Black Hole Spacetimes Research Articles

Riemann surfaces and winding numbers of Rényi phase structure of charged-flat black holes

It’s widely recognized that the free energy landscape captures the essentials of thermodynamic phase transitions. In this work, we extend the findings of [1] by incorporating the nonextensive nature of black hole entropy. Specifically, the connection between black hole phase transitions and the winding number of Riemann surfaces derived through complex analysis is extended to the Rényi entropy framework. This new geometrical and nonextensive formalism is employed to predict the phase portraits of charged-flat black holes within both the canonical and grand canonical ensembles. Furthermore, we elucidate novel relations between the number of sheets comprising the Riemann surface of the Hawking–Page and Van der Waals transitions and the dimensionality of black hole spacetimes. Notably, these new numbers are consistent with those found for charged-AdS black holes in Gibbs–Boltzmann statistics, providing another significant example of the potential connection between the cosmological constant and the nonextensive Rényi parameter.

Massive scalar clouds and black hole spacetimes in Gauss-Bonnet gravity

We study static black holes in scalar-Gauss-Bonnet (sGB) gravity with a massive scalar field as an example of higher curvature gravity. The scalar mass introduces an additional scale and leads to a strong suppression of the scalar field beyond its Compton wavelength. We numerically compute sGB black hole spacetimes and scalar configurations and also compare with perturbative results for small couplings, where we focus on a dilatonic coupling function. We analyze the constraints on the parameters from requiring the curvature singularity to be located inside the black hole horizon r_hrh and the relation to the regularity condition for the scalar field. For scalar field masses m r_h \gtrsim 10^{-1}mrh≳10−1, this leads to a new and currently most stringent bound on sGB coupling constant \alphaα of \alpha/r_h^2\sim 10^{-1}α/rh2∼10−1 in the context of stellar mass black holes. Lastly, we look at several properties of the black hole configurations relevant for further work on observational consequences, including the scalar monopole charge, Arnowitt–Deser–Misner mass, curvature invariants and the frequencies of the innermost stable circular orbit and light ring.

Quantum nature of black hole and the superposition of fermionic field

The operational framework for the superposition of spacetime is fundamentally important in developing a comprehensive description of quantum gravity (Foo et al. in Phys Rev Lett 129:181301, 2022). As a “bottom-up” unifying theory of quantum gravity, it allows us to investigate how mass superposition of spacetime influences the performance of quantum information processing. In this paper, we study how the quantum-gravitational effects produced by the mass superposition of a black hole influence the quantum coherence of fermionic fields. It is shown that the spacetime effects associated with a classical black hole lead to inevitable decoherence. Notably, compared to classical black hole spacetime scenarios, fermionic fields near a black hole with superposed masses can retain more quantum coherence. This suggests that the quantum properties of spacetime may serve as resources to mitigate coherent degradation caused by gravitational effects. The bottom-up perspective on spacetime superposition proposed in this work serves as an indication of quantum-gravitational effects and holds significant theoretical implications.

Eikonal amplitudes on the celestial sphere

Celestial scattering amplitudes for massless particles are Mellin transforms of momentum-space scattering amplitudes with respect to the energies of the external particles, and behave as conformal correlators on the celestial sphere. However, there are few explicit cases of well-defined celestial amplitudes, particularly for gravitational theories: the mixing between low- and high-energy scales induced by the Mellin transform generically yields divergent integrals. In this paper, we argue that the most natural object to consider is the gravitational amplitude dressed by an oscillating phase arising from semi-classical effects known as eikonal exponentiation. This leads to gravitational celestial amplitudes which are analytic, apart from a set of poles at integer negative conformal dimensions, whose degree and residues we characterize. We also study the large conformal dimension limits, and provide an asymptotic series representation for these celestial eikonal amplitudes. Our investigation covers two different frameworks, related by eikonal exponentiation: 2 → 2 scattering of scalars in flat spacetime and 1 → 1 scattering of a probe scalar particle in a curved, stationary spacetime. These provide data which any putative celestial dual for Minkowski, shockwave or black hole spacetimes must reproduce. We also derive dispersion and monodromy relations for these celestial amplitudes and discuss Carrollian eikonal-probe amplitudes in curved spacetimes.

