study, as its classical dynamics ranges from regular to mixed to fully chaotic depending on the Hamiltonian parameters. We show that when a regular evolution is superposed with a chaotic one, the resulting subsystem entropy can exceed that of the classical mixture, provided the contribution of the chaotic branch dominates in the superposed quantum evolution. We further demonstrate that entropy production in such superpositions is strongly influenced by the structure of the underlying classical phase space. We further show that increased entropy generation can occur for purely regular dynamics at small values of the chaos parameter, given an appropriate choice of post-selection. These results reveal a nontrivial interplay between classical chaos and quantum interference in superposed quantum dynamics

We study slowly rotating black hole solutions in the Einstein-Bel-Robinson gravity (EBR) in four dimensions. At the leading order in the rotation parameter, the only modification with respect to the static case is the appearance of a nonvanishing gt & ccedil;b component. We construct approximate solutions to these equations and study how physical properties of the solutions, such as the angular velocity, photon sphere, black hole shadow, and innermost stable circular orbit, are modified, working to leading order in the coupling constant and the rotation parameter. Finally, we study the superradiance of a massive scalar wave scattering off slowly rotating black holes. Using direct integration, we derive the superradiant conditions and compute the energy flux through the event horizon. We demonstrate how the flux will change as a function of the black hole rotation and frequency of the incident wave. Finally, we showed how black hole parameters, including the gravitational coupling of EBR, change during superradiance. We study the impact of the superradiant evolution on the black hole shadow and show that the shadow radius can either shrink or grow depending on the competition between the involved components during the evolution.

We present the first realization of multicritical points in four-dimensional general relativity, specifically within the context of Plebański nonlinear electrodynamics, using a polynomial structural function denoted as ℋ(P). We show that this construction provides a systematic mechanism to engineer multicritical behavior in gravitational systems. By establishing an explicit mapping between matter theories expressed as power series in the Maxwell invariant F and the Plebański formulation, we construct new families of electrically charged asymptotically anti-de Sitter black holes and magnetically charged solitons. In the grand-canonical ensemble, we analyze their thermodynamic properties and uncover a rich phase structure. We demonstrate that the soliton sector develops multiple swallowtail structures, signaling first-order phase transitions and allowing the coexistence of several magnetically charged solitons with a single electrically charged black hole. These configurations define multicritical points that generalize previously known triple points. We further show that the number of coexisting phases is controlled by the degree of the polynomial structural function, providing a direct link between the nonlinear electrodynamics couplings and the thermodynamic phase structure. In contrast, the black hole branch does not display swallowtail behavior, and it does not allow multiple electrically charged black holes to coexist with a magnetically charged soliton.

We show that spacetime symmetries on any background give rise to stealth vector fields obeying Proca-type equations supplemented by curvature terms. This observation, which is true for solutions of any theory of gravity and with arbitrary matter content, effectively promotes spacetime symmetries to "physical fields" whose characteristic property is that their backreaction on the geometry vanishes. In particular, this allows one to construct exact Proca hair charged and magnetized rotating black holes in all dimensions. In fact, such a construction is not limited to Killing vector fields and equally works for conformal Killing vectors and hidden symmetries encoded in Killing-Yano tensors.

We study soliton-black hole phase transitions in asymptotically AdS planar spacetimes sourced by a cloud of strings. In the planar background, the string cloud exhibits a brush-like configuration, where the strings are aligned parallel to each other and extend along the radial direction. This leads to a stress tensor with nonvanishing components only along the temporal and radial directions. By comparing the Euclidean on-shell actions of the planar black hole and the corresponding AdS soliton under the same boundary conditions, we obtain the free energy difference between the two phases. Our results show that the string cloud parameter significantly modifies the competition between the black hole phase and the soliton phase. In particular, positive and negative values of the string cloud parameter affect the phase structure in different ways, changing the dominance relation between the black hole and soliton configurations.

We comment on an error in the charged quark star literature ( Phys. Rev. D, 102(3):034031, 2020 ) that resulted in erroneous solutions to the radial stability equations for charged interacting quark stars in ( Phys. Rev. D, 104(12):123007, 2021 )[2]. In this comment article we recalculate the fundamental radial eigenfrequencies for charged, interacting quark stars in general relativity and discuss any departure from previous results [2]. Most of the qualitative trends persist, but the magnitudes of the separation between the maximum mass and stability points on a given branch can change significantly. We also note that all branches in [2] that contained no stable solutions now have stable solutions in their corrected counterparts. The net effect is that in all of the studied cases charged quark stars have a greater range of stability than originally predicted. We also compare four recent observational constraints not included in previous studies, and find that these constraints are satisfied by a subset of the mass-radius relations we obtain.

