In this work, generalizing our previous results, we determine in an original and the simplest way three most important thermodynamical characteristics (Bekenstein-Hawking entropy, Bekenstein quantization of the entropy or (outer) horizon surface area and Hawking temperature) of Kerr-Newman black hole. We start physically by assumption that circumference of Kerr-Newman black hole (outer) horizon holds the natural (integer) number of corresponding reduced Compton's wave length and use mathematically, practically, only simple algebraic equations. (It is conceptually similar to Bohr's quantization postulate in Bohr's atomic model interpreted by de Broglie relation.)
A coordinate system that blockwise-simplifies the Kerr-Newman black hole's thermodynamical state space Ruppeiner metric geometry is constructed, with discussion of the limiting cases corresponding to simpler black holes. It is deduced that one of the three conformal Killing vectors of the Reissner-Nordstrom and Kerr cases (whose thermodynamical state space metrics are 2 by 2 and conformally flat) survives generalization to the Kerr-Newman case's 3 by 3 thermodynamical state space metric.
In this work we explore the connections between Newman-Penrose scalars, including the Penrose-Rindler $\mathcal{K}$-curvature, with the equation of state of asymptotically Anti-de Sitter Reissner-Nordström black holes. After briefly reviewing the equation of state for these black holes from the point of view of both the Extended Phase Space and the Horizon Thermodynamics approaches, a geometric splitting is given for such an equation in terms of the non vanishing Newman-Penrose scalars which define the $\mathcal{K}$-curvature at the horizon. From this splitting, a possible thermodynamical inte…
In this work, generalizing our previous results, we determine in an original and the simplest way three most important thermodynamical characteristics (Bekenstein-Hawking entropy, Bekenstein quantization of the entropy or (outer) horizon surface area and Hawking temperature) of Schwarzschild, Kerr and Reissner-Nordstrom black hole. We start physically by assumption that circumference of black hole (outer) horizon holds the natural (integer) number of corresponding reduced Compton's wave length and use mathematically only simple algebraic equations. (It is conceptually similar to Bohr's quantiz…
In this work we present a simple, approximate method for analysis of the basic dynamical and thermodynamical characteristics of Kerr-Newman black hole. Instead of the complete dynamics of the black hole self-interaction we consider only such stable (stationary) dynamical situations determined by condition that black hole (outer) horizon circumference holds the integer number of the reduced Compton wave lengths corresponding to mass spectrum of a small quantum system (representing quant of the black hole self-interaction). Then, we show that Kerr-Newman black hole entropy represents simply the …
In the present paper binary configurations of identical corotating Kerr-Newman black holes separated by a massless strut are derived and studied. After solving the axis conditions and establishing the absence of magnetic charges in the solution, one gets two 4-parametric corotating binary black hole models endowed with electric charge, where each source contains equal/opposite electric charge in the first/second configuration. Since the black hole horizons are given by concise expressions in terms of physical parameters, all their thermodynamical properties satisfying the Smarr relation for th…
In this paper, binary systems of unequal Kerr-Newman black holes located on the axis and apart by a massless strut are investigated. After adopting a fitting parametrization, the conditions on the axis and the one eliminating the individual magnetic charges are solved exactly with the aim to obtain a 7-parametric asymptotically flat exact solution. It is also deduced explicit analytical formulas for each half-length horizon $σ_{i}$, $i = 1,2$, in terms of arbitrary physical Komar parameters: mass $M_{i}$, electric charge $Q_{i}$, angular momentum $J_{i}$, and a coordinate distance $R$. All the…
It is demonstrated that the generic four-dimensional Taub-Newman-Unti-Tamburino (Taub-NUT) spacetimes can be perfectly described in terms of three or four different kinds of thermodynamic hairs: the Komar mass ($M = m$), the "angular momentum" ($J_n = mn$), the gravitomagnetic charge ($N = n$), and/or the dual (magnetic) mass ($\widetilde{M} = n$). In other words, the NUT charge is a thermodynamic multihair which means that it simultaneously has both rotation-like and electromagnetic charge-like characteristics; this is in sharp contrast with the previous knowledge that it has only one physica…