Self-gravitating matter in stationary and axisymmetric black hole spacetimes

Abstract All black holes (BHs) in nature are expected to be described by the Kerr vacuum solution of general relativity. However, the Kerr BH interior contains several problematic features such as a Cauchy horizon, a curvature singularity, and a causality-violating region. Non-Kerr BH models, which are used to examine the genericity of these features, typically contain nontrivial matter content. When such self-gravitating matter is minimally-coupled to Einstein–Hilbert gravity, the Einstein equations can be directly used to investigate its physical properties. We examine here the properties of matter in a broad class of stationary and axisymmetric, geodesically-integrable BH spacetimes, and how they are linked to various features of the spacetime geometry. In these spacetimes, we find the matter to typically flow along timelike Killing orbits in the BH exterior, usually exhibiting differential rotation but sometimes additionally also non-rigid rotation. At a horizon, the matter rest-frame energy density, ε, and principal normal pressure, pn , are shown to necessarily satisfy p n = − ϵ , implying that only specific types of matter can thread stationary event horizons (e.g. electromagnetic fields but not massless real scalar fields). Furthermore, we introduce Boyer–Lindquist-like coordinates for the nonstationary regions in the BH interior, which show the matter to be comoving with the interior cosmology. We also obtain simple expressions for the expansions of the ingoing and outgoing zero angular momentum null congruences and comment on the light-focussing behavior of the cosmology. Finally, we verify above results explicitly by working with a representative set of well-known BH spacetimes which contain various types of matter—scalar fields, electromagnetic fields, anisotropic fluids. Some spacetimes have singularities while others have regular interiors. In the exterior, the matter satisfies the weak energy condition. The framework developed here can be extended to cover more general spacetimes.

Across-horizon propagation and infinite time-dilation: An independent approach to Hawking radiation

The conformal scalar propagator as an explicit function of the Schwarzschild black-hole space-time has been established in the preceding three projects. The present project examines the precise relation which that propagator has to the amplitude the Schwarzschild black hole emit a scalar particle in a particular mode of positive energy. It is thereby established that the effect of infinite time-dilation on the event horizon results in both, the thermal radiation in the background of a static exterior space-time geometry and the detraction from thermality if energy-conservation is properly imposed as a constraint on scalar propagation. The derivation of the latter signifies an equivalent approach to the result of Parikh and Wilczek from the semi-classical perspective of the distant observer. From that perspective for that matter, Hawking radiation emerges in both contexts as the exclusive consequence of infinite time-dilation on the event horizon. These results are consistent with Hawking radiation as the exclusive consequence of the causal structure of the Schwarzschild black-hole space-time both, in a static exterior geometry and in such dynamical exterior geometry as energy-conservation signifies. The extension of the thermal case to other spin-fields and black-hole geometries is discussed.

Revisiting Buchdahl transformations: new static and rotating black holes in vacuum, double copy, and hairy extensions

This paper investigates Buchdahl transformations within the framework of Einstein and Einstein-Scalar theories. Specifically, we establish that the recently proposed Schwarzschild–Levi-Civita spacetime can be obtained by means of a Buchdahl transformation of the Schwarschild metric along the spacelike Killing vector. The study extends Buchdahl’s original theorem by combining it with the Kerr–Schild representation. In doing so, we construct new vacuum-rotating black holes in higher dimensions which can be viewed as the Levi-Civita extensions of the Myers–Perry geometries. Furthermore, it demonstrates that the double copy scheme within these new generated geometries still holds, providing an example of an algebraically general double copy framework. In the context of the Einstein-Scalar system, the paper extends the corresponding Buchdahl theorem to scenarios where a static vacuum seed configuration, transformed with respect to a spacelike Killing vector, generates a hairy black hole spacetime. We analyze the geometrical features of these spacetimes and investigate how a change of frame, via conformal transformations, leads to a new family of black hole spacetimes within the Einstein-Conformal-Scalar system.

Thermodynamics and null geodesics of a Schwarzschild black hole surrounded by a Dehnen type dark matter halo

In this work, we derive a novel black hole solution surrounded by a Dehnen-(1,4,0) type dark matter halo by embedding a Schwarzschild black hole within the halo, constituting a composite dark matter-black hole system. The thermodynamics of the resulting effective black hole spacetime is then studied with particular attention to the influence of the dark matter parameters on various thermodynamic properties. We examine the specific heat and free energy to assess the thermodynamic stability of the model. Furthermore, the null geodesics and the effective potential of light rays are studied to investigate how the dark matter parameters affect these geodesics and the radii of circular orbits. The stability of circular null geodesics is analysed using dynamical systems and Lyapunov exponents, which represent the dynamical behaviour of the circular photon orbits. Finally, we studied if the circular geodesics exhibit chaotic behaviour using the chaos-bound condition.