In this paper we consider quark star solutions to Liu et al.'s \cite{Liu_2019} quasi-topological electromagnetism (QTEM), a recently proposed form of dark energy. Since the QTEM contribution is trivial for pure electric/magnetic charge, we consider the dyonic case in pure QTEM which does induce (dark) non-trivial dynamics from the non-linear theory. Besides the introduction of a dyonic charge distribution generally pushing the characteristic quark star `hook' shape to larger masses and radii, it also induces a second branch at very large mass and radius for stars with a small dyonic charge ratio. This second set of solutions have a negative pressure envelope surrounding a positive pressure core. As we explore the parameter space these features interact and evolve in interesting ways, with the two branches eventually merging in $M/R$ space before settling into a characteristic `paperclip' shape as the dyonic charge ratio becomes large.

Several inequivalent thermodynamic formulations of spacetimes with NUT charge obey their own first laws and Smarr relations, so macroscopic consistency alone does not fix the black hole state space. We introduce a two-horizon sector diagnostic whose temperatures are fixed by harmonic-mean relations rather than adjusted as potentials. For uncharged Taub-NUT, the sum sector closes with the mass and NUT charge, whereas the difference sector closes, within a restricted homogeneous diagnostic class tested here, only after including the rotation-like thermodynamic secondary hair $J_n=mn$. Thus, within this sector diagnostic, the NUT parameter enters through both $N=n$ and the homogeneous combination $J_n=mn$. The secondary hair is defined off shell in the homogeneous mass representation, not as a new metric parameter or asymptotic charge. Hidden conformal symmetry of the rotating Kerr-NUT parent gives a consistency check, without assuming a holographic dual.

In this study, we extend the application of the Lee-Yang phase transition theorem to the realm of anti-de Sitter (AdS) black hole thermodynamics, thereby deriving a comprehensive complex phase diagram for such systems. Our research augments extant studies on black hole thermodynamic phase diagrams, particularly in the regime above the critical point, by delineating the Widom line of AdS black holes. This boundary segregates the supercritical domain of the phase diagram into two disparate zones. As the system traverses the thermodynamic crossover within the supercritical region, it undergoes a transition from one supercritical phase to another, while maintaining the continuity of its thermodynamic state functions. This behavior is fundamentally different from that below the critical point, where crossing the coexistence line results in discontinuities of thermodynamic state functions. The Widom line enables a thermodynamic crossover between single-phase states without traversing the spinodal that emerges in the critical region.

In a recent paper, Arxiv:2605.23077, we have demonstrated that (conformal) Killing vectors give rise to stealth vector solutions of a specific bumblebee-type Proca theory supplemented by fine tuned curvature terms. Here we show that such a construction readily generalizes to hidden symmetries encoded in (conformal) Killing-Yano tensors, giving rise to the corresponding p-form stealth solutions. Similar to what happens with Killing vectors, the construction works on any background, providing a "physical visualization" of its symmetries. Several examples of spacetimes with so constructed p-form stealth hair are presented.

It is univocally anticipated that in a theory of quantum gravity, there exist quantum superpositions of semiclassical states of spacetime geometry. Such states could arise for example, from a source mass in a superposition of spatial configurations. In this paper we introduce a framework for describing such ”quantum superpositions of spacetime states.” We introduce the notion of the relativity of spacetime superpositions, demonstrating that for states in which the superposed amplitudes differ by a coordinate transformation, it is always possible to re-express the scenario in terms of dynamics on a single, fixed background. Our result unveils an inherent ambiguity in labelling such superpositions as genuinely quantum-gravitational, which has been done extensively in the literature, most notably with reference to recent proposals to test gravitationally-induced entanglement. We apply our framework to the the above mentioned scenarios looking at gravitationally-induced entanglement, the problem of decoherence of gravitational sources, and clarify commonly overlooked assumptions. In the context of decoherence of gravitational sources, our result implies that the resulting decoherence is not fundamental, but depends on the existence of external systems that define a relative set of coordinates through which the notion of spatial superposition obtains physical meaning.