We construct a Kerr-Newman-like spacetimes starting from higher dimensional (HD) Einstein-Yang-Mills black holes via complex transformations suggested by Newman-Janis. The new metrics are HD generalization of Kerr-Newman spacetimes which has a geometry precisely that of Kerr-Newman in 4D corresponding to Yang-Mills (YM) gauge charge, but the sign of charge term gets flipped in the HD spacetimes. It is interesting to note that gravitational contribution of YM gauge charge, in HD, is indeed opposite (attractive rather than repulsive) that of Maxwell charge. The effect of YM gauge charge on the s…
We investigate the weak cosmic censorship conjecture in extremal and near-extremal Kerr-Newman-(anti-)de Sitter black holes by the scattering of a massive scalar field with an electric charge. Under this scattering, the scalar field fluxes change the black hole state, as determined by the mass, angular momentum, and electric charge. The black hole may exceed its extremal condition because of these changes. However, we find that the black hole cannot be overcharged or overspun by the scattering. In particular, although the fluxes are closely associated with the asymptotic boundary conditions al…
We consider the regular black holes solution with cosmic strings(RBHCS) in the rotation parameter by assuming the Newman-Janis method. After this, we study thermodynamical property (i.e., Hawking temperature $T_H$) for the RBHCS in the presence of spin parameter. Moreover, we study the graphical interpretation of Hawking temperature with event horizon to check the physical and stable form of RBHCS under the effect of Newman-Janis algorithm. We graphically show that the RBHCS in the context of Newman-Janis algorithm are colder than the Schwarzschild black hole. Furthermore, we investigate the q…
We show that the Hawking--Bekenstein entropy formula is modified by a factor of $8/3$ if one also considers a work term in the 1st law of thermodynamics by a pressure stemming from the Hawking radiation. We give an intuitive definition for the corresponding thermodynamical volume by the implicit definition $ε=Mc^2/V$, which is the average energy density of the Hawking radiation. This volume scales as $V \sim M^5$, agreeing with other suggestions. As a result the corresponding Smarr relation describes an extensive entropy and a stable effective equation of state $S(E,V)\sim E^{3/4}V^{1/4}$. The…
While the formalism of isolated horizons is known for some time, only quite recently the near horizon solution of Einstein's equations has been found in the Bondi-like coordinates by Krishnan in 2012. In this framework, the space-time is regarded as the characteristic initial value problem with the initial data given on the horizon and another null hypersurface. It is not clear, however, what initial data reproduce the simplest physically relevant black hole solution, namely that of Kerr-Newman which describes stationary, axisymmetric black hole with charge. Moreover, Krishnan's construction e…
We construct asymptotically flat black hole solutions of Einstein-scalar gravity sourced by a nontrivial scalar field with 1/r asymptotic behaviour. Near the singularity the black hole behaves as the Janis-Newmann-Winicour-Wyman solution. The hairy black hole solutions allow for a consistent thermodynamical description. At large mass they have the same thermodynamical behaviour of the Schwarzschild black hole, whereas for small masses they differ substantially from the latter.
In this work we have presented a special class of Kerr-Newman-NUT black hole, having its horizon located precisely at $r=2M$, for $Q^{2}=l^{2}-a^{2}$, where $M$, $l$, $a$ and $Q$ are respectively mass, NUT, rotation and electric charge parameters of the black hole. Clearly this choice radically alters the causal structure as there exists no Cauchy horizon indicating spacelike nature of the singularity when it exists. On the other hand, there is no curvature singularity for $l^2 > a^2$, however it may have conical singularities. Furthermore there is no upper bound on specific rotation parameter…
Four classical laws of black hole thermodynamics are extended from exterior (event) horizon to interior (Cauchy) horizon. Especially, the first law of classical thermodynamics for Kerr-Newman black hole (KNBH) is generalized to those in quantum form. Then five quantum conservation laws on the KNBH evaporation effect are derived in virtue of thermodynamical equilibrium conditions. As a by-product, Bekenstein-Hawking's relation $ S=A/4 $ is exactly recovered.
