Search Results (43)

We investigate the statistical entropy of black holes within the framework of the generalized uncertainty principle (GUP) by employing effective metrics that incorporate leading-order and all-order quantum gravitational corrections. We construct three distinct effective metrics induced by the GUP, which are derived from the GUP-corrected temperature, entropy, and all-order GUP corrections, and analyze their impact on black hole entropy using ’t Hooft’s brick wall method. Our results show that, despite the differences in the effective metrics and the corresponding ultraviolet cutoffs, the statistical entropy consistently satisfies the Bekenstein–Hawking area law when expressed in terms of an invariant (coordinate-independent) distance near the horizon. Furthermore, we demonstrate that the GUP naturally regularizes the ultraviolet divergence in the density of states, eliminating the need for artificial cutoffs and yielding finite entropy even when counting quantum states only in the vicinity of the event horizon. These findings highlight the universality and robustness of the area law under GUP modifications and provide new insights into the interplay between quantum gravity effects and black hole thermodynamics. Full article

We investigated the thermodynamic topology of quantum-corrected AdS-Reissner-Nordström black holes in Kiselev spacetime using non-extensive entropy formulation derived from Loop Quantum Gravity (LQG). Through systematic analysis, we examined how the Tsallis parameter $\lambda$ influences topological charge classification with respect to various equation of state parameters. Our findings revealed a consistent pattern of topological transitions: for $\lambda =0.1$, the system exhibited a single topological charge $(\omega =-1)$ with total charge $W=-1$, as $\lambda$ increased to 0.8, the system transitioned to a configuration with two topological charges $(\omega =+1,-1)$ and total charge $W=0$. When $\lambda =1$, corresponding to the Bekenstein–Hawking entropy limit, the system displayed a single topological charge $(\omega =+1)$ with $W=+1$, signifying thermodynamic stability. The persistence of this pattern across different fluid compositions—from exotic negative pressure environments to radiation—demonstrates the universal nature of quantum gravitational effects on black hole topology. Full article

We present a study of relic gravitational waves based on a foliated gauge field theory defined over a spacetime endowed with a noncommutative algebraic–geometric structure. As an ontological extension of general relativity—concerning manifolds, metrics, and fiber bundles—the conventional space and time coordinates, typically treated as classical numbers, are replaced by complementary quantum dual fields. Within this framework, consistent with the Bekenstein criterion and the Hawking–Hertog multiverse conception, singularities merge into a helix-like cosmic scale factor that encodes the topological transition between the contraction and expansion phases of the universe analytically continued into the complex plane. This scale factor captures the essence of an intricate topological quantum-leap transition between two phases of the branching universe: a contraction phase preceding the now-surpassed conventional concept of a primordial singularity and a subsequent expansion phase, whose transition region is characterized by a Riemannian topological foliated structure. The present linearized formulation, based on a slight gravitational field perturbation, also reveals a high sensitivity of relic gravitational wave amplitudes to the primordial matter and energy content during the universe’s phase transition. It further predicts stochastic homogeneous distributions of gravitational wave intensities arising from the interplay of short- and long-spacetime effects within the non-commutative algebraic framework. These results align with the anticipated future observations of relic gravitational waves, expected to pervade the universe as a stochastic, homogeneous background. Full article

We reformulate holographic space–time models in terms of Hilbert bundles over the space of the time-like geodesics in a Lorentzian manifold. This reformulation resolves the issue of the action of non-compact isometry groups on finite-dimensional Hilbert spaces. Following Jacobson, I view the background geometry as a hydrodynamic flow, whose connection to an underlying quantum system follows from the Bekenstein–Hawking relation between area and entropy, generalized to arbitrary causal diamonds. The time-like geodesics are equivalent to the nested sequences of causal diamonds, and the area of the holoscreen (The holoscreen is the maximal $d-2$ volume (“area”) leaf of a null foliation of the diamond boundary. I use the term area to refer to its volume.) encodes the entropy of a certain density matrix on a finite-dimensional Hilbert space. I review arguments that the modular Hamiltonian of a diamond is a cutoff version of the Virasoro generator $L_0$ of a $1+1$-dimensional CFT of a large central charge, living on an interval in the longitudinal coordinate on the diamond boundary. The cutoff is chosen so that the von Neumann entropy is $\ln {\mathrm{D}}_{\diamond },$ up to subleading corrections, in the limit of a large-dimension diamond Hilbert space. I also connect those arguments to the derivation of the ’t Hooft commutation relations for horizon fluctuations. I present a tentative connection between the ’t Hooft relations and $U\left(1\right)$ currents in the CFTs on the past and future diamond boundaries. The ’t Hooft relations are related to the Schwinger term in the commutator of the vector and axial currents. The paper in can be read as evidence that the near-horizon dynamics for causal diamonds much larger than the Planck scale is equivalent to a topological field theory of the ’t Hooft CR plus small fluctuations in the transverse geometry. Connes’ demonstration that the Riemannian geometry is encoded in the Dirac operator leads one to a completely finite theory of transverse geometry fluctuations, in which the variables are fermionic generators of a superalgebra, which are the expansion coefficients of the sections of the spinor bundle in Dirac eigenfunctions. A finite cutoff on the Dirac spectrum gives rise to the area law for entropy and makes the geometry both “fuzzy” and quantum. Following the analysis of Carlip and Solodukhin, I model the expansion coefficients as two-dimensional fermionic fields. I argue that the local excitations in the interior of a diamond are constrained states where the spinor variables vanish in the regions of small area on the holoscreen. This leads to an argument that the quantum gravity in asymptotically flat space must be exactly supersymmetric. Full article