Detecting the tidal heating with the generic extreme mass-ratio inspirals

The horizon of a classical black hole (BH), functioning as a one-way membrane, plays a vital role in the dynamic evolution of binary BHs, capable of absorbing fluxes entirely.Tidal heating, stemming from this phenomenon, exerts a notable influence on the production of gravitational waves (GWs). If at least one member of a binary is an exotic compact object (ECO) instead of a BH, the absorption of fluxes is expected to be incomplete and the tidal heating would be different. Thus, tidal heating can be utilized for model-independent investigations into the nature of compact object. In this paper, assuming that the extreme mass-ratio inspiral (EMRI) contains a stellar-mass compact object orbiting around a massive ECO with a reflective surface, we compute the GWs from the generic EMRI orbits. Using the accurate and analytic flux formulas in the black hole spacetime, we adapted these formulas in the vicinity of the ECO surface by incorporating a reflectivity parameter.Under the adiabatic approximation, we can evolve the orbital parameters and compute the EMRI waveforms. The effect of tidal heating for the spinning and non-spinning objects can be used to constrain the reflectivity of the surface at the level of 𝒪(10-6) by computing the mismatch and fisher information matrix.

Probing the effect of time conformal factor on the particle dynamics around AdS Reissner–Nordström black hole

This study entails the effect of time on particle dynamics (both charged and uncharged) in the surrounding of the Reissner–Nordström AdS black hole in light of a general time conformal factor by acquiring Noether symmetry relation using the Lagrangian of the considered black hole spacetime. Upon acquiring the required time conformal spacetime as well as the Noether and approximated Noether symmetries along with their respective laws of conservation, the study further aims at investigating different parameters, like effective potential, effective force, and trajectories of escape velocity for the particle dynamics of the specified black hole. Additionally, in order to investigate orbit stability, the study employs the Lyapunov exponent.

Circular motion and QPOs near black holes in Kalb–Ramond gravity

General relativity (GR) theory modifications include different scalar, vector, and tensor fields with non-minimal gravitational coupling. Kalb–Ramond (KR) gravity is a modified theory formulated based on the presence of the bosonic field. One astrophysical way to test gravity is by studying the motion of test particles in the spacetime of black holes (BHs) using observational data. In the present work, we aimed to test KR gravity through theoretical studies of epicyclic frequencies of particle oscillations using quasi-periodic oscillation (QPO) frequency data from microquasars. First, we derive equations of motion and analyze the effective potential for circular orbits. Also, we studied the energy and angular momentum of particles corresponding to circular orbits. In addition, we analyze the stability of circular orbits. It is shown that the radius of the innermost stable circular orbits is inversely proportional to the KR parameter. We are also interested in how the energy and angular momentum of test particles at ISCO behave around the KR BHs. We found that the Keplerian frequency for the test particles in KR gravity is the same as that in GR. Finally, we study the QPOs by applying epicyclic oscillations in the relativistic precession (RP), warped disc (WD), and epicyclic resonance (ER) models. We also analyze QPO orbits in the resonance cases of upper and lower frequencies 3:2, 4:3, and 5:4 in the QPO as mentioned above models. We obtain constraints on the KR gravity parameter and BH mass using a Monte Carlo Markov Chain simulation in the multidimensional parameter space for the microquasars GRO J1655-40 & XTE J1550-564, M82 X-1, and Sgr A*.

A New Gauge for Gravitational Perturbations of Kerr Spacetimes II: The Linear Stability of Schwarzschild Revisited

We present a new proof of linear stability of the Schwarzschild solution to gravitational perturbations. Our approach employs the system of linearised gravity in the new geometric gauge of Benomio (A new gauge for gravitational perturbations of Kerr spacetimes I: the linearised theory, 2022, https://arxiv.org/abs/2211.00602), specialised to the |a|=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|a|=0$$\\end{document} case. The proof fundamentally relies on the novel structure of the transport equations in the system. Indeed, while exploiting the well-known decoupling of two gauge invariant linearised quantities into spin ±2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm 2$$\\end{document} Teukolsky equations, we make enhanced use of the red-shifted transport equations and their stabilising properties to control the gauge dependent part of the system. As a result, an initial-data gauge normalisation suffices to establish both orbital and asymptotic stability for all the linearised quantities in the system. The absence of future gauge normalisations is a novel element in the linear stability analysis of black hole spacetimes in geometric gauges governed by transport equations. In particular, our approach simplifies the proof of Dafermos et al. (Acta Math 222:1–214, 2019), which requires a future normalised (double-null) gauge to establish asymptotic stability for the full system.