Starting from metric of the general nonextreme stationary axisymmetric black hole in four-dimensional spacetime, both statistical-mechanical and thermodynamical entropies are studied. First, by means of the "brick wall" model in which the Dirichlet condition is replaced by a scattering ansatz for the field functions at the horizon and with Pauli-Villars regularization scheme, an expression for the statistical-mechanical entropy arising from the nonminimally coupled scalar fields is obtained. Then, by using the conical singularity method Mann and Solodukhin's result for the Kerr-Newman black ho…
We obtain the charged rotating black hole in conformal gravity. The metric is asymptotic to the (anti-)de Sitter spacetime. The contribution to the metric from the charges has a slower falloff than that in the Kerr-Newman AdS black hole. We analyse the global structure and obtain all the thermodynamical quantities including the mass, angular momentum, electric/magnetic charges and their thermodynamical conjugates. We verify that the first law of thermodynamics holds. We also obtain the new neutral rotating black holes that are beyond Einstein metrics. In contrast to the static ones, these rota…
Rotating black hole solutions in theories of modified gravity are important as they offer an arena to test these theories through astrophysical observation. The non-rotating black hole can be hardly tested since the black hole spin is very important in any astrophysical process. We present rotating counterpart of a recently obtained spherically symmetric exact black hole solution surrounded by perfect fluid in the context of Rastall theory, viz, rotating Rastall black hole that generalize the Kerr-Newman black hole solution. In turn, we analyze the specific cases of the Kerr-Newman black holes…
By using the 't Hooft "brick wall" model and the Pauli-Villars regularization scheme we calculate the statistical-mechanical entropy arising from the minimally coupled scalar fields which rotate with the azimuthal angular velocity $Ω_0=Ω_H$ ($Ω_H$ is the angular velocity of the black hole horizon) in the general four-dimensional non-extreme stationary axisymmetric black hole space-time. We also show, for the Kerr-Newman and the Einstein-Maxwell dilaton-axion black holes, that the statistical-mechanical entropy obtained from our derivation and the quantum thermodynamical entropy by the conical …
We derive exact, asymptotically flat black hole solutions of Einstein-scalar gravity sourced by a non trivial scalar field with $1/r$ asymptotic behaviour. They are determined using an ansatz for the scalar field profile and working out, together with the metric functions, the corresponding form of the scalar self-interaction potential. Near to the singularity the black hole behaves as the Janis-Newmann-Winicour-Wyman solution. We also work out a consistent thermodynamical description of our black hole solutions. For large mass our hairy black holes have the same thermodynamical behaviour of t…
The Janis-Newman-Winicour and Papapetrou metrics represent counterparts to the Schwarzschild black hole with scalar and antiscalar background fields, correspondingly (where "anti" is to be understood as in "anti-de Sitter"). There is also a scalar counterpart (the Krori-Bhattacharjee metric) to the Kerr black hole. Here we study analytical connections between these solutions and obtain the exact rotational generalization of the antiscalar Papapetrou spacetime as a viable alternative to the Kerr black hole. The antiscalar metrics appear to be the simplest ones as they do not reveal event horizo…
The final fate of gravitational collapse of massive stars has been a subject of interest for a long time since such a collapse may lead to black holes and naked singularities alike. Since, the formation of naked singularities is forbidden by the cosmic censorship conjecture, exploring their observational differences from black holes may be a possible avenue to search for these exotic objects. The simplest possible naked singularity spacetime emerges from the Einstein massless scalar field theory with the advantage that it smoothly translates to the Schwarzschild solution by the variation of th…
In this paper we present and analyze the simplest physically meaningful model for stationary black diholes - a binary configuration of counter-rotating Kerr-Newman black holes endowed with opposite electric charges - elaborated in a physical parametrization on the basis of one of the Ernst-Manko-Ruiz equatorially antisymmetric solutions of the Einstein-Maxwell equations. The model saturates the Gabach-Clement inequality for interacting black holes with struts, and in the absence of rotation it reduces to the Emparan-Teo electric dihole solution. The physical characteristics of each dihole cons…
The Rastall theory of gravity is the generalized form of the Einstein theory which describes the conservation law of energy and momentum tensor. In our work, we compute the charged black strings solution in the background of Rastall theory by applying the Newman-Janis approach. After computing the charged black strings solution in the background of Rastall theory, we study the thermodynamical property (i.e., Hawking temperature) for the charged black strings. Furthermore, we investigate the graphical representation of Hawking temperature via event horizon to check the stability conditions of c…