We investigate holographic complexity within the Schwarzschild-de Sitter (SdS) black hole spacetime. Two distinct de Sitter holography prescriptions are examined: the static patch scheme restricted to the stretched horizon and the de Sitter/Conformal Field Theory (dS/CFT) correspondence scheme defined at asymptotic future and past infinities. We evaluate the Complexity equals Volume (CV) conjecture and extend the analysis to codimension-zero proposals, specifically Complexity equals Spacetime Volume (CV2.0) and Complexity equals Action (CA), through the Wheeler-DeWitt (WDW) patch we construct. The behaviors of the complexity in the static patch holography at late time and in the dS/CFT at infinite spacelike boundary coordinate are studied, respectively. We find that under both the CV and CV2.0 conjectures, the static patch holographic complexity and the dS/CFT holographic complexity consistently exhibit linear growth. Conversely, regarding the CA conjecture, the holographic complexity growth rates for both the static patch and the dS/CFT correspondence vanish. This behavior is attributed to the finiteness of the (regularized) action within the restricted WDW region. Furthermore, it is demonstrated that the complexity growth rate of the static patch scheme is identical to that in the dS/CFT scheme. This equivalence implies the existence of a unified description for bulk dynamics within de Sitter holography.

We develop a framework for holographic thermodynamics in finite-cutoff holography, extending the anti-de Sitter/conformal field theory (AdS/CFT) correspondence to incorporate a finite radial cutoff in the bulk and a T^2-deformed CFT on the boundary. We formulate the first laws of thermodynamics for a Schwarzschild-AdS (SAdS) black hole with a Dirichlet cutoff on the quasilocal boundary and its dual deformed CFT, introducing the deformation parameter as a thermodynamic variable. The holographic Euler relation for the deformed CFT and its equation of state are derived, alongside the Smarr relation for the bulk. We show that the Rupert teardrop coexistence curve defines a phase space island where deformation flow alters states, with up to three deformed CFTs or cut-off SAdS sharing a same phase transition temperature, one matching the seed CFT or original SAdS. These results offer insights into gravitational thermodynamics with boundary constraints and quantum gravity in finite spacetime regions.

We investigate the thermodynamic and holographic properties of charged and rotating quantum black holes in a doubly holographic braneworld setup. These quantum black holes are derived from the anti-de Sitter C-metric and are exact solutions to a semiclassical gravitational theory which incorporates all orders of the backreaction of quantum fields on spacetime. The inclusion of both charge and rotation extends and generalizes previous studies. The thermodynamics and critical behavior of the black holes are examined from the bulk, brane, and boundary perspectives, and we demonstrate that the inclusion of either charge or rotation removes the reentrant phase transitions seen in the neutral-static case. The critical exponents of the system are calculated using numerical methods and found to differ from the standard mean field theory values for the neutral-static black holes’ reentrant phase transitions, but in agreement with mean-field theory for the phase transitions of the black holes with charge and rotation. Additionally, to test the validity of the semiclassical treatment, we study a mass-gap energy scale to identify regimes where quantum fluctuations of spacetime geometry are expected to become significant and speculate about a connection with weak cosmic censorship gedankenexperiments. We also generalize the quantum Penrose inequality and the quantum reverse isoperimetric inequality to include charge and rotation. Finally, we compute a renormalized gyromagnetic ratio and analyze it in the limit of large backreaction.

We present a comprehensive study of the C-metric in 2+1 dimensions, placing it within a shell of stress energy and matching it to an exterior vacuum anti-de Sitter metric. The 2+1 C-metric is not circularly symmetric and hence neither are the constructed shells, which instead take on a cuspoidal or teardrop shape. We interpret the stress energy of the shells as a perfect fluid, calculating the energy density and pressure. For accelerating particles (Class I), we find the stress energy is concentrated on the part of shell farthest from the direction of acceleration and always respects the strong and weak energy conditions. For accelerating black holes (Class I C, II, and III), the shell stress energy may either respect or violate the energy conditions depending on the parameter of the exterior metric-between the two regimes lies a critical value of the external parameter for which the shell stress energy vanishes, leading to new solutions of Einstein's field equations, which fall into three categories: an accelerated black hole pulled by a finite-length string with a point particle at the other end, an accelerated black hole pushed by a finite-length strut with a point particle at the other end, and an accelerated black hole pushed from one side by a finite-length strut and pulled from the other by a finite-length string, each with a point particle at the other end.