Impact of chaplygin-like equation of state on Joule–Thomson expansion and tidal forces of AdS black holes

This study examines a recently hypothesized black hole. We study the Joule–Thomson coefficient, the inversion temperature and also the isenthalpic curves in the Ti−Pi plane. The Joule–Thomson coefficient, the inversion curves and the isenthalpic curves are discussed in AdS black holes surrounded by Chaplygin dark fluid. In T−P plane, the inversion temperature curves and isenthalpic curves are obtained with different parameters. Next, we explore the radial time-like geodesics that leads us to explore the tidal force effects for a radially in-falling particle in such black hole spacetime. We also numerically solve the geodesic deviation equation for two nearby radial geodesics for a freely falling particle. Our analysis shows that contrary to the Schwarzschild spacetime, the tidal forces do not become zero at spatial infinity due to the lack of asymptotic flatness because of the presence of a non-zero cosmological constant. The geodesic separation profile shows an oscillating trend and depends on the dynamic spacetime parameters q,B and Λ.

Space-time structures, light trajectories and shadows for Kerr-Newman-AdS black hole with surrounding perfect fluid matter in Rastall gravity

We present the horizon structures and the shadows for Kerr-Newman-AdS black hole located in perfect fluid matter field in Rastall gravity. By considering the Hamilton-Jacobi equation and Carter constant separable method, we obtain the null geodesic equations of the black hole space-time as well as the unstable circular photon orbits in terms of the impact parameters. The horizon structures of the space-time are calculated numerically. The results show that there are four roots for a general case of the horizon equation (the Cauchy horizon r−h , the event horizon r+h , the cosmological horizon r q of Rastall gravity and the cosmological horizon r c of cosmological constant), which lead to a specific characteristic with the subregions of the space-time. The influences of the cosmological horizons r q and r c on the light trajectories around the black hole are also investigated. Furthermore, we study the effects of the parameters, including the perfect fluid matter intensity N s , the Rastall parameter k λ, the cosmological constant Λ, the black hole spin a and the black hole charge Q on black hole shadows in detail.

Stability Analysis of Stable Circular Orbit in Multi-Static Black Hole Spacetime

We herein study the circular orbit stability of a static black hole system composed of multiple Reissner–Nordstrom (RN) black holes. By comparing the circular orbits of two static black holes, three static black holes (TBHs), four static black holes and five static black holes at different spacetime, we find that the continuity of their stable circular orbits changes, i.e., the peaks of the effective potentials are transformed from single-peaked to bi-peaked, and that the distance a between the black holes is the main reason for this change. This characteristic is completely different from the continuity of the stable circular orbit interval of any kind of single black hole in the past. After calculation, we obtain several critical values that lead to the change in circular orbit stability. The three fundamental frequencies (orbital frequency, radial local frequency, and vertical local frequency) are derived and compared for two different spacetimes of double and three black holes. We also analyse the effect of the black hole distance a on the three fundamental frequencies of circular orbits.

QPOs and circular orbits around black holes in Chaplygin-like cold dark matter

Understanding the nature of dark energy in the universe is an actual issue in theoretical astrophysics and cosmology. One way to do it is by probing dark fluids with different equations of states (EoS). In the present work, we consider a Schwarzschild black hole (BH) surrounded by a dark fluid with a Chaplygin-like EoS as a generalized version of the Chaplygin EoS. We first investigate the effects of the dark fluid parameters on the horizon properties of the BH. The effective mass of the spacetime is calculated and analyzed under the dark fluid parameters. The scalar invariants of the BH spacetime are also calculated, and it is shown that the spacetime curvature increases as the dark fluid parameter increases. Next, we studied the circular motion of the test particle around the BH. As standard particle motion investigations, we analyze the effective potential of the particles for circular motion, specific energy, and angular corresponding to circular orbits with zero and nonvanishing values of the dark fluid intensity. In addition, we study the innermost stable circular orbits (ISCO). It is observed that there is an outermost stable circular orbit (OSCO) due to the presence of the dark fluid. It also shows that at a critical value of the dark fluid intensity parameter, ISCO and OSCO take the same radius. We calculate the frequency of Keplerian orbits and radial and vertical oscillations of the particles along stable circular orbits. We also applied orbital data from hotspots observed near Sgr A* to obtain upper and lower values for the EoS parameter. Finally, we investigate quasiperiodic oscillations and obtain the mass-to-EoS parameter relations for GRS J1915-105 and XTE 1550-564.