We investigate static and rotating charged spherically symmetric solutions in the framework of $f({\cal R})$ gravity, allowing additionally the electromagnetic sector to depart from linearity. Applying a convenient, dual description for the electromagnetic Lagrangian, and using as an example the square-root $f({\cal R})$ correction, we solve analytically the involved field equations. The obtained solutions belong to two branches, one that contains the Kerr-Newman solution of general relativity as a particular limit and one that arises purely from the gravitational modification. The novel black…
In this paper we focus on the relation between quasinormal modes (QNMs) and a rotating black hole shadows. As a specific example, we consider the quantum deformed Kerr black hole obtained via Newman--Janis--Azreg-A\"ınou algorithm. In particular, using the geometric-optics correspondence between the parameters of a QNMs and the conserved quantities along geodesics, we show that, in the eikonal limit, the real part of QNMs is related to the Keplerian frequency for equatorial orbits. To this end, we explore the typical shadow radius for the viewing angles, $θ_0=π/2$, and obtained an interesting …
The Newman-Janis (NJ) method is a prescription to derive the Kerr space-time from the Schwarzschild metric. The BTZ, Kerr and five-dimensional Myers-Perry (MP) black hole solutions have already been generated by different versions of the NJ method. However, it is not known how to generate the metric of higher-dimensional (d > 6) rotating black holes by this method. In this paper, we propose the simplest algorithm for generation of the five-dimensional MP metric with two arbitrary angular momenta by using the Kerr-Schild form of the metric and quaternions. Then, we present another new two-step …
Pure thermodynamical considerations to describe the entropic evolution of the universe seem to violate the Second Law of Thermodynamics. This suggests that the gravitational field itself has entropy. In this paper we expand recent work done by Rudjord, GrØn and SigbjØrn where they suggested a method to calculate the gravitational entropy in black holes based on the so-called `Weyl curvature conjecture'. We study the formulation of an estimator for the gravitational entropy of Reissner-Nordström, Kerr, Kerr-Newman black holes, and a simple case of wormhole. We calculate in each case the entropy…
Kerr-Vaidya metrics are the simplest nonstationary extensions of the Kerr metric. We explore their properties and compare them with the near-horizon limits of the spherically symmetric self-consistent solutions (the ingoing Vaidya metric with decreasing mass and the outgoing Vaidya metric with increasing mass) for the evaporating and accreting physical black holes. The Newman-Janis transformation relates the corresponding Vaidya and Kerr-Vaidya metrics. For nonzero angular momentum, the energy-momentum tensor violates the null energy condition (NEC). However, we show that its structure differs…
We derive an exact solution of the spherically symmetric Bardeen black hole surrounded by perfect fluid dark matter (PFDM). By treating the magnetic charge $g$ and dark matter parameter $α$ as thermodynamic variables, we find that the thermodynamic first law and the corresponding Smarr formula are satisfied. The thermodynamic stability of the black hole is also studied. The result show that, there exists a critical radius $r_{+}^{C}$, where the heat capacity diverges, suggesting that the black hole is thermodynamically stable in the range $0<r_{+}<r_{+}^{C}$. In addition, the critical radius $…
Although black holes are eminent manifestations of very strong gravity, the geometry of space-time around and even inside them can be significantly affected by additional bodies present in their surroundings. We study such an influence within static and axially symmetric (electro-)vacuum space-times described by exact solutions of Einstein's equations, considering astrophysically motivated configurations (such as black holes surrounded by rings) as well as those of pure academic interest (such as specifically "tuned" systems of multiple black holes). The geometry is represented by the simplest…
We derive various important thermodynamic relations of the inner and outer horizon in the background of Taub-NUT(Newman-Unti-Tamburino) black hole in four dimensional \emph{Lorentzian geometry}. We compare these properties with the properties of Reissner Nordstrøm black hole. We compute \emph{area product, area sum, area minus and area division} of black hole horizons. We show that they all are not universal quantities. Based on these relations, we compute the area bound of all horizons. From area bound, we derive entropy bound and irreducible mass bound for both the horizons. We further study…
We study topological black hole solutions of the simplest quadratic gravity action and we find that two classes are allowed. The first is asymptotically flat and mimics the Reissner-Nordström solution, while the second is asymptotically de Sitter or anti-de Sitter. In both classes, the geometry of the horizon can be spherical, toroidal or hyperbolic. We focus in particular on the thermodynamical properties of the asymptotically anti-de Sitter solutions and we compute the entropy and the internal energy with Euclidean methods. We find that the entropy is positive-definite for all horizon geomet…
We investigate the near horizon geometry of the simplest representative of the class of axisymmetric space-times: the Kerr Vaidya metrics. Kerr Vaidya metrics can be derived from the Vaidya metric by the complex coordinate transformation suggested by Newman and Janis. We show that the energy momentum tensor belongs to type 3 in the Segre Hawking Ellis classification but has a special form with all Lorentz invariant eigenvalues belonging to zero. We find a location of the apparent horizon for quasi-stationary Kerr Vaidya black holes. The energy-momentum tensor of the Kerr Vaidya geometries viol…