The first part of this work provides a review of recent research on generalised entropies and their origin, as well as its application to black hole thermodynamics. To start, it is shown that the Hawking temperature and the Bekenstein–Hawking entropy are, respectively, the only possible thermodynamical temperature and entropy of the Schwarzschild black hole. Moreover, it is investigated if the other known generalised entropies, which include Rényi’s entropy, Tsallis entropy, and the four- and five-parameter generalised entropies, could correctly yield the Hawking temperature and the ADM mass. The possibility that generalised entropies could describe hairy black hole thermodynamics is also considered, both for the Reissner–Nordström black hole and for Einstein’s gravity coupled with two scalar fields. Two possibilities are investigated, namely, the case when the ADM mass does not yield the Bekenstein–Hawking entropy, and the case in which the effective mass expressing the energy inside the horizon does not yield the Hawking temperature. For the model with two scalar fields, the radii of the photon sphere and of the black hole shadow are calculated, which gives constraints on the BH parameters. These constraints are seen to be consistent, provided that the black hole is of the Schwarzschild type. Subsequently, the origin of the generalised entropies is investigated, by using their microscopic particle descriptions in the frameworks of a microcanonical ensemble and canonical ensemble, respectively. Finally, the McLaughlin expansion for the generalised entropies is used to derive, in each case, the microscopic interpretation of the generalised entropies, via the canonical and the grand canonical ensembles. Full article

It is often assumed that the maximum number of independent states a black hole may contain is $N_{BH}=e^{S_{BH}}$, where $S_{BH}=A/4$ is the Bekenstein–Hawking entropy and A is the horizon area in Planck units. I present a simple and straightforward argument showing that the number of states that can be distinguished by local observers inside the hole must be greater than this number. Full article

A hot NUT–Kerr–Newman black hole is a general stationary axisymmetric black hole. In this black hole spacetime, the dynamical equations of fermions at the horizon are modified by considering Lorentz breaking. The corrections to the Hawking temperature and Bekenstein–Hawking entropy at the horizon of the black hole are studied in depth. Based on the semiclassical theory correction, the Bekenstein–Hawking entropy of this black hole is quantum-corrected by considering the perturbation effect of the Planck constant ℏ. The latter part of this paper presents a detailed discussion of the obtained results and their physical implications. Full article

We evaluate here the quantum gravity partition function that counts the dimension of the Hilbert space of a simply connected spatial region of a fixed proper volume in the context of Lovelock gravity, generalizing the results for Einstein gravity. It is found that there are sphere saddle metrics for a partition function at a fixed spatial volume in Lovelock theory. Those stationary points take exactly the same forms as in Einstein gravity. The logarithm of Z corresponding to a zero effective cosmological constant indicates that the Bekenstein–Hawking entropy of the boundary area and that corresponding to a positive effective cosmological constant points to the Wald entropy of the boundary area. We also show the existence of zeroth-order phase transitions between different vacua, a phenomenon distinct from Einstein gravity. Full article

In spirit of the recently proposed four-parameter generalized entropy of apparent horizon, we investigate inflationary cosmology where the matter field inside of the horizon is dominated by a scalar field with a power law potential (i.e., the form of ${\varphi }^n$ where $\varphi$ is the scalar field under consideration). Actually without any matter inside of the horizon, the entropic cosmology leads to a de-Sitter spacetime, or equivalently, an eternal inflation with no exit. Thus in order to achieve a viable inflation, we consider a minimally coupled scalar field inside the horizon, and moreover, with the simplest quadratic potential. It is well known that the ${\varphi }^2$ potential in standard scalar field cosmology is ruled out from inflationary perspective as it is not consistent with the recent Planck 2018 data; (here it may be mentioned that in the realm of “apparent horizon thermodynamics”, the standard scalar field cosmology is analogous to the case where the entropy of the apparent horizon is given by the Bekenstein–Hawking entropy). However, the story becomes different if the horizon entropy is of generalized entropic form, in which case, the effective energy density coming from the horizon entropy plays a significant role during the evolution of the universe. In particular, it turns out that in the context of generalized entropic cosmology, the ${\varphi }^2$ potential indeed leads to a viable inflation (according to the Planck data) with a graceful exit, and thus the potential can be made back in the scene. Full article