The introduction of thermodynamics into gravitational physics began 5 decades ago with the discovery that black holes behave like thermodynamic systems once semiclassical quantum effects are taken into account. Notions of temperature, entropy, work and phase changes that were introduced into gravitational physics and originally applied to black holes, were later extended to cosmological horizons and other settings as well. A major development occurred 15 years ago with the introduction of pressure in the form of a cosmological constant. By extending the thermodynamic phase-space to include this term, along with its conjugate volume, black holes were found to exhibit a broad variety of phase transitions that resembled phenomena seen in chemistry labs. Black hole thermodynamics has become Black Hole Chemistry, which has led to a wealth of insights into the nature of black holes, introducing concepts such as Van der Waals fluids, reentrant phase transitions and triple points into gravitational physics. I discuss the origins of Black Hole Chemistry and its basic features covered in an earlier review [D. Kubiznak, R. B. Mann and M. Teo, Black hole chemistry: Thermodynamics with Lambda, Class. Quantum Grav. 34 (2017) 063001, [arXiv:1608.06147]], and then go on to describe developments in the subject that have taken place since then. Examples include multicritical behaviour, polymeric transitions, superfluid transitions, scalar hair, heat engines, NUT-charge, acceleration thermodynamics, the Joule-Thompson expansion, holography, complexity, central charge criticality, microstructure, thermodynamic tension, phase dynamics and thermodynamic topology. This wealth of new phenomena suggest that we likely still have a lot to learn from Black Hole Chemistry.

We study the implications of an isentropic processes applied to a Reissner-Nordstr & ouml;m black hole. This process is possible if a black hole absorbs a particle with a specific ratio of energy and charge. We show that such an absorption process is not classically allowed, not only in Einstein gravity but also in several modified gravity theories, indicating that this prohibition is quite generic. However, an isentropic absorption process is quantum mechanically allowed: the particle can penetrate the potential barrier on the event horizon. We compute the probability of this absorption process and compare it to that of semiclassical effects. Nonperturbatively, if this process is accumulated, it is possible that the entanglement entropy can be greater than its Bekenstein-Hawking entropy and violate the entropybound relation.

By viewing black hole solutions as topological defects in thermodynamic parameter space, we unveil a novel topological class and two new topological subclasses, respectively, denoted as W0−↔1+, W¯1+, and W^1+, that extend beyond the four established categories proposed by Wei []. Within the newly identified class and these two novel subclasses, the innermost small black hole states exhibit a distinct sequence of unstable, stable, and stable behaviors, while the outermost large black hole states display a uniform pattern of stable behaviors. These classifications indicate thermodynamic properties both in the low and high Hawking temperature regimes that are strikingly different from the previously known four topological classes. In particular, we demonstrate that the static charged anti–de Sitter black holes in gauged supergravity exhibit an intricate thermodynamic evolution that is notably distinct from that of the Reissner-Nordström anti–de Sitter black hole. From a topological perspective, we emphasize the advantages and potential of investigating thermodynamic phase transitions in these black hole spacetimes, an area that has been rarely explored in the previous research. Our findings not only enrich and sharpen the framework of topological classifications in black hole thermodynamics but also represent a significant stride toward unraveling the fundamental nature of black holes and gravity.

Since the derivation of a well-defined D -* 4 limit for four-dimensional Einstein Gauss-Bonnet (4DEGB) gravity coupled to a scalar field, there has been interest in testing it as an alternative to Einstein's general theory of relativity. Using the Tolman-Oppenheimer-Volkoff equations modified for charge and 4DEGB gravity, we model the stellar structure of charged, noninteracting quark stars. We find that increasing the Gauss-Bonnet coupling constant alpha or the charge Q both tend to increase the mass-radius profiles of quark stars described by this theory, allowing a given central pressure to support larger quark stars in general. We also derive a generalization of the Buchdahl bound for charged stars in 4DEGB gravity. As in the uncharged case, we find that quark stars can exist below the general relativistic Buchdahl bound and Schwarzschild radius R = 2M, due to the lack of a mass gap between black holes and compact stars in the 4DEGB theory. Even for alpha well within current observational constraints, we find that quark star solutions in this theory can describe extreme compact charged objects, objects whose radii are smaller than what is allowed by general relativity.

We study massive charged scalar field perturbations in four- and five- dimensional charged anti-de Sitter soliton spacetimes. Appropriate boundary conditions are established via a local analysis of the perturbation equations. The normal mode spectra are then calculated numerically using the Horowitz-Hubeny method and a collocation method. We reveal scaling laws and asymptotic behaviors governing the normal mode spectra. The reality of the normal mode frequencies indicates the dynamic stability of the soliton, which in turn provides support for the positive energy conjecture in asymptotically locally anti-de Sitter spacetime.