We study the method of extended gravitational decoupling in obtaining static black hole solutions satisfying Einstein's equations with a tensor vacuum. The source has quite generic characteristics and satisfies the strong energy condition. The stationary, axisymmetric counterpart of the static metric is obtained by applying the Newman-Janis and Azreg-Aïnou algorithms. The thermodynamics of the rotating solution is studied and the expressions of various thermodynamic quantities are derived. The dependence of the temperature, free energy and specific heat on the horizon radius is studied for var…
When probed with conformally invariant matter fields, light cones in Minkowski spacetime satisfy thermodynamical relations which are the analog of those satisfied by stationary black holes coupled to standard matter fields. These properties stem from the fact that light cones are conformal Killing horizons stationary with respect to observers following the radial conformal Killing fields in flat spacetime. The four laws of light cone thermodynamics relate notions such as (conformal) temperature, (conformal) surface gravity, (conformal) energy and a conformally invariant notion related to area …
We give a new and conceptually simple approach to obtain the first law of black hole thermodynamics from a basic thermodynamical property that entropy (S) for any stationary black hole is a state function implying that dS must be an exact differential. Using this property we obtain some conditions which are analogous to Maxwell's relations in ordinary thermodynamics. From these conditions we are able to explicitly calculate the semiclassical Bekenstein-Hawking entropy, considering the most general metric represented by the Kerr-Newman spacetime. We extend our method to find the corrected entro…
We explore some (especially, thermodynamical) properties of the dyonic Kerr-Sen-AdS$_4$ black hole and its ultraspinning counterpart, and check whether or not both black holes satisfy the first law and Bekenstein-Smarr mass formulas. To this end, new Christodoulou-Ruffini-like squared-mass formulae for the usual dyonic Kerr-Sen-AdS$_4$ solution and its ultraspinning cousin are deduced. Similar to the ultraspinning Kerr-Sen-AdS$_4$ black hole case, we demonstrate that the ultraspinning dyonic Kerr-Sen-AdS$_4$ black hole does not always violate the reverse isoperimetric inequality (RII) since th…
Perturbations of massless fields in the Kerr-Newman black hole background enjoy a (``Love'') SL$(2,\mathbb{R})$ symmetry in the suitably defined near zone approximation. We present a detailed study of this symmetry and show how the intricate behavior of black hole responses in four and higher dimensions can be understood from the SL$(2,\mathbb{R})$ representation theory. In particular, static perturbations of four-dimensional black holes belong to highest weight SL$\left(2,\mathbb{R}\right)$ representations. It is this highest weight property that forces the static Love numbers to vanish. We f…
We revisit the derivation by Tomimatsu of the generalized Komar integrals giving the mass and angular momentum of rotating Einstein-Maxwell black holes. We show that, contrary to Tomimatsu's claim, the usual Smarr formula relating the horizon mass and angular momentum still holds in the presence of both electric and magnetic charges. The simplest case is that of dyonic Kerr-Newman black holes, for which we recover the modified Smarr formula relating the asymptotic mass and angular momentum, the difference between asymptotic and horizon masses being equal to the sum of the two Dirac string mass…
We first review the general class of accelerating, rotating and charged Plebanski-Demianski (PD) black holes in presence of cosmological constant, which includes the Kerr-Newman rotating black hole and the Taub-NUT spacetime. We assume that the thermodynamical pressure may be described by the negative cosmological constant and so the black hole represents anti-de Sitter (AdS) PD black hole. The thermodynamic quantities like surface area, entropy, volume, temperature, Gibb's and Helmholtz's free energies of the AdS PD black hole are obtained due to the thermodynamic system. Next we find the cri…
Phase Structure of Scalarized Black Holes in Einstein-Scalar-Gauss-Bonnet Gravity
Universidade de Aveiro（阿威罗大学）；Centre for Research and Development in Mathematics and Applications (CIDMA)（数学与应用研究中心（CIDMA））；UFPA（帕拉联邦大学）；Jiangxi Normal University（江西师范大学）；Universität Oldenburg（奥尔登堡大学）
Thermodynamics of the Weyl Geometric Gravity Black Holes
Chulalongkorn University（朱拉隆功大学）；National Institute of Physics and Nuclear Engineering (IFIN-HH)（国家物理与核工程研究所（IFIN-HH））；Babes-Bolyai University（巴贝什-玻尧伊大学）
Black holes are the simplest objects in the universe. They correspond to extreme deformations of spacetime geometry, and can exist even devoid of matter. In general relativity, (electro)vacuum black holes are uniquely determined by their mass, charge and angular momentum. This feature follows from a uniqueness theorem, which can be evaded if one considers higher dimensions or matter fields coupled to gravity. Here we find that Einsteinian cubic gravity, a well-motivated modification of Einstein gravity that includes third-order curvature corrections in accordance with low-energy effective theo…