With the introduction of CFJ correction term, Chiral correction term, and aether-like correction term, based on Lorentz breaking, WKB approximate, and quantum tunneling radiation theory of black holes, the modified fermion dynamics equation is studied in the general non-stationary spherically symmetric black hole space-time, and the new modified expressions of the fermion tunneling rate, the Hawking temperature, and the Bekenstein–Hawking entropy of the black hole are obtained. This black hole has both thermal and non-thermal radiation. In this article, the influence of Lorentz breaking on the energy levels of Dirac particles was also studied, and the distribution characteristics of Dirac energy levels in the space-time and the maximum value of the crossing of positive and negative energy levels were obtained. The necessary discussion and the explanation of the corresponding results are made. Full article

The paper explores the thermodynamic properties of primordial black holes (PBHs) in the braneworld. Specifically, the researchers examined Hawking radiation and the lifetime of PBHs. Through their analysis, an exact analytical expression for the Bekenstein–Hawking entropy, temperature, and heat capacity was derived. Their findings suggest that the lifetime of PBHs in the early universe is reduced by at least one order of magnitude, ultimately leading to their evaporation. This could explain why we have not observed the final rapid evaporation of PBHs in the recent epoch of the universe. Full article

We consider a correspondence between the tachyon dark energy model and Barrow holographic dark energy (BHDE). The latter is a modified scenario based on the application of the holographic principle with Barrow entropy instead of the usual Bekenstein–Hawking one. We reconstruct the dynamics of the tachyon scalar field T in a curved Friedmann–Robertson–Walker universe both in the presence and absence of interactions between dark energy and matter. As a result, we show that the tachyon field exhibits non-trivial dynamics. In a flat universe, ${\dot{T}}^2$ must always be vanishing, independently of the existence of interaction. This implies ${\omega }_D=-1$ for the equation-of-state parameter, which in turn can be used for modeling the cosmological constant behavior. On the other hand, for a non-flat universe and various values of the Barrow parameter, we find that ${\dot{T}}^2$ decreases monotonically for increasing $cos(R_h/a)$ and $cosh(R_h/a)$, where $R_h$ and a are the future event horizon and the scale factor, respectively. Specifically, ${\dot{T}}^2\ge 0$ for a closed universe, while ${\dot{T}}^2<0$ for an open one, which is physically not allowed. We finally comment on the inflation mechanism and trans-Planckian censorship conjecture in BHDE and discuss observational consistency of our model. Full article

We exploit the properties of complex time to obtain an analytical relationship based on considerations of causality between the two Noether-conserved quantities of a system: its Hamiltonian and its entropy production. In natural units, when complexified, the one is simply the Wick-rotated complex conjugate of the other. A Hilbert transform relation is constructed in the formalism of quantitative geometrical thermodynamics, which enables system irreversibility to be handled analytically within a framework that unifies both the microscopic and macroscopic scales, and which also unifies the treatment of both reversibility and irreversibility as complementary parts of a single physical description. In particular, the thermodynamics of two unitary entities are considered: the alpha particle, which is absolutely stable (that is, trivially reversible with zero entropy production), and a black hole whose unconditional irreversibility is characterized by a non-zero entropy production, for which we show an alternate derivation, confirming our previous one. The thermodynamics of a canonical decaying harmonic oscillator are also considered. In this treatment, the complexification of time also enables a meaningful physical interpretation of both “imaginary time” and “imaginary energy”. Full article

Hawking radiation is an essential property of the quantum black hole. It results in the information loss paradox and provides an important clue with regard to the unification of quantum mechanics and general relativity. In previous work, the boundary scalar fields on the horizon of black holes were used to determine the microstates of BTZ black holes and Kerr black holes. They account for Bekenstein–Hawking entropy. In this paper, we show that the Hawking radiation can also be derived from those scalar fields. Hawking radiation is a mixture of the thermal radiation of right- and left-moving sectors at different temperatures. Based on this result, for static BTZ black holes and Schwarzschild black holes, we propose a simple solution for the information loss paradox; i.e., the Hawking radiation is pure due to its entanglement between the left-moving sector and the right-moving sector. This entanglement may be detected in an analogue black hole in the near future. Full article

This manuscript reports the dynamics of a time-conformal quantum-corrected AdS–Schwarzschild black hole. The quantum-corrected parameter and the time-conformal factors are inserted in the AdS–Schwarzschild black. These insertions in the said space- time are taken to study and understand the phenomena of the formation of gravitational waves and Hawking radiations. The Hawking temperature distributions and Bekenstein–Hawking entropy for the inner and outer horizon of the new developed black hole solution are calculated and discussed. The motion of neutral and charged particles in the orbits of the said black hole is discussed under the influence of effective potential and effective force in the new development of the black hole solution. The escape velocity for the time-conformal black hole is obtained and compared with the escape velocity of the exact black hole. The roles of the quantum-corrected parameter and the effect of the time-conformal factor are high- lighted, and their influences are discussed in different situations. Einstein’s field equations are also obtained for the time-conformal quantum-corrected AdS–Schwarzschild black hole. The Lyapunov exponent is used for the stability of the said black hole spacetime. The effects of different parameters on different dynamical aspects of the black hole are explored. Full article