Efficiency of magnetic Penrose process in higher dimensional Myers-Perry black hole spacetimes

Efficiency of magnetic Penrose process in higher dimensional Myers-Perry black hole spacetimes

Embedding diagrams in stationary spacetimes

We find the spatial and dynamic embedding diagrams in stationary black hole spacetimes. The spatial embeddings include the NUT, pure NUT and Kerr spacetimes. In the case of pure NUT spacetime, the spatial embedding equations are solved in terms of the elliptic integrals. In other cases we obtain the spatial embedding diagrams by numerical integration of the corresponding embedding equations. These embedding diagrams are then compared through their Gaussian and mean curvatures. We also find the dynamic embedding diagrams of NUT and pure NUT spacetimes, and compare them with the dynamic embedding diagram of Schwarzschild spacetime.

Axial gravitational quasi-normal modes of spherically symmetric black hole in f(R) gravity and its optical appearance

This paper investigates the axial gravitational perturbations originating from spherically symmetric black holes in f(R) gravity, along with the optical appearance of such a black hole. The aim is to search for evidence of the existence of these black holes in astrophysical observations and thereby test the correctness of the f(R) theory. In literature Kalita and Mukhopadhyay (Eur Phys J C 79:877, 2019), the spherically symmetric black hole metric in f(R) gravity is obtained. By comparing it with the metric for spherically symmetric black holes in general relativity, we find that the modification of gravity due to f(R) can be described in this black hole spacetime using a parameter Cf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_f$$\\end{document}. Next, we study axial gravitational perturbations in this spacetime and successfully derive a decoupled axial perturbation equation. We also discuss the impact of f(R) gravity on the quasi-normal mode frequencies. Additionally, we have also investigated the optical appearance of the black hole. We discuss the impact of the parameter Cf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_f$$\\end{document} on the observable characteristics of the accretion disk. In principle, both of these effects can be observed using gravitational wave detectors and astronomical telescopes.

Entanglement and Generalized Berry Geometrical Phases in Quantum Gravity

A new formalism is introduced that makes it possible to elucidate the physical and geometric content of quantum space–time. It is based on the Minimum Group Representation Principle (MGRP). Within this framework, new results for entanglement and geometrical/topological phases are found and implemented in cosmological and black hole space–times. Our main results here are as follows: (i) We find the Berry phases for inflation and for the cosmological perturbations and express them in terms of the observables, such as the spectral scalar and tensor indices, nS and nT, and the tensor-to-scalar ratio r. The Berry phase for de Sitter inflation is imaginary with the sign describing the exponential acceleration. (ii) The pure entangled states in the minimum group (metaplectic) Mp(n) representation for quantum de Sitter space–time and black holes are found. (iii) For entanglement, the relation between the Schmidt type representation and the physical states of the Mp(n) group is found: This is a new non-diagonal coherent state representation complementary to the known Sudarshan diagonal one. (iv) Mean value generators of Mp(2) are related to the adiabatic invariant and topological charge of the space–time, (matrix element of the transition −∞<t<∞). (v) The basic even and odd n-sectors of the Hilbert space are intrinsic to the quantum space–time and its discrete levels (in particular, continuum for n→∞), they do not require any extrinsic generation process such as the standard Schrodinger cat states, and are entangled. (vi) The gravity or cosmological on one side and another of the Planck scale are entangled. Examples: The quantum primordial trans-Planckian de Sitter vacuum and the classical late de Sitter vacuum today; the central quantum gravity region and the external classical gravity region of black holes. The classical and quantum dual gravity regions of the space–time are entangled. (vii) The general classical-quantum gravity duality is associated with the Metaplectic Mp(n) group symmetry which provides the complete full covering of the phase space and of the quantum space–time mapped from